%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO633-1 : TPTP v9.0.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO633-1 : TPTP v9.0.0. Released v7.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:22:38 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(tptp_fun__E__type, type, (
% 0.18/0.37 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun__0__type, type, (
% 0.18/0.37 tptp_fun__0_: $i)).
% 0.18/0.37 tff(f_type, type, (
% 0.18/0.37 f: $i > $i)).
% 0.18/0.37 tff(tptp_fun__AP__type, type, (
% 0.18/0.37 tptp_fun__AP_: ( $i * $i ) > $i)).
% 0.18/0.37 tff(elem_0_type, type, (
% 0.18/0.37 elem_0: $i)).
% 0.18/0.37 tff(s_type, type, (
% 0.18/0.37 s: $i > $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[B_0: $i] : refl(tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))) <=> tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))) <=> ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|))))) <=> ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,axiom,(![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6_04')).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.37 tff(6,plain,(
% 0.18/0.37 ![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[5])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 ((~![B_0: $i] : tptp_fun__E_(f(B_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.37 tff(10,assumption,(~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (^[B: $i] : refl(tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))) <=> tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))) <=> ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|)))))) <=> ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(14,axiom,(![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8_05')).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.37 tff(16,plain,(
% 0.18/0.37 ![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ((~![B: $i] : tptp_fun__E_(f(B), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.18/0.37 tff(20,plain,(tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (^[B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (^[B_0: $i, A_0: $i] : rewrite((((~tptp_fun__E_(f(A_0), 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(|'0'|))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (![B_0: $i, A_0: $i] : (((~tptp_fun__E_(f(A_0), 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(|'0'|))))) <=> ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.38 tff(26,axiom,(![B_0: $i, A_0: $i] : (((~tptp_fun__E_(f(A_0), 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(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1_10')).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.18/0.38 tff(29,plain,(
% 0.18/0.38 ![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[28])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))))) <=> ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(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(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))) <=> ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|))))))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))) <=> ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))))) | tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 ((~![B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(B_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(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (tptp_fun__E_(f(elem!0), s(s(s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[36, 30, 20])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[37, 9])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (^[A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (^[A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|)))) <=> ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.38 tff(44,axiom,(![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4_12')).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.38 tff(47,plain,(
% 0.18/0.38 ![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[46])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))) <=> ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(s(|'0'|))))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 ((~![A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[54, 48, 20, 38, 9])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (^[A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (^[A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), ((((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))), ((((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|))) <=> ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.39 tff(61,axiom,(![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : (((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_12_09')).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.39 tff(64,plain,(
% 0.18/0.39 ![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[63])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))) <=> ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (((~tptp_fun__E_(f(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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))) <=> ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))) <=> ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[67])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))) <=> ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[68, 66])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 ((~![A_2: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), s(|'0'|)))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[71, 65, 20, 38, 9, 55])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (^[A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) <=> ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (^[A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> (((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)))), rewrite((((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|)) <=> ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.40 tff(78,axiom,(![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2_07')).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.18/0.41 tff(81,plain,(
% 0.18/0.41 ![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[80])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))) <=> ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))) <=> ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[84])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))) <=> ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[85, 83])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | ((~tptp_fun__E_(f(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(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 ((~![A_2: $i, A_3: $i, A_1: $i, K: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), K)), |'0'|) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[88, 82, 20, 38, 9, 55, 72])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (^[A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : refl(((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 (^[A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))))), rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), (((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) <=> (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_4), |'0'|))))), rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_4), |'0'|))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) <=> ((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> (((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))))), rewrite((((~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))), (((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|)))))))) <=> ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.18/0.42 tff(95,axiom,(![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((((((~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_3), s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|))) | (~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5_03')).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.18/0.42 tff(98,plain,(
% 0.18/0.42 ![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[97])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 (![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))) <=> ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 (((~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.18/0.43 tff(103,plain,
% 0.18/0.43 (((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))))) <=> ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), s(|'0'|))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[102, 100])).
% 0.18/0.43 tff(104,plain,
% 0.18/0.43 ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), 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(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(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(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(105,plain,
% 0.18/0.43 ((~![A_4: $i, A_2: $i, A_3: $i, A_1: $i, B_0: $i, A_0: $i] : ((~tptp_fun__E_(f(B_0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(A_0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(A_2), s(s(|'0'|)))) | (~tptp_fun__E_(f(A_4), |'0'|)) | (~tptp_fun__E_(f(A_3), s(|'0'|))) | (~tptp_fun__E_(f(A_1), s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__E_(f(elem!0), s(s(s(|'0'|))))) | (~tptp_fun__E_(f(elem!0), s(s(s(s(|'0'|)))))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), |'0'|)) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(s(|'0'|)))) | (~tptp_fun__E_(f(tptp_fun__AP_(s(s(s(s(s(s(|'0'|)))))), elem!0)), s(|'0'|)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.43 tff(106,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[105, 99, 20, 38, 9, 55, 72, 89])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------