%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO634-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:00 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO634-1 : TPTP v9.0.0. Released v7.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:22:47 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(tptp_fun__E__type, type, (
% 0.19/0.50 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.19/0.50 tff(s_type, type, (
% 0.19/0.50 s: $i > $i)).
% 0.19/0.50 tff(tptp_fun__0__type, type, (
% 0.19/0.50 tptp_fun__0_: $i)).
% 0.19/0.50 tff(f_type, type, (
% 0.19/0.50 f: $i > $i)).
% 0.19/0.50 tff(tptp_fun__AP__type, type, (
% 0.19/0.50 tptp_fun__AP_: ( $i * $i ) > $i)).
% 0.19/0.50 tff(elem_0_type, type, (
% 0.19/0.50 elem_0: $i)).
% 0.19/0.50 tff(1,plain,
% 0.19/0.50 (^[B_0: $i] : refl(tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(4,axiom,(![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17_09')).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.50 tff(6,plain,(
% 0.19/0.50 ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[5])).
% 0.19/0.50 tff(7,plain,
% 0.19/0.50 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 ((~![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (^[B: $i] : refl(tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(13,axiom,(![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_11_03')).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.50 tff(15,plain,(
% 0.19/0.50 ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[14])).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 ((~![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (^[B_0: $i, A_0: $i] : refl((tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (^[B_0: $i, A_0: $i] : rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (![B_0: $i, A_0: $i] : (((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.50 tff(24,axiom,(![B_0: $i, A_0: $i] : (((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_21_01')).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.50 tff(27,plain,(
% 0.19/0.50 ![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[26])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 ((tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[30])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (^[A_1: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 (![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (^[A_1: $i, B_0: $i, A_0: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (![A_1: $i, B_0: $i, A_0: $i] : ((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.50 tff(41,axiom,(![A_1: $i, B_0: $i, A_0: $i] : ((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_12_14')).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 (![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 (![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.51 tff(44,plain,(
% 0.19/0.51 ![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[43])).
% 0.19/0.51 tff(45,plain,
% 0.19/0.51 (![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.51 tff(46,plain,
% 0.19/0.51 (((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(48,plain,
% 0.19/0.51 (((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.51 tff(49,plain,
% 0.19/0.51 (((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 ((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(51,plain,
% 0.19/0.51 ((~![A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[51, 45, 18, 9])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[52, 35])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.51 (^[A_2: $i, A_1: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 (![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (^[A_2: $i, A_1: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|)))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|)))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))), ((((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(58,plain,
% 0.19/0.51 (![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : (((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|)))))))) <=> ![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.51 tff(59,axiom,(![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : (((((~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1_06')).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 (![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.51 tff(62,plain,(
% 0.19/0.51 ![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[61])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.19/0.51 tff(64,plain,
% 0.19/0.51 (((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(66,plain,
% 0.19/0.51 (((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[65])).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 ((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 ((~![A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[69, 63, 18, 9])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[70, 53, 35])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (^[A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 (![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(75,plain,
% 0.19/0.51 (^[A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) <=> ![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.51 tff(77,axiom,(![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_15_20')).
% 0.19/0.51 tff(78,plain,
% 0.19/0.51 (![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.51 tff(80,plain,(
% 0.19/0.51 ![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[79])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 (![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 (((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))))) <=> ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(83,plain,
% 0.19/0.52 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(84,plain,
% 0.19/0.52 (((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.52 tff(85,plain,
% 0.19/0.52 (((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[84, 82])).
% 0.19/0.52 tff(86,plain,
% 0.19/0.52 ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(87,plain,
% 0.19/0.52 ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.52 tff(88,plain,
% 0.19/0.52 ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[87, 81, 18, 9])).
% 0.19/0.52 tff(89,plain,
% 0.19/0.52 (tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[88, 71, 35, 53])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (^[A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(91,plain,
% 0.19/0.52 (![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> ![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 (![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> ![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 (^[A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(94,plain,
% 0.19/0.52 (![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|)))))) <=> ![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.52 tff(95,axiom,(![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_9_12')).
% 0.19/0.52 tff(96,plain,
% 0.19/0.52 (![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.52 tff(97,plain,
% 0.19/0.52 (![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.52 tff(98,plain,(
% 0.19/0.52 ![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[97])).
% 0.19/0.52 tff(99,plain,
% 0.19/0.52 (![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.52 tff(100,plain,
% 0.19/0.52 (((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(101,plain,
% 0.19/0.52 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(102,plain,
% 0.19/0.52 (((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.52 tff(103,plain,
% 0.19/0.52 (((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.53 tff(104,plain,
% 0.19/0.53 ((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(105,plain,
% 0.19/0.53 ((~![A_4: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.53 tff(106,plain,
% 0.19/0.53 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[105, 99, 18, 9, 71, 53, 35, 89])).
% 0.19/0.53 tff(107,plain,
% 0.19/0.53 (^[A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(108,plain,
% 0.19/0.53 (![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> ![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.53 tff(109,plain,
% 0.19/0.53 (![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> ![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(110,plain,
% 0.19/0.53 (^[A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), rewrite((((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), 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s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(111,plain,
% 0.19/0.53 (![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|))))) <=> ![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.53 tff(112,axiom,(![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_18_15')).
% 0.19/0.53 tff(113,plain,
% 0.19/0.53 (![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.53 tff(114,plain,
% 0.19/0.53 (![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.19/0.53 tff(115,plain,(
% 0.19/0.53 ![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(skolemize,[status(sab)],[114])).
% 0.19/0.53 tff(116,plain,
% 0.19/0.53 (![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.19/0.53 tff(117,plain,
% 0.19/0.53 (((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(118,plain,
% 0.19/0.53 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(119,plain,
% 0.19/0.53 (((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))))) <=> ((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[118])).
% 0.19/0.54 tff(120,plain,
% 0.19/0.54 (((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))))) <=> ((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[119, 117])).
% 0.19/0.54 tff(121,plain,
% 0.19/0.54 ((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(122,plain,
% 0.19/0.54 ((~![A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.54 tff(123,plain,
% 0.19/0.54 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[122, 116, 18, 9, 71, 53, 35, 89, 106])).
% 0.19/0.54 tff(124,plain,
% 0.19/0.54 (^[A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(125,plain,
% 0.19/0.54 (![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> ![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.54 tff(126,plain,
% 0.19/0.54 (![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> ![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(127,plain,
% 0.19/0.54 (^[A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), rewrite((((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(128,plain,
% 0.19/0.54 (![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|)))) <=> ![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.54 tff(129,axiom,(![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_0_19')).
% 0.19/0.54 tff(130,plain,
% 0.19/0.54 (![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.54 tff(131,plain,
% 0.19/0.54 (![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.54 tff(132,plain,(
% 0.19/0.54 ![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[131])).
% 0.19/0.54 tff(133,plain,
% 0.19/0.54 (![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.19/0.54 tff(134,plain,
% 0.19/0.54 (((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(135,plain,
% 0.19/0.55 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(136,plain,
% 0.19/0.55 (((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[135])).
% 0.19/0.55 tff(137,plain,
% 0.19/0.55 (((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[136, 134])).
% 0.19/0.55 tff(138,plain,
% 0.19/0.55 ((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(139,plain,
% 0.19/0.55 ((~![A_6: $i, A_4: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.55 tff(140,plain,
% 0.19/0.55 ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[139, 133, 18, 9, 71, 53, 35, 89, 106])).
% 0.19/0.55 tff(141,plain,
% 0.19/0.55 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[140, 123])).
% 0.19/0.55 tff(142,plain,
% 0.19/0.55 ((~![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(143,plain,
% 0.19/0.55 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[142, 16])).
% 0.19/0.55 tff(144,plain,
% 0.19/0.55 (((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(145,plain,
% 0.19/0.55 ((tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(146,plain,
% 0.19/0.55 (((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.55 tff(147,plain,
% 0.19/0.55 (((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.55 tff(148,plain,
% 0.19/0.55 ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(149,plain,
% 0.19/0.55 ((~![B_0: $i, A_0: $i] : (tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.55 tff(150,plain,
% 0.19/0.55 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[149, 28, 9, 143])).
% 0.19/0.55 tff(151,plain,
% 0.19/0.55 ((~![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(152,plain,
% 0.19/0.55 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[151, 7])).
% 0.19/0.55 tff(153,plain,
% 0.19/0.55 (((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(154,plain,
% 0.19/0.55 (((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(155,plain,
% 0.19/0.55 (((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.55 tff(156,plain,
% 0.19/0.55 (((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[155, 153])).
% 0.19/0.55 tff(157,plain,
% 0.19/0.55 ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(158,plain,
% 0.19/0.56 ((~![A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.56 tff(159,plain,
% 0.19/0.56 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[158, 81, 71, 53, 35])).
% 0.19/0.56 tff(160,plain,
% 0.19/0.56 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[159, 152, 143])).
% 0.19/0.56 tff(161,plain,
% 0.19/0.56 (^[A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(162,plain,
% 0.19/0.56 (![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> ![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[161])).
% 0.19/0.56 tff(163,plain,
% 0.19/0.56 (![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> ![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(164,plain,
% 0.19/0.56 (^[A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))), (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(165,plain,
% 0.19/0.56 (![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|))) <=> ![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.56 tff(166,axiom,(![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8_11')).
% 0.19/0.56 tff(167,plain,
% 0.19/0.56 (![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.56 tff(168,plain,
% 0.19/0.56 (![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.19/0.56 tff(169,plain,(
% 0.19/0.56 ![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[168])).
% 0.19/0.56 tff(170,plain,
% 0.19/0.56 (![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.19/0.56 tff(171,plain,
% 0.19/0.56 (((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(172,plain,
% 0.41/0.57 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(173,plain,
% 0.41/0.57 (((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[172])).
% 0.41/0.57 tff(174,plain,
% 0.41/0.57 (((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[173, 171])).
% 0.41/0.57 tff(175,plain,
% 0.41/0.57 ((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(176,plain,
% 0.41/0.57 ((~![A_6: $i, A_4: $i, A_7: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.41/0.57 tff(177,plain,
% 0.41/0.57 ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[176, 170, 18, 9, 71, 53, 106, 123])).
% 0.41/0.57 tff(178,plain,
% 0.41/0.57 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[177, 141, 160, 150])).
% 0.41/0.57 tff(179,plain,
% 0.41/0.57 (^[A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(180,plain,
% 0.41/0.57 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[179])).
% 0.41/0.57 tff(181,plain,
% 0.41/0.57 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(182,plain,
% 0.41/0.57 (^[A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (((~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), rewrite((((~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), 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(~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))), ((((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(183,plain,
% 0.41/0.58 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|)) <=> ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[182])).
% 0.41/0.58 tff(184,axiom,(![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10_22')).
% 0.41/0.58 tff(185,plain,
% 0.41/0.58 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.41/0.58 tff(186,plain,
% 0.41/0.58 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.41/0.58 tff(187,plain,(
% 0.41/0.58 ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.58 inference(skolemize,[status(sab)],[186])).
% 0.41/0.58 tff(188,plain,
% 0.41/0.58 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.41/0.58 tff(189,plain,
% 0.41/0.58 (((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(190,plain,
% 0.41/0.58 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(191,plain,
% 0.41/0.58 (((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[190])).
% 0.43/0.58 tff(192,plain,
% 0.43/0.58 (((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[191, 189])).
% 0.43/0.59 tff(193,plain,
% 0.43/0.59 ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(194,plain,
% 0.43/0.59 ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), K)), |'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.43/0.59 tff(195,plain,
% 0.43/0.59 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|)))))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[194, 188, 18, 9, 71, 53, 89, 106])).
% 0.43/0.59 tff(196,plain,
% 0.43/0.59 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[195, 178, 150, 141, 123])).
% 0.43/0.59 tff(197,plain,
% 0.43/0.59 (^[A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(198,plain,
% 0.43/0.59 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[197])).
% 0.43/0.59 tff(199,plain,
% 0.43/0.59 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(200,plain,
% 0.43/0.59 (^[A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))))), (((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), ((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), (((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), ((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), (((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), ((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))))), ((((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_9), |'0'|))) <=> (((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|))))), rewrite((((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))), ((((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_9), |'0'|))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(201,plain,
% 0.43/0.60 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_9), |'0'|))) <=> ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[200])).
% 0.43/0.60 tff(202,axiom,(![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : (((((((((((~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_8), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_9), |'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3_17')).
% 0.43/0.60 tff(203,plain,
% 0.43/0.60 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.43/0.60 tff(204,plain,
% 0.43/0.60 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.43/0.60 tff(205,plain,(
% 0.43/0.60 ![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.60 inference(skolemize,[status(sab)],[204])).
% 0.43/0.60 tff(206,plain,
% 0.43/0.60 (![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.43/0.60 tff(207,plain,
% 0.43/0.60 (((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(208,plain,
% 0.43/0.60 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|))))))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(209,plain,
% 0.43/0.60 (((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[208])).
% 0.43/0.60 tff(210,plain,
% 0.43/0.60 (((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))) <=> ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[209, 207])).
% 0.43/0.60 tff(211,plain,
% 0.43/0.60 ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(212,plain,
% 0.43/0.61 ((~![A_6: $i, A_4: $i, A_7: $i, A_8: $i, A_9: $i, A_5: $i, A_3: $i, A_2: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(A_1), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(A_2), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(A_6), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_7), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_8), s(|'0'|))) | (~tptp_fun__E_(f(A_4), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_9), |'0'|)) | (~tptp_fun__E_(f(A_3), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_5), s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.43/0.61 tff(213,plain,
% 0.43/0.61 ((~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))), elem!0)), |'0'|))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[212, 206, 18, 9, 71, 53, 35, 89, 106])).
% 0.43/0.61 tff(214,plain,
% 0.43/0.61 ($false),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[213, 196, 178, 141, 123])).
% 0.43/0.61 % SZS output end Proof
% 0.43/0.61 % E exiting
%------------------------------------------------------------------------------