%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN065+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:22:36 AM UTC 2025
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN065+2 : TPTP v9.0.0. Released v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:10:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(tptp_fun_Y24_0_type, type, (
% 0.12/0.40 tptp_fun_Y24_0: $i)).
% 0.12/0.40 tff(tptp_fun_Y21_1_type, type, (
% 0.12/0.40 tptp_fun_Y21_1: $i > $i)).
% 0.12/0.40 tff(tptp_fun_Y3_14_type, type, (
% 0.12/0.40 tptp_fun_Y3_14: $i > $i)).
% 0.12/0.40 tff(r1_type, type, (
% 0.12/0.40 r1: $i > $o)).
% 0.12/0.40 tff(r2_type, type, (
% 0.12/0.40 r2: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y15_5_type, type, (
% 0.12/0.40 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.12/0.40 tff(r3_type, type, (
% 0.12/0.40 r3: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_Y7_6_type, type, (
% 0.12/0.40 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_Y4_4_type, type, (
% 0.12/0.40 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[X11: $i, X12: $i] : refl(((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (^[X11: $i, X12: $i] : rewrite((((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.12/0.40 inference(pull_quant,[status(thm)],[])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(7,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.40 tff(9,plain,(
% 0.12/0.40 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[8])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (($false | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 ((~(~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | $false) <=> (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 ((tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[19, 17])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | $false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[21, 16])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> (~(~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[22])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[23, 15])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | $true) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | $true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[26, 25])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[28, 17])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))) <=> ($false | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[29, 24])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[30, 14])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[32, 13])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[35, 12])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.41 tff(42,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.41 tff(45,plain,(
% 0.19/0.41 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[44])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (^[Y1: $i] : refl((r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1))))) <=> (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1))))) <=> ![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[Y1: $i] : rewrite(((~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))) | r1(Y1)) <=> (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![Y1: $i] : ((~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))) | r1(Y1)) <=> ![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1)))) <=> (~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))) <=> (~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(57,axiom,(~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nononesexist')).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (~?[Y1: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (^[Y1: $i] : nnf_neg(sk($oeq((~![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1)))), (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))), refl($oeq(r1(Y1), r1(Y1))), $oeq((~(![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y1))) & (~r1(Y1)))), ((~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))) | r1(Y1))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(63,plain,(
% 0.19/0.41 ![Y1: $i] : ((~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))) | r1(Y1))),
% 0.19/0.41 inference(nnf-neg,[status(sab)],[61, 62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 54])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 52])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (((~![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))) | (r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))) | r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ((~![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))) | (r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~![Y1: $i] : (r1(Y1) | (~((~r1(tptp_fun_Y3_14(Y1))) | (~r2(tptp_fun_Y3_14(Y1), Y1)))))) | r1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 65, 50])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)) | (~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.41 tff(81,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.41 tff(84,plain,(
% 0.19/0.41 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.19/0.41 inference(transitivity,[status(sab)],[83])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (~((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[89, 86, 73])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~r1(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[93, 69])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (^[X3: $i, X10: $i, Y12: $i] : trans(monotonicity(rewrite(((~r2(X3, Y12)) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))), (((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))), rewrite(((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))), (((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (^[X3: $i, X10: $i, Y12: $i] : refl(((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(pull_quant,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (^[X3: $i, X10: $i] : pull_quant(((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[102, 98])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (^[X3: $i, X10: $i] : rewrite(((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (^[X3: $i, X10: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y12: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y13: $i] : rewrite(((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), trans(der(![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) <=> ![Y13: $i] : (~r2(X3, Y12))), elim_unused(![Y13: $i] : (~r2(X3, Y12)) <=> (~r2(X3, Y12))), (![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) <=> (~r2(X3, Y12)))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> (~r2(X3, Y12)))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12))))), rewrite(((~r2(X3, Y12)) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))))), (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> (![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))) | (X3 = X10)))), rewrite((![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.42 tff(110,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_3a')).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.19/0.42 tff(113,plain,(
% 0.19/0.42 ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[112])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[114, 96])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 115, 36, 94])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (tptp_fun_Y21_1(Y24!0) = Y24!0),
% 0.19/0.42 inference(transitivity,[status(thm)],[119, 92])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (^[X1: $i, X8: $i] : rewrite((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> ![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (^[X1: $i, X8: $i] : rewrite(((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> ![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[X1: $i, X8: $i] : quant_intro(proof_bind(^[Y4: $i] : rewrite((?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))))), (?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.42 tff(128,axiom,(![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.42 tff(131,plain,(
% 0.19/0.42 ![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[142, 12, 139])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.19/0.42 inference(symmetry,[status(thm)],[145])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (r1(tptp_fun_Y21_1(Y24!0)) <=> r1(tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[146])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (r1(tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r1(tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(symmetry,[status(thm)],[147])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) <=> (~r1(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (~r1(tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[152, 46, 137])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (~r1(tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0))) | r1(tptp_fun_Y21_1(Y24!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 ((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 ((~((~r1(tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[159, 86])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (~(r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[160, 156])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 ((r1(tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = Y24!0)) | (~(tptp_fun_Y21_1(Y24!0) = Y24!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (~(tptp_fun_Y21_1(Y24!0) = Y24!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[163, 120])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------