%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM524+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:21:16 AM UTC 2025
% Result : Theorem 0.48s 0.66s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : NUM524+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:22:41 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.48/0.66 % SZS status Theorem
% 0.48/0.66 % SZS output start Proof
% 0.48/0.66 tff(sdtasdt0_type, type, (
% 0.48/0.66 sdtasdt0: ( $i * $i ) > $i)).
% 0.48/0.66 tff(xq_type, type, (
% 0.48/0.66 xq: $i)).
% 0.48/0.66 tff(xp_type, type, (
% 0.48/0.66 xp: $i)).
% 0.48/0.66 tff(xm_type, type, (
% 0.48/0.66 xm: $i)).
% 0.48/0.66 tff(sdtsldt0_type, type, (
% 0.48/0.66 sdtsldt0: ( $i * $i ) > $i)).
% 0.48/0.66 tff(xn_type, type, (
% 0.48/0.66 xn: $i)).
% 0.48/0.66 tff(aNaturalNumber0_type, type, (
% 0.48/0.66 aNaturalNumber0: $i > $o)).
% 0.48/0.66 tff(sz00_type, type, (
% 0.48/0.66 sz00: $i)).
% 0.48/0.66 tff(tptp_fun_W0_7_type, type, (
% 0.48/0.66 tptp_fun_W0_7: $i)).
% 0.48/0.66 tff(doDivides0_type, type, (
% 0.48/0.66 doDivides0: ( $i * $i ) > $o)).
% 0.48/0.66 tff(tptp_fun_W2_1_type, type, (
% 0.48/0.66 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.48/0.66 tff(tptp_fun_W0_6_type, type, (
% 0.48/0.66 tptp_fun_W0_6: $i)).
% 0.48/0.66 tff(1,plain,
% 0.48/0.66 ((xq = sdtsldt0(xn, xp)) <=> (xq = sdtsldt0(xn, xp))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(2,axiom,((aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))) & (xq = sdtsldt0(xn, xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3059')).
% 0.48/0.66 tff(3,plain,
% 0.48/0.66 (xq = sdtsldt0(xn, xp)),
% 0.48/0.66 inference(and_elim,[status(thm)],[2])).
% 0.48/0.66 tff(4,plain,
% 0.48/0.66 (xq = sdtsldt0(xn, xp)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.48/0.66 tff(5,plain,
% 0.48/0.66 (sdtsldt0(xn, xp) = xq),
% 0.48/0.66 inference(symmetry,[status(thm)],[4])).
% 0.48/0.66 tff(6,plain,
% 0.48/0.66 (sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)) = sdtasdt0(xq, xq)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[5, 5])).
% 0.48/0.66 tff(7,plain,
% 0.48/0.66 (sdtasdt0(xq, xq) = sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))),
% 0.48/0.66 inference(symmetry,[status(thm)],[6])).
% 0.48/0.66 tff(8,plain,
% 0.48/0.66 (sdtasdt0(xp, sdtasdt0(xq, xq)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[7])).
% 0.48/0.66 tff(9,plain,
% 0.48/0.66 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xp, sdtasdt0(xq, xq))),
% 0.48/0.66 inference(symmetry,[status(thm)],[8])).
% 0.48/0.66 tff(10,plain,
% 0.48/0.66 (aNaturalNumber0(sdtsldt0(xn, xp)) <=> aNaturalNumber0(xq)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[5])).
% 0.48/0.66 tff(11,plain,
% 0.48/0.66 (aNaturalNumber0(xq) <=> aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.48/0.66 inference(symmetry,[status(thm)],[10])).
% 0.48/0.66 tff(12,plain,
% 0.48/0.66 (aNaturalNumber0(xq) <=> aNaturalNumber0(xq)),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(13,plain,
% 0.48/0.66 (aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))),
% 0.48/0.66 inference(and_elim,[status(thm)],[2])).
% 0.48/0.66 tff(14,plain,
% 0.48/0.66 (aNaturalNumber0(xq)),
% 0.48/0.66 inference(and_elim,[status(thm)],[13])).
% 0.48/0.66 tff(15,plain,
% 0.48/0.66 (aNaturalNumber0(xq)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.48/0.66 tff(16,plain,
% 0.48/0.66 (aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.48/0.66 tff(17,plain,
% 0.48/0.66 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(18,axiom,(((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))) & (~(xp = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2987')).
% 0.48/0.66 tff(19,plain,
% 0.48/0.66 ((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))),
% 0.48/0.66 inference(and_elim,[status(thm)],[18])).
% 0.48/0.66 tff(20,plain,
% 0.48/0.66 (((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))),
% 0.48/0.66 inference(and_elim,[status(thm)],[19])).
% 0.48/0.66 tff(21,plain,
% 0.48/0.66 ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)),
% 0.48/0.66 inference(and_elim,[status(thm)],[20])).
% 0.48/0.66 tff(22,plain,
% 0.48/0.66 (aNaturalNumber0(xp)),
% 0.48/0.66 inference(and_elim,[status(thm)],[21])).
% 0.48/0.66 tff(23,plain,
% 0.48/0.66 (aNaturalNumber0(xp)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.48/0.66 tff(24,plain,
% 0.48/0.66 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(25,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[24])).
% 0.48/0.66 tff(26,plain,
% 0.48/0.66 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(27,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[26])).
% 0.48/0.66 tff(28,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(29,plain,
% 0.48/0.66 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(30,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[29])).
% 0.48/0.66 tff(31,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 0.48/0.66 tff(32,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.48/0.66 tff(33,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.48/0.66 tff(34,plain,(
% 0.48/0.66 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.66 inference(skolemize,[status(sab)],[33])).
% 0.48/0.66 tff(35,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.48/0.66 tff(36,plain,
% 0.48/0.66 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.48/0.66 tff(37,plain,
% 0.48/0.66 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(38,plain,
% 0.48/0.66 (((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(39,plain,
% 0.48/0.66 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[38])).
% 0.48/0.66 tff(40,plain,
% 0.48/0.66 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[39, 37])).
% 0.48/0.66 tff(41,plain,
% 0.48/0.66 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(42,plain,
% 0.48/0.66 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.48/0.66 tff(43,plain,
% 0.48/0.66 ((~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[42, 36, 23])).
% 0.48/0.66 tff(44,plain,
% 0.48/0.66 (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[43, 16])).
% 0.48/0.66 tff(45,plain,
% 0.48/0.66 ((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) <=> (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp)))),
% 0.48/0.66 inference(commutativity,[status(thm)],[])).
% 0.48/0.66 tff(46,plain,
% 0.48/0.66 ((sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))) <=> (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7))),
% 0.48/0.66 inference(symmetry,[status(thm)],[45])).
% 0.48/0.66 tff(47,plain,
% 0.48/0.66 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, xq)),
% 0.48/0.66 inference(monotonicity,[status(thm)],[5])).
% 0.48/0.66 tff(48,plain,
% 0.48/0.66 (sdtasdt0(xp, xq) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.48/0.66 inference(symmetry,[status(thm)],[47])).
% 0.48/0.66 tff(49,plain,
% 0.48/0.66 ((xn = sdtasdt0(xp, xq)) <=> (xn = sdtasdt0(xp, xq))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(50,plain,
% 0.48/0.66 (xn = sdtasdt0(xp, xq)),
% 0.48/0.66 inference(and_elim,[status(thm)],[13])).
% 0.48/0.66 tff(51,plain,
% 0.48/0.66 (xn = sdtasdt0(xp, xq)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.48/0.66 tff(52,plain,
% 0.48/0.66 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(53,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) & doDivides0(xp, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3046')).
% 0.48/0.66 tff(54,plain,
% 0.48/0.66 ((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.48/0.66 inference(and_elim,[status(thm)],[53])).
% 0.48/0.66 tff(55,plain,
% 0.48/0.66 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.48/0.66 inference(and_elim,[status(thm)],[54])).
% 0.48/0.66 tff(56,plain,
% 0.48/0.66 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.48/0.66 tff(57,plain,(
% 0.48/0.66 aNaturalNumber0(W0!7) & (xn = sdtasdt0(xp, W0!7))),
% 0.48/0.66 inference(skolemize,[status(sab)],[56])).
% 0.48/0.66 tff(58,plain,
% 0.48/0.66 (xn = sdtasdt0(xp, W0!7)),
% 0.48/0.66 inference(and_elim,[status(thm)],[57])).
% 0.48/0.66 tff(59,plain,
% 0.48/0.66 (sdtasdt0(xp, W0!7) = xn),
% 0.48/0.66 inference(symmetry,[status(thm)],[58])).
% 0.48/0.66 tff(60,plain,
% 0.48/0.66 (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.48/0.66 inference(transitivity,[status(thm)],[59, 51, 48])).
% 0.48/0.66 tff(61,plain,
% 0.48/0.66 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[60, 46])).
% 0.48/0.66 tff(62,plain,
% 0.48/0.66 (((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))) | (~(sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)))),
% 0.48/0.66 inference(tautology,[status(thm)],[])).
% 0.48/0.66 tff(63,plain,
% 0.48/0.66 ((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.48/0.66 tff(64,plain,
% 0.48/0.66 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(65,plain,
% 0.48/0.66 (~(xp = sz00)),
% 0.48/0.66 inference(and_elim,[status(thm)],[18])).
% 0.48/0.66 tff(66,plain,
% 0.48/0.66 (~(xp = sz00)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.48/0.66 tff(67,plain,
% 0.48/0.66 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(68,plain,
% 0.48/0.66 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[67])).
% 0.48/0.66 tff(69,plain,
% 0.48/0.66 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.48/0.66 inference(bind,[status(th)],[])).
% 0.48/0.66 tff(70,plain,
% 0.48/0.66 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.48/0.66 inference(quant_intro,[status(thm)],[69])).
% 0.48/0.66 tff(71,plain,
% 0.48/0.66 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[70, 68])).
% 0.48/0.66 tff(72,plain,
% 0.48/0.66 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 0.51/0.66 inference(bind,[status(th)],[])).
% 0.51/0.66 tff(73,plain,
% 0.51/0.66 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.51/0.66 inference(quant_intro,[status(thm)],[72])).
% 0.51/0.66 tff(74,plain,
% 0.51/0.66 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.51/0.66 inference(rewrite,[status(thm)],[])).
% 0.51/0.66 tff(75,plain,
% 0.51/0.66 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(76,plain,
% 0.51/0.67 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[75])).
% 0.51/0.67 tff(77,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulCanc')).
% 0.51/0.67 tff(78,plain,
% 0.51/0.67 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.51/0.67 tff(79,plain,
% 0.51/0.67 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.51/0.67 tff(80,plain,(
% 0.51/0.67 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.51/0.67 inference(skolemize,[status(sab)],[79])).
% 0.51/0.67 tff(81,plain,
% 0.51/0.67 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.51/0.67 tff(82,plain,
% 0.51/0.67 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.51/0.67 tff(83,plain,
% 0.51/0.67 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(84,plain,
% 0.51/0.67 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(85,plain,
% 0.51/0.67 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(86,plain,
% 0.51/0.67 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[85])).
% 0.51/0.67 tff(87,plain,
% 0.51/0.67 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[86])).
% 0.51/0.67 tff(88,plain,
% 0.51/0.67 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.51/0.67 inference(transitivity,[status(thm)],[87, 84])).
% 0.51/0.67 tff(89,plain,
% 0.51/0.67 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[88])).
% 0.51/0.67 tff(90,plain,
% 0.51/0.67 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.51/0.67 inference(transitivity,[status(thm)],[89, 83])).
% 0.51/0.67 tff(91,plain,
% 0.51/0.67 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(92,plain,
% 0.51/0.67 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.51/0.67 tff(93,plain,
% 0.51/0.67 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[92, 82, 23, 66])).
% 0.51/0.67 tff(94,plain,
% 0.51/0.67 (aNaturalNumber0(W0!7)),
% 0.51/0.67 inference(and_elim,[status(thm)],[57])).
% 0.51/0.67 tff(95,plain,
% 0.51/0.67 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(96,plain,
% 0.51/0.67 (((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))) <=> ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(97,plain,
% 0.51/0.67 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[96])).
% 0.51/0.67 tff(98,plain,
% 0.51/0.67 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.51/0.67 inference(transitivity,[status(thm)],[97, 95])).
% 0.51/0.67 tff(99,plain,
% 0.51/0.67 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(100,plain,
% 0.51/0.67 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.51/0.67 tff(101,plain,
% 0.51/0.67 (sdtsldt0(xn, xp) = W0!7),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[100, 94, 16, 93, 63])).
% 0.51/0.67 tff(102,plain,
% 0.51/0.67 (sdtasdt0(xp, xq) = xn),
% 0.51/0.67 inference(symmetry,[status(thm)],[51])).
% 0.51/0.67 tff(103,plain,
% 0.51/0.67 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)),
% 0.51/0.67 inference(transitivity,[status(thm)],[47, 102, 58])).
% 0.51/0.67 tff(104,plain,
% 0.51/0.67 (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[103, 101])).
% 0.51/0.67 tff(105,plain,
% 0.51/0.67 (sdtasdt0(sdtasdt0(xp, W0!7), W0!7) = sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp))),
% 0.51/0.67 inference(symmetry,[status(thm)],[104])).
% 0.51/0.67 tff(106,plain,
% 0.51/0.67 (aNaturalNumber0(sdtasdt0(xp, W0!7)) <=> aNaturalNumber0(xn)),
% 0.51/0.67 inference(monotonicity,[status(thm)],[59])).
% 0.51/0.67 tff(107,plain,
% 0.51/0.67 (aNaturalNumber0(xn) <=> aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.51/0.67 inference(symmetry,[status(thm)],[106])).
% 0.51/0.67 tff(108,plain,
% 0.51/0.67 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(109,plain,
% 0.51/0.67 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.51/0.67 inference(and_elim,[status(thm)],[21])).
% 0.51/0.67 tff(110,plain,
% 0.51/0.67 (aNaturalNumber0(xn)),
% 0.51/0.67 inference(and_elim,[status(thm)],[109])).
% 0.51/0.67 tff(111,plain,
% 0.51/0.67 (aNaturalNumber0(xn)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[110, 108])).
% 0.51/0.67 tff(112,plain,
% 0.51/0.67 (aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.51/0.67 tff(113,plain,
% 0.51/0.67 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(114,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[113])).
% 0.51/0.67 tff(115,plain,
% 0.51/0.67 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(116,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[115])).
% 0.51/0.67 tff(117,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(118,plain,
% 0.51/0.67 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(119,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[118])).
% 0.51/0.67 tff(120,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 0.51/0.67 tff(121,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.51/0.67 tff(122,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.51/0.67 tff(123,plain,(
% 0.51/0.67 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.51/0.67 inference(skolemize,[status(sab)],[122])).
% 0.51/0.67 tff(124,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.51/0.67 tff(125,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.51/0.67 tff(126,plain,
% 0.51/0.67 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(127,plain,
% 0.51/0.67 (((sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7))) <=> ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(128,plain,
% 0.51/0.67 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7))))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[127])).
% 0.51/0.67 tff(129,plain,
% 0.51/0.67 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)))),
% 0.51/0.67 inference(transitivity,[status(thm)],[128, 126])).
% 0.51/0.67 tff(130,plain,
% 0.51/0.67 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)))),
% 0.51/0.67 inference(quant_inst,[status(thm)],[])).
% 0.51/0.67 tff(131,plain,
% 0.51/0.67 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7))),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.51/0.67 tff(132,plain,
% 0.51/0.67 (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)),
% 0.51/0.67 inference(unit_resolution,[status(thm)],[131, 125, 94, 112])).
% 0.51/0.67 tff(133,plain,
% 0.51/0.67 ((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)) <=> (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(134,axiom,(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3014')).
% 0.51/0.67 tff(135,plain,
% 0.51/0.67 (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.51/0.67 tff(136,plain,
% 0.51/0.67 (sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(xm, xm))),
% 0.51/0.67 inference(symmetry,[status(thm)],[135])).
% 0.51/0.67 tff(137,plain,
% 0.51/0.67 (aNaturalNumber0(sdtasdt0(xn, xn)) <=> aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm)))),
% 0.51/0.67 inference(monotonicity,[status(thm)],[136])).
% 0.51/0.67 tff(138,plain,
% 0.51/0.67 (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))) <=> aNaturalNumber0(sdtasdt0(xn, xn))),
% 0.51/0.67 inference(symmetry,[status(thm)],[137])).
% 0.51/0.67 tff(139,plain,
% 0.51/0.67 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(140,plain,
% 0.51/0.67 (aNaturalNumber0(xm)),
% 0.51/0.67 inference(and_elim,[status(thm)],[109])).
% 0.51/0.67 tff(141,plain,
% 0.51/0.67 (aNaturalNumber0(xm)),
% 0.51/0.67 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.51/0.67 tff(142,plain,
% 0.51/0.67 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(143,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[142])).
% 0.51/0.67 tff(144,plain,
% 0.51/0.67 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.67 tff(145,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.67 inference(quant_intro,[status(thm)],[144])).
% 0.51/0.67 tff(146,plain,
% 0.51/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.51/0.67 inference(rewrite,[status(thm)],[])).
% 0.51/0.67 tff(147,plain,
% 0.51/0.67 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.51/0.67 inference(bind,[status(th)],[])).
% 0.51/0.68 tff(148,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.51/0.68 inference(quant_intro,[status(thm)],[147])).
% 0.51/0.68 tff(149,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.51/0.68 tff(150,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.51/0.68 tff(151,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.51/0.68 tff(152,plain,(
% 0.51/0.68 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.51/0.68 inference(skolemize,[status(sab)],[151])).
% 0.51/0.68 tff(153,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.51/0.68 tff(154,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[153, 143])).
% 0.51/0.68 tff(155,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(156,plain,
% 0.51/0.68 ((aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm))) <=> (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(157,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[156])).
% 0.51/0.68 tff(158,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)))),
% 0.51/0.68 inference(transitivity,[status(thm)],[157, 155])).
% 0.51/0.68 tff(159,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xm)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(160,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xm, xm)) | (~aNaturalNumber0(xm))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.51/0.68 tff(161,plain,
% 0.51/0.68 (aNaturalNumber0(sdtasdt0(xm, xm))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[160, 154, 141])).
% 0.51/0.68 tff(162,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(163,plain,
% 0.51/0.68 ((aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(164,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm)))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[163])).
% 0.51/0.68 tff(165,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))))),
% 0.51/0.68 inference(transitivity,[status(thm)],[164, 162])).
% 0.51/0.68 tff(166,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm))) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~aNaturalNumber0(xp)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(167,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm)))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.51/0.68 tff(168,plain,
% 0.51/0.68 (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xm, xm)))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[167, 154, 23, 161])).
% 0.51/0.68 tff(169,plain,
% 0.51/0.68 (aNaturalNumber0(sdtasdt0(xn, xn))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[168, 138])).
% 0.51/0.68 tff(170,plain,
% 0.51/0.68 (doDivides0(xp, sdtasdt0(xn, xn)) <=> doDivides0(xp, sdtasdt0(xn, xn))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(171,plain,
% 0.51/0.68 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))),
% 0.51/0.68 inference(and_elim,[status(thm)],[54])).
% 0.51/0.68 tff(172,plain,
% 0.51/0.68 (doDivides0(xp, sdtasdt0(xn, xn))),
% 0.51/0.68 inference(and_elim,[status(thm)],[171])).
% 0.51/0.68 tff(173,plain,
% 0.51/0.68 (doDivides0(xp, sdtasdt0(xn, xn))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[172, 170])).
% 0.51/0.68 tff(174,plain,
% 0.51/0.68 (^[W0: $i, W1: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))))),
% 0.51/0.68 inference(bind,[status(th)],[])).
% 0.51/0.68 tff(175,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.51/0.68 inference(quant_intro,[status(thm)],[174])).
% 0.51/0.68 tff(176,plain,
% 0.51/0.68 (^[W0: $i, W1: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))))),
% 0.51/0.68 inference(bind,[status(th)],[])).
% 0.51/0.68 tff(177,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.51/0.68 inference(quant_intro,[status(thm)],[176])).
% 0.51/0.68 tff(178,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.51/0.68 inference(transitivity,[status(thm)],[177, 175])).
% 0.51/0.68 tff(179,plain,
% 0.51/0.68 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(trans(monotonicity(rewrite((aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))) <=> (~((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))), (((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> ((W2 = sdtsldt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))), rewrite(((W2 = sdtsldt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))), (((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))), rewrite((~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))), (((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0))))))), (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))), trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(rewrite(((~(W0 = sz00)) & doDivides0(W0, W1)) <=> (~((W0 = sz00) | (~doDivides0(W0, W1))))), ((~((~(W0 = sz00)) & doDivides0(W0, W1))) <=> (~(~((W0 = sz00) | (~doDivides0(W0, W1))))))), rewrite((~(~((W0 = sz00) | (~doDivides0(W0, W1))))) <=> ((W0 = sz00) | (~doDivides0(W0, W1)))), ((~((~(W0 = sz00)) & doDivides0(W0, W1))) <=> ((W0 = sz00) | (~doDivides0(W0, W1))))), ((![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = sz00) | (~doDivides0(W0, W1)))))), rewrite((![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = sz00) | (~doDivides0(W0, W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))), ((![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))))),
% 0.51/0.68 inference(bind,[status(th)],[])).
% 0.51/0.68 tff(180,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.51/0.68 inference(quant_intro,[status(thm)],[179])).
% 0.51/0.68 tff(181,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1)))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(182,plain,
% 0.51/0.68 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((~((~(W0 = sz00)) & doDivides0(W0, W1))) | ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = sz00)) & doDivides0(W0, W1))) | ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = sz00)) & doDivides0(W0, W1))) | ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))))),
% 0.51/0.68 inference(bind,[status(th)],[])).
% 0.51/0.68 tff(183,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.51/0.68 inference(quant_intro,[status(thm)],[182])).
% 0.51/0.68 tff(184,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = sz00)) & doDivides0(W0, W1)) => ![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefQuot')).
% 0.51/0.68 tff(185,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.51/0.68 tff(186,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.51/0.68 tff(187,plain,(
% 0.51/0.68 ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtsldt0(W1, W0)) <=> (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = sz00)) & doDivides0(W0, W1))))),
% 0.51/0.68 inference(skolemize,[status(sab)],[186])).
% 0.51/0.68 tff(188,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.51/0.68 tff(189,plain,
% 0.51/0.68 (![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.51/0.68 tff(190,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(191,plain,
% 0.51/0.68 (((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(192,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[191])).
% 0.51/0.68 tff(193,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))),
% 0.51/0.68 inference(transitivity,[status(thm)],[192, 190])).
% 0.51/0.68 tff(194,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | ((xp = sz00) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp)))))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(195,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : ((W0 = sz00) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))) <=> (W2 = sdtsldt0(W1, W0)))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.51/0.68 tff(196,plain,
% 0.51/0.68 ((~aNaturalNumber0(sdtasdt0(xn, xn))) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[195, 189, 23, 66, 173])).
% 0.51/0.68 tff(197,plain,
% 0.51/0.68 (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[196, 169])).
% 0.51/0.68 tff(198,plain,
% 0.51/0.68 ((~![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))) | (~(((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))))) <=> (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtsldt0(sdtasdt0(xn, xn), xp))))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(199,plain,
% 0.51/0.68 (~(((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))))) <=> (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtsldt0(sdtasdt0(xn, xn), xp)))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.51/0.68 tff(200,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(201,plain,
% 0.51/0.68 ((aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7))) <=> ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(202,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[201])).
% 0.51/0.68 tff(203,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))),
% 0.51/0.68 inference(transitivity,[status(thm)],[202, 200])).
% 0.51/0.68 tff(204,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)))),
% 0.51/0.68 inference(quant_inst,[status(thm)],[])).
% 0.51/0.68 tff(205,plain,
% 0.51/0.68 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))),
% 0.51/0.68 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.51/0.68 tff(206,plain,
% 0.51/0.68 (aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))),
% 0.51/0.68 inference(unit_resolution,[status(thm)],[205, 154, 94, 112])).
% 0.51/0.68 tff(207,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(208,plain,
% 0.51/0.68 (((sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))),
% 0.51/0.68 inference(rewrite,[status(thm)],[])).
% 0.51/0.68 tff(209,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7)))))),
% 0.51/0.68 inference(monotonicity,[status(thm)],[208])).
% 0.51/0.68 tff(210,plain,
% 0.51/0.68 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))),
% 0.51/0.68 inference(transitivity,[status(thm)],[209, 207])).
% 0.51/0.68 tff(211,plain,
% 0.51/0.69 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(xp)))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(212,plain,
% 0.51/0.69 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7)))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.51/0.69 tff(213,plain,
% 0.51/0.69 ((sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!7)))),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[212, 36, 23, 94])).
% 0.51/0.69 tff(214,plain,
% 0.51/0.69 (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[213, 112])).
% 0.51/0.69 tff(215,plain,
% 0.51/0.69 (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7)) = sdtasdt0(xn, xn)),
% 0.51/0.69 inference(monotonicity,[status(thm)],[59, 59])).
% 0.51/0.69 tff(216,plain,
% 0.51/0.69 (sdtasdt0(xn, xn) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(xp, W0!7))),
% 0.51/0.69 inference(symmetry,[status(thm)],[215])).
% 0.51/0.69 tff(217,plain,
% 0.51/0.69 (sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))),
% 0.51/0.69 inference(transitivity,[status(thm)],[216, 214])).
% 0.51/0.69 tff(218,plain,
% 0.51/0.69 ((~((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))))) | (~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))))),
% 0.51/0.69 inference(tautology,[status(thm)],[])).
% 0.51/0.69 tff(219,plain,
% 0.51/0.69 ((~((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))))) | (~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.51/0.69 tff(220,plain,
% 0.51/0.69 (~((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7))))))),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[219, 206])).
% 0.51/0.69 tff(221,plain,
% 0.51/0.69 ((((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))))) <=> (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtsldt0(sdtasdt0(xn, xn), xp))) | ((~aNaturalNumber0(sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(W0!7, sdtasdt0(xp, W0!7)))))) | (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtsldt0(sdtasdt0(xn, xn), xp))),
% 0.51/0.69 inference(tautology,[status(thm)],[])).
% 0.51/0.69 tff(222,plain,
% 0.51/0.69 (sdtasdt0(W0!7, sdtasdt0(xp, W0!7)) = sdtsldt0(sdtasdt0(xn, xn), xp)),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[221, 220, 199])).
% 0.51/0.69 tff(223,plain,
% 0.51/0.69 (sdtsldt0(sdtasdt0(xn, xn), xp) = sdtasdt0(W0!7, sdtasdt0(xp, W0!7))),
% 0.51/0.69 inference(symmetry,[status(thm)],[222])).
% 0.51/0.69 tff(224,plain,
% 0.51/0.69 ((~![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))) <=> (W2 = sdtsldt0(sdtasdt0(xn, xn), xp))))) | (~(((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) <=> (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp))))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(225,plain,
% 0.51/0.69 (~(((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) <=> (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp)))),
% 0.51/0.69 inference(unit_resolution,[status(thm)],[224, 197])).
% 0.51/0.69 tff(226,plain,
% 0.51/0.69 (^[W0: $i, W1: $i] : refl(((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))))),
% 0.51/0.69 inference(bind,[status(th)],[])).
% 0.51/0.69 tff(227,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 0.51/0.69 inference(quant_intro,[status(thm)],[226])).
% 0.51/0.69 tff(228,plain,
% 0.51/0.69 (^[W0: $i, W1: $i] : rewrite(((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))))),
% 0.51/0.69 inference(bind,[status(th)],[])).
% 0.51/0.69 tff(229,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 0.51/0.69 inference(quant_intro,[status(thm)],[228])).
% 0.51/0.69 tff(230,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 0.51/0.69 inference(transitivity,[status(thm)],[229, 227])).
% 0.51/0.69 tff(231,plain,
% 0.51/0.69 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(rewrite(((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) <=> ((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))), rewrite((doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> (doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))), ((((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))))) & (doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))), rewrite((((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))))) & (doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))) <=> (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))), ((((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))) <=> (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2))))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))))),
% 0.51/0.69 inference(bind,[status(th)],[])).
% 0.51/0.69 tff(232,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 0.51/0.69 inference(quant_intro,[status(thm)],[231])).
% 0.51/0.69 tff(233,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(234,plain,
% 0.51/0.69 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))) <=> (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))))),
% 0.51/0.69 inference(bind,[status(th)],[])).
% 0.51/0.69 tff(235,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2))))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 0.51/0.69 inference(quant_intro,[status(thm)],[234])).
% 0.51/0.69 tff(236,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefDiv')).
% 0.51/0.69 tff(237,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.51/0.69 tff(238,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (doDivides0(W0, W1) <=> ?[W2: $i] : (aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[237, 233])).
% 0.51/0.69 tff(239,plain,(
% 0.51/0.69 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (((~doDivides0(W0, W1)) | (aNaturalNumber0(tptp_fun_W2_1(W1, W0)) & (W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0))))) & (doDivides0(W0, W1) | ![W2: $i] : (~(aNaturalNumber0(W2) & (W1 = sdtasdt0(W0, W2)))))))),
% 0.51/0.69 inference(skolemize,[status(sab)],[238])).
% 0.51/0.69 tff(240,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.51/0.69 tff(241,plain,
% 0.51/0.69 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[240, 230])).
% 0.51/0.69 tff(242,plain,
% 0.51/0.69 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(243,plain,
% 0.51/0.69 (((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))))))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(244,plain,
% 0.51/0.69 ((~((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))))) <=> (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))))))),
% 0.51/0.69 inference(rewrite,[status(thm)],[])).
% 0.51/0.69 tff(245,plain,
% 0.51/0.69 (((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2))))))))) <=> ((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[244])).
% 0.51/0.69 tff(246,plain,
% 0.51/0.69 (((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2))))))))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))))),
% 0.51/0.69 inference(transitivity,[status(thm)],[245, 243])).
% 0.51/0.69 tff(247,plain,
% 0.51/0.69 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))))))))),
% 0.51/0.69 inference(monotonicity,[status(thm)],[246])).
% 0.51/0.69 tff(248,plain,
% 0.51/0.69 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))))),
% 0.51/0.69 inference(transitivity,[status(thm)],[247, 242])).
% 0.51/0.69 tff(249,plain,
% 0.51/0.69 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | ((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~aNaturalNumber0(xp)) | (~((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))))))),
% 0.51/0.69 inference(quant_inst,[status(thm)],[])).
% 0.51/0.69 tff(250,plain,
% 0.51/0.69 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~((~doDivides0(W0, W1)) | (~((~aNaturalNumber0(tptp_fun_W2_1(W1, W0))) | (~(W1 = sdtasdt0(W0, tptp_fun_W2_1(W1, W0)))))))) | (~(doDivides0(W0, W1) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(W1 = sdtasdt0(W0, W2)))))))))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))))))),
% 0.51/0.69 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.51/0.69 tff(251,plain,
% 0.51/0.69 ((~aNaturalNumber0(sdtasdt0(xn, xn))) | (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))))))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[250, 241, 23])).
% 0.51/0.70 tff(252,plain,
% 0.51/0.70 (~((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[251, 169])).
% 0.51/0.70 tff(253,plain,
% 0.51/0.70 (((~(doDivides0(xp, sdtasdt0(xn, xn)) | ![W2: $i] : ((~aNaturalNumber0(W2)) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, W2)))))) | (~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))))) | ((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(254,plain,
% 0.51/0.70 ((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.51/0.70 tff(255,plain,
% 0.51/0.70 ((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(256,plain,
% 0.51/0.70 ((~((~doDivides0(xp, sdtasdt0(xn, xn))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))))) | (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[255, 173])).
% 0.51/0.70 tff(257,plain,
% 0.51/0.70 (~((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[256, 254])).
% 0.51/0.70 tff(258,plain,
% 0.51/0.70 ((((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) <=> (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp))) | ((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(259,plain,
% 0.51/0.70 ((((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) <=> (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.51/0.70 tff(260,plain,
% 0.51/0.70 (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = sdtsldt0(sdtasdt0(xn, xn), xp)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[259, 225])).
% 0.51/0.70 tff(261,plain,
% 0.51/0.70 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(262,plain,
% 0.51/0.70 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0)))),
% 0.51/0.70 inference(and_elim,[status(thm)],[171])).
% 0.51/0.70 tff(263,plain,
% 0.51/0.70 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.51/0.70 tff(264,plain,(
% 0.51/0.70 aNaturalNumber0(W0!6) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0!6))),
% 0.51/0.70 inference(skolemize,[status(sab)],[263])).
% 0.51/0.70 tff(265,plain,
% 0.51/0.70 (sdtasdt0(xn, xn) = sdtasdt0(xp, W0!6)),
% 0.51/0.70 inference(and_elim,[status(thm)],[264])).
% 0.51/0.70 tff(266,plain,
% 0.51/0.70 (((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) | (sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(267,plain,
% 0.51/0.70 (sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[266, 257])).
% 0.51/0.70 tff(268,plain,
% 0.51/0.70 (sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xn, xn)),
% 0.51/0.70 inference(symmetry,[status(thm)],[267])).
% 0.51/0.70 tff(269,plain,
% 0.51/0.70 (sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)),
% 0.51/0.70 inference(transitivity,[status(thm)],[268, 265])).
% 0.51/0.70 tff(270,plain,
% 0.51/0.70 (((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp))) | (~(sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(271,plain,
% 0.51/0.70 ((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[270, 269])).
% 0.51/0.70 tff(272,plain,
% 0.51/0.70 (((~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~(sdtasdt0(xn, xn) = sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp))))) | aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(273,plain,
% 0.51/0.70 (aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[272, 257])).
% 0.51/0.70 tff(274,plain,
% 0.51/0.70 (aNaturalNumber0(W0!6)),
% 0.51/0.70 inference(and_elim,[status(thm)],[264])).
% 0.51/0.70 tff(275,plain,
% 0.51/0.70 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(276,plain,
% 0.51/0.70 (((tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp))))) <=> ((~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(277,plain,
% 0.51/0.70 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp))))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[276])).
% 0.51/0.70 tff(278,plain,
% 0.51/0.70 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[277, 275])).
% 0.51/0.70 tff(279,plain,
% 0.51/0.70 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(280,plain,
% 0.51/0.70 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp))) | (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6) | (~((sdtasdt0(xp, tptp_fun_W2_1(sdtasdt0(xn, xn), xp)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(tptp_fun_W2_1(sdtasdt0(xn, xn), xp), xp) = sdtasdt0(W0!6, xp))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.51/0.70 tff(281,plain,
% 0.51/0.70 (tptp_fun_W2_1(sdtasdt0(xn, xn), xp) = W0!6),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[280, 274, 93, 273, 271])).
% 0.51/0.70 tff(282,plain,
% 0.51/0.70 (W0!6 = tptp_fun_W2_1(sdtasdt0(xn, xn), xp)),
% 0.51/0.70 inference(symmetry,[status(thm)],[281])).
% 0.51/0.70 tff(283,plain,
% 0.51/0.70 (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)),
% 0.51/0.70 inference(transitivity,[status(thm)],[135, 265])).
% 0.51/0.70 tff(284,plain,
% 0.51/0.70 (((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp))) | (~(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)))),
% 0.51/0.70 inference(tautology,[status(thm)],[])).
% 0.51/0.70 tff(285,plain,
% 0.51/0.70 ((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.51/0.70 tff(286,plain,
% 0.51/0.70 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(xm, xm) = W0!6) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(xm, xm) = W0!6) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(287,plain,
% 0.51/0.71 (((sdtasdt0(xm, xm) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp))))) <=> ((~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(xm, xm) = W0!6) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(288,plain,
% 0.51/0.71 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(xm, xm) = W0!6) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp))))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[287])).
% 0.51/0.71 tff(289,plain,
% 0.51/0.71 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(xm, xm) = W0!6) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.71 inference(transitivity,[status(thm)],[288, 286])).
% 0.51/0.71 tff(290,plain,
% 0.51/0.71 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtasdt0(xm, xm) = W0!6) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp)))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(291,plain,
% 0.51/0.71 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!6)) | (~aNaturalNumber0(sdtasdt0(xm, xm))) | (sdtasdt0(xm, xm) = W0!6) | (~((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, W0!6)) | (sdtasdt0(sdtasdt0(xm, xm), xp) = sdtasdt0(W0!6, xp))))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.51/0.71 tff(292,plain,
% 0.51/0.71 (sdtasdt0(xm, xm) = W0!6),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[291, 274, 161, 93, 285])).
% 0.51/0.71 tff(293,plain,
% 0.51/0.71 (sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq))),
% 0.51/0.71 inference(transitivity,[status(thm)],[292, 282, 260, 223, 132, 105, 44, 9])).
% 0.51/0.71 tff(294,plain,
% 0.51/0.71 ((~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))) <=> (~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(295,axiom,(~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.51/0.71 tff(296,plain,
% 0.51/0.71 (~(sdtasdt0(xm, xm) = sdtasdt0(xp, sdtasdt0(xq, xq)))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.51/0.71 tff(297,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[296, 293])).
% 0.51/0.71 % SZS output end Proof
% 0.51/0.71 % E exiting
%------------------------------------------------------------------------------