%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM459+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:03 AM UTC 2025
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM459+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:12:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(sz00_type, type, (
% 0.21/0.49 sz00: $i)).
% 0.21/0.49 tff(tptp_fun_W0_1_type, type, (
% 0.21/0.49 tptp_fun_W0_1: $i)).
% 0.21/0.49 tff(sdtmndt0_type, type, (
% 0.21/0.49 sdtmndt0: ( $i * $i ) > $i)).
% 0.21/0.49 tff(xm_type, type, (
% 0.21/0.49 xm: $i)).
% 0.21/0.49 tff(xn_type, type, (
% 0.21/0.49 xn: $i)).
% 0.21/0.49 tff(sdtpldt0_type, type, (
% 0.21/0.49 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.49 tff(aNaturalNumber0_type, type, (
% 0.21/0.49 aNaturalNumber0: $i > $o)).
% 0.21/0.49 tff(sdtlseqdt0_type, type, (
% 0.21/0.49 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.21/0.49 tff(tptp_fun_W0_2_type, type, (
% 0.21/0.49 tptp_fun_W0_2: $i)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 ((sz00 = W0!1) <=> (W0!1 = sz00)),
% 0.21/0.49 inference(commutativity,[status(thm)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 (sdtlseqdt0(xm, xn) <=> sdtlseqdt0(xm, xn)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 ((~((((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm))) & sdtlseqdt0(xn, xm)) => (xm = xn))) <=> (~((~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm)) & sdtlseqdt0(xn, xm))) | (xm = xn)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(~((((?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm))) & sdtlseqdt0(xn, xm)) => (xm = xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (~((~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm)) & sdtlseqdt0(xn, xm))) | (xm = xn))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) & sdtlseqdt0(xm, xn) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm)) & sdtlseqdt0(xn, xm)),
% 0.21/0.49 inference(or_elim,[status(thm)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (sdtlseqdt0(xm, xn)),
% 0.21/0.49 inference(and_elim,[status(thm)],[6])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 (sdtlseqdt0(xm, xn)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(10,axiom,(aNaturalNumber0(xm) & aNaturalNumber0(xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__745')).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (aNaturalNumber0(xn)),
% 0.21/0.49 inference(and_elim,[status(thm)],[10])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (aNaturalNumber0(xn)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (aNaturalNumber0(xm)),
% 0.21/0.49 inference(and_elim,[status(thm)],[10])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (aNaturalNumber0(xm)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 (^[W0: $i, W1: $i] : refl(((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (^[W0: $i, W1: $i] : rewrite(((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(trans(monotonicity(rewrite((aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)) <=> (~((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))), (((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> ((W2 = sdtmndt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))), rewrite(((W2 = sdtmndt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))), (((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))), rewrite((~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))), (((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))))), (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(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))))), ((![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~sdtlseqdt0(W0, W1))))), rewrite((![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~sdtlseqdt0(W0, W1))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))), ((![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ((~sdtlseqdt0(W0, W1)) | ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~sdtlseqdt0(W0, W1)) | ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~sdtlseqdt0(W0, W1)) | ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.49 tff(26,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefDiff')).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.49 tff(29,plain,(
% 0.21/0.49 ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[28])).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 (((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aNaturalNumber0(xm)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm))))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aNaturalNumber0(xm)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aNaturalNumber0(xm)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aNaturalNumber0(xm)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)) | (~sdtlseqdt0(xm, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[37, 31, 15, 12, 8])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 ((~![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm))))) | (~(((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn))) <=> (W0!1 = sdtmndt0(xn, xm))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(40,plain,
% 0.21/0.50 (~(((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn))) <=> (W0!1 = sdtmndt0(xn, xm)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.50 tff(41,plain,
% 0.21/0.50 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.21/0.50 inference(and_elim,[status(thm)],[6])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.50 tff(44,plain,(
% 0.21/0.50 aNaturalNumber0(W0!1) & (sdtpldt0(xm, W0!1) = xn)),
% 0.21/0.50 inference(skolemize,[status(sab)],[43])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 (sdtpldt0(xm, W0!1) = xn),
% 0.21/0.50 inference(and_elim,[status(thm)],[44])).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (aNaturalNumber0(W0!1)),
% 0.21/0.50 inference(and_elim,[status(thm)],[44])).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 ((~((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn)))) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 (~((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[47, 46, 45])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 ((((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn))) <=> (W0!1 = sdtmndt0(xn, xm))) | ((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn))) | (W0!1 = sdtmndt0(xn, xm))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 ((((~aNaturalNumber0(W0!1)) | (~(sdtpldt0(xm, W0!1) = xn))) <=> (W0!1 = sdtmndt0(xn, xm))) | (W0!1 = sdtmndt0(xn, xm))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (W0!1 = sdtmndt0(xn, xm)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[50, 40])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 (sdtmndt0(xn, xm) = W0!1),
% 0.21/0.50 inference(symmetry,[status(thm)],[51])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 ((sz00 = sdtmndt0(xn, xm)) <=> (sz00 = W0!1)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 ((sz00 = sdtmndt0(xn, xm)) <=> (W0!1 = sz00)),
% 0.21/0.50 inference(transitivity,[status(thm)],[53, 1])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 ((~(sz00 = sdtmndt0(xn, xm))) <=> (~(W0!1 = sz00))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[54])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 ((~![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xm, W2) = xn))) <=> (W2 = sdtmndt0(xn, xm))))) | (~(((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xm, sz00) = xn))) <=> (sz00 = sdtmndt0(xn, xm))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 (~(((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xm, sz00) = xn))) <=> (sz00 = sdtmndt0(xn, xm)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[56, 38])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.50 tff(65,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_AddZero')).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.50 tff(68,plain,(
% 0.21/0.50 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[67])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aNaturalNumber0(xm)) | (~((~(sdtpldt0(xm, sz00) = xm)) | (~(xm = sdtpldt0(sz00, xm))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aNaturalNumber0(xm)) | (~((~(sdtpldt0(xm, sz00) = xm)) | (~(xm = sdtpldt0(sz00, xm))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aNaturalNumber0(xm)) | (~((~(sdtpldt0(xm, sz00) = xm)) | (~(xm = sdtpldt0(sz00, xm))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aNaturalNumber0(xm)) | (~((~(sdtpldt0(xm, sz00) = xm)) | (~(xm = sdtpldt0(sz00, xm)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (~((~(sdtpldt0(xm, sz00) = xm)) | (~(xm = sdtpldt0(sz00, xm))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[73, 70, 15])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (((~(sdtpldt0(xm, sz00) = xm)) | (~(xm = sdtpldt0(sz00, xm)))) | (sdtpldt0(xm, sz00) = xm)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (sdtpldt0(xm, sz00) = xm),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 ((sdtpldt0(xm, sz00) = xn) <=> (xm = xn)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 ((xm = xn) <=> (sdtpldt0(xm, sz00) = xn)),
% 0.21/0.50 inference(symmetry,[status(thm)],[77])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 ((~(xm = xn)) <=> (~(sdtpldt0(xm, sz00) = xn))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 ((~(xm = xn)) <=> (~(xm = xn))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (~(xm = xn)),
% 0.21/0.50 inference(or_elim,[status(thm)],[5])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 (~(xm = xn)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (~(sdtpldt0(xm, sz00) = xn)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xm, sz00) = xn))) | (sdtpldt0(xm, sz00) = xn)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 ((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xm, sz00) = xn))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.50 tff(86,plain,
% 0.21/0.50 ((((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xm, sz00) = xn))) <=> (sz00 = sdtmndt0(xn, xm))) | (~((~aNaturalNumber0(sz00)) | (~(sdtpldt0(xm, sz00) = xn)))) | (~(sz00 = sdtmndt0(xn, xm)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(87,plain,
% 0.21/0.50 (~(sz00 = sdtmndt0(xn, xm))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[86, 85, 57])).
% 0.21/0.50 tff(88,plain,
% 0.21/0.50 (~(W0!1 = sz00)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[87, 55])).
% 0.21/0.50 tff(89,plain,
% 0.21/0.50 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(sdtpldt0(xn, sz00) = xn)) | (~(xn = sdtpldt0(sz00, xn))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aNaturalNumber0(xn)) | (~((~(sdtpldt0(xn, sz00) = xn)) | (~(xn = sdtpldt0(sz00, xn))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(90,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aNaturalNumber0(xn)) | (~((~(sdtpldt0(xn, sz00) = xn)) | (~(xn = sdtpldt0(sz00, xn))))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(91,plain,
% 0.21/0.50 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aNaturalNumber0(xn)) | (~((~(sdtpldt0(xn, sz00) = xn)) | (~(xn = sdtpldt0(sz00, xn)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.50 tff(92,plain,
% 0.21/0.50 (~((~(sdtpldt0(xn, sz00) = xn)) | (~(xn = sdtpldt0(sz00, xn))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[91, 70, 12])).
% 0.21/0.50 tff(93,plain,
% 0.21/0.50 (((~(sdtpldt0(xn, sz00) = xn)) | (~(xn = sdtpldt0(sz00, xn)))) | (xn = sdtpldt0(sz00, xn))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(94,plain,
% 0.21/0.50 (xn = sdtpldt0(sz00, xn)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.50 tff(95,plain,
% 0.21/0.50 (^[W0: $i, W1: $i] : refl(((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(96,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.50 tff(97,plain,
% 0.21/0.50 (^[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))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(98,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.50 tff(99,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(100,plain,
% 0.21/0.50 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(101,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.50 tff(102,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddComm')).
% 0.21/0.50 tff(103,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.50 tff(104,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.50 tff(105,plain,(
% 0.21/0.50 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[104])).
% 0.21/0.50 tff(106,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.21/0.50 tff(107,plain,
% 0.21/0.50 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.21/0.50 tff(108,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)) | (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)) | (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(109,plain,
% 0.21/0.50 (((sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!1))) <=> ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)) | (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(110,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)) | (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.50 tff(111,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)) | (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[110, 108])).
% 0.21/0.50 tff(112,plain,
% 0.21/0.50 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(113,plain,
% 0.21/0.50 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xm)) | (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.50 tff(114,plain,
% 0.21/0.50 (sdtpldt0(W0!1, xm) = sdtpldt0(xm, W0!1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[113, 107, 15, 46])).
% 0.21/0.50 tff(115,plain,
% 0.21/0.50 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(116,plain,
% 0.21/0.50 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm))),
% 0.21/0.50 inference(and_elim,[status(thm)],[6])).
% 0.21/0.50 tff(117,plain,
% 0.21/0.50 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xm))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.50 tff(118,plain,(
% 0.21/0.50 aNaturalNumber0(W0!2) & (sdtpldt0(xn, W0!2) = xm)),
% 0.21/0.50 inference(skolemize,[status(sab)],[117])).
% 0.21/0.50 tff(119,plain,
% 0.21/0.50 (sdtpldt0(xn, W0!2) = xm),
% 0.21/0.50 inference(and_elim,[status(thm)],[118])).
% 0.21/0.50 tff(120,plain,
% 0.21/0.50 (aNaturalNumber0(W0!2)),
% 0.21/0.50 inference(and_elim,[status(thm)],[118])).
% 0.21/0.50 tff(121,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xn)) | (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xn)) | (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(122,plain,
% 0.21/0.50 (((sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2))) <=> ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xn)) | (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(123,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xn)) | (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.50 tff(124,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xn)) | (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)))),
% 0.21/0.50 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.50 tff(125,plain,
% 0.21/0.50 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(126,plain,
% 0.21/0.50 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(xn)) | (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.50 tff(127,plain,
% 0.21/0.50 (sdtpldt0(W0!2, xn) = sdtpldt0(xn, W0!2)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[126, 107, 12, 120])).
% 0.21/0.50 tff(128,plain,
% 0.21/0.50 (sdtpldt0(W0!2, xn) = xm),
% 0.21/0.50 inference(transitivity,[status(thm)],[127, 119])).
% 0.21/0.50 tff(129,plain,
% 0.21/0.50 (sdtpldt0(W0!1, sdtpldt0(W0!2, xn)) = sdtpldt0(W0!1, xm)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.50 tff(130,plain,
% 0.21/0.50 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(131,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.50 tff(132,plain,
% 0.21/0.50 (^[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))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(133,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.50 tff(134,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(135,plain,
% 0.21/0.50 (^[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)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(136,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.50 tff(137,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddAsso')).
% 0.21/0.50 tff(138,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.50 tff(139,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.50 tff(140,plain,(
% 0.21/0.50 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[139])).
% 0.21/0.50 tff(141,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.21/0.50 tff(142,plain,
% 0.21/0.50 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.21/0.50 tff(143,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(144,plain,
% 0.21/0.50 (((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1))) <=> ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(145,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.50 tff(146,plain,
% 0.21/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.50 tff(147,plain,
% 0.21/0.50 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(148,plain,
% 0.21/0.50 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~aNaturalNumber0(xn)) | (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.50 tff(149,plain,
% 0.21/0.50 (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(W0!1, sdtpldt0(W0!2, xn))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[148, 142, 12, 46, 120])).
% 0.21/0.50 tff(150,plain,
% 0.21/0.50 (sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)),
% 0.21/0.50 inference(transitivity,[status(thm)],[149, 129, 114, 45, 94])).
% 0.21/0.50 tff(151,plain,
% 0.21/0.50 (((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00))) | (~(sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(152,plain,
% 0.21/0.51 ((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.21/0.51 tff(153,plain,
% 0.21/0.51 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(154,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[153])).
% 0.21/0.51 tff(155,plain,
% 0.21/0.51 (^[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(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(156,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.51 tff(157,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(158,plain,
% 0.21/0.51 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(159,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.51 tff(160,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB')).
% 0.21/0.51 tff(161,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.51 tff(162,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.21/0.51 tff(163,plain,(
% 0.21/0.51 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[162])).
% 0.21/0.51 tff(164,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.21/0.51 tff(165,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.21/0.51 tff(166,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(167,plain,
% 0.21/0.51 ((aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1))) <=> ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(168,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.51 tff(169,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[168, 166])).
% 0.21/0.51 tff(170,plain,
% 0.21/0.51 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(W0!1, W0!2)) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(171,plain,
% 0.21/0.51 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | aNaturalNumber0(sdtpldt0(W0!1, W0!2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.51 tff(172,plain,
% 0.21/0.51 (aNaturalNumber0(sdtpldt0(W0!1, W0!2))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[171, 165, 46, 120])).
% 0.21/0.51 tff(173,plain,
% 0.21/0.51 (^[W0: $i, W1: $i, W2: $i] : refl(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(174,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.51 tff(175,plain,
% 0.21/0.51 (^[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))))), (((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(176,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.51 tff(177,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(178,plain,
% 0.21/0.51 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), trans(monotonicity(rewrite(((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) <=> ((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))), ((((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)) <=> (((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))) => (W1 = W2)))), rewrite((((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))) => (W1 = W2)) <=> ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))), ((((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2)))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(179,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[178])).
% 0.21/0.51 tff(180,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddCanc')).
% 0.21/0.51 tff(181,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.21/0.51 tff(182,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.21/0.51 tff(183,plain,(
% 0.21/0.51 ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[182])).
% 0.21/0.51 tff(184,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.21/0.51 tff(185,plain,
% 0.21/0.51 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[184, 174])).
% 0.21/0.51 tff(186,plain,
% 0.21/0.51 (aNaturalNumber0(sz00) <=> aNaturalNumber0(sz00)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(187,axiom,(aNaturalNumber0(sz00)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsC')).
% 0.21/0.51 tff(188,plain,
% 0.21/0.51 (aNaturalNumber0(sz00)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.51 tff(189,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(190,plain,
% 0.21/0.51 (((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(191,plain,
% 0.21/0.51 ((~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) <=> (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(192,plain,
% 0.21/0.51 (((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn))) <=> ((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.51 tff(193,plain,
% 0.21/0.51 (((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.51 tff(194,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[193])).
% 0.21/0.51 tff(195,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[194, 189])).
% 0.21/0.51 tff(196,plain,
% 0.21/0.51 ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!1, W0!2) = sz00) | (~aNaturalNumber0(sz00)) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00)))) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (~aNaturalNumber0(xn)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(197,plain,
% 0.21/0.51 ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sz00)) | (~aNaturalNumber0(sdtpldt0(W0!1, W0!2))) | (sdtpldt0(W0!1, W0!2) = sz00) | (~((sdtpldt0(sdtpldt0(W0!1, W0!2), xn) = sdtpldt0(sz00, xn)) | (sdtpldt0(xn, sdtpldt0(W0!1, W0!2)) = sdtpldt0(xn, sz00))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.51 tff(198,plain,
% 0.21/0.51 (sdtpldt0(W0!1, W0!2) = sz00),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[197, 188, 185, 12, 172, 152])).
% 0.21/0.51 tff(199,plain,
% 0.21/0.51 (^[W0: $i, W1: $i] : refl(((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00))))) <=> ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(200,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[199])).
% 0.21/0.51 tff(201,plain,
% 0.21/0.51 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((W0 = sz00) & (W1 = sz00)) <=> (~((~(W1 = sz00)) | (~(W0 = sz00))))), 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))))), ((((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00))) <=> ((~((~(W1 = sz00)) | (~(W0 = sz00)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~(sdtpldt0(W0, W1) = sz00))))), rewrite(((~((~(W1 = sz00)) | (~(W0 = sz00)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~(sdtpldt0(W0, W1) = sz00))) <=> ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))), ((((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00))) <=> ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(202,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[201])).
% 0.21/0.51 tff(203,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00))) <=> ![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(204,plain,
% 0.21/0.51 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtpldt0(W0, W1) = sz00) => ((W0 = sz00) & (W1 = sz00))) <=> ((~(sdtpldt0(W0, W1) = sz00)) | ((W0 = sz00) & (W1 = sz00)))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtpldt0(W0, W1) = sz00) => ((W0 = sz00) & (W1 = sz00)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtpldt0(W0, W1) = sz00)) | ((W0 = sz00) & (W1 = sz00)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtpldt0(W0, W1) = sz00)) | ((W0 = sz00) & (W1 = sz00)))) <=> (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtpldt0(W0, W1) = sz00) => ((W0 = sz00) & (W1 = sz00)))) <=> (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(205,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtpldt0(W0, W1) = sz00) => ((W0 = sz00) & (W1 = sz00)))) <=> ![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.51 tff(206,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtpldt0(W0, W1) = sz00) => ((W0 = sz00) & (W1 = sz00))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mZeroAdd')).
% 0.21/0.51 tff(207,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.21/0.51 tff(208,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.21/0.51 tff(209,plain,(
% 0.21/0.51 ![W0: $i, W1: $i] : (((W0 = sz00) & (W1 = sz00)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtpldt0(W0, W1) = sz00)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[208])).
% 0.21/0.51 tff(210,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.21/0.51 tff(211,plain,
% 0.21/0.51 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[210, 200])).
% 0.21/0.51 tff(212,plain,
% 0.21/0.51 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(213,plain,
% 0.21/0.51 (((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00))))) <=> ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(214,plain,
% 0.21/0.51 ((~((~(W0!2 = sz00)) | (~(W0!1 = sz00)))) <=> (~((~(W0!1 = sz00)) | (~(W0!2 = sz00))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(215,plain,
% 0.21/0.51 (((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!2 = sz00)) | (~(W0!1 = sz00))))) <=> ((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[214])).
% 0.36/0.52 tff(216,plain,
% 0.36/0.52 (((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!2 = sz00)) | (~(W0!1 = sz00))))) <=> ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[215, 213])).
% 0.36/0.52 tff(217,plain,
% 0.36/0.52 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | ((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!2 = sz00)) | (~(W0!1 = sz00)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | ((~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00))))))),
% 0.36/0.52 inference(monotonicity,[status(thm)],[216])).
% 0.36/0.52 tff(218,plain,
% 0.36/0.52 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | ((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!2 = sz00)) | (~(W0!1 = sz00)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[217, 212])).
% 0.36/0.52 tff(219,plain,
% 0.36/0.52 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | ((~aNaturalNumber0(W0!2)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~aNaturalNumber0(W0!1)) | (~((~(W0!2 = sz00)) | (~(W0!1 = sz00)))))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(220,plain,
% 0.36/0.52 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~(sdtpldt0(W0, W1) = sz00)) | (~aNaturalNumber0(W0)) | (~((~(W1 = sz00)) | (~(W0 = sz00)))))) | (~aNaturalNumber0(W0!2)) | (~aNaturalNumber0(W0!1)) | (~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.36/0.52 tff(221,plain,
% 0.36/0.52 ((~(sdtpldt0(W0!1, W0!2) = sz00)) | (~((~(W0!1 = sz00)) | (~(W0!2 = sz00))))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[220, 211, 46, 120])).
% 0.36/0.52 tff(222,plain,
% 0.36/0.52 (~((~(W0!1 = sz00)) | (~(W0!2 = sz00)))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[221, 198])).
% 0.36/0.52 tff(223,plain,
% 0.36/0.52 (((~(W0!1 = sz00)) | (~(W0!2 = sz00))) | (W0!1 = sz00)),
% 0.36/0.52 inference(tautology,[status(thm)],[])).
% 0.36/0.52 tff(224,plain,
% 0.36/0.52 (W0!1 = sz00),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.36/0.52 tff(225,plain,
% 0.36/0.52 ($false),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[224, 88])).
% 0.36/0.52 % SZS output end Proof
% 0.36/0.52 % E exiting
%------------------------------------------------------------------------------