%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM021+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:00:59 AM UTC 2025
% Result : Theorem 0.67s 0.86s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM021+4 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:22:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.67/0.86 % SZS status Theorem
% 0.67/0.86 % SZS output start Proof
% 0.67/0.86 tff(aReductOfIn0_type, type, (
% 0.67/0.86 aReductOfIn0: ( $i * $i * $i ) > $o)).
% 0.67/0.86 tff(xR_type, type, (
% 0.67/0.86 xR: $i)).
% 0.67/0.86 tff(xd_type, type, (
% 0.67/0.86 xd: $i)).
% 0.67/0.86 tff(sdtmndtasgtdt0_type, type, (
% 0.67/0.86 sdtmndtasgtdt0: ( $i * $i * $i ) > $o)).
% 0.67/0.86 tff(xw_type, type, (
% 0.67/0.86 xw: $i)).
% 0.67/0.86 tff(aElement0_type, type, (
% 0.67/0.86 aElement0: $i > $o)).
% 0.67/0.86 tff(aNormalFormOfIn0_type, type, (
% 0.67/0.86 aNormalFormOfIn0: ( $i * $i * $i ) > $o)).
% 0.67/0.86 tff(tptp_fun_W3_10_type, type, (
% 0.67/0.86 tptp_fun_W3_10: ( $i * $i ) > $i)).
% 0.67/0.86 tff(sdtmndtplgtdt0_type, type, (
% 0.67/0.86 sdtmndtplgtdt0: ( $i * $i * $i ) > $o)).
% 0.67/0.86 tff(xu_type, type, (
% 0.67/0.86 xu: $i)).
% 0.67/0.86 tff(xv_type, type, (
% 0.67/0.86 xv: $i)).
% 0.67/0.86 tff(aRewritingSystem0_type, type, (
% 0.67/0.86 aRewritingSystem0: $i > $o)).
% 0.67/0.86 tff(xx_type, type, (
% 0.67/0.86 xx: $i)).
% 0.67/0.86 tff(tptp_fun_W0_23_type, type, (
% 0.67/0.86 tptp_fun_W0_23: $i)).
% 0.67/0.86 tff(xb_type, type, (
% 0.67/0.86 xb: $i)).
% 0.67/0.86 tff(xa_type, type, (
% 0.67/0.86 xa: $i)).
% 0.67/0.86 tff(xc_type, type, (
% 0.67/0.86 xc: $i)).
% 0.67/0.86 tff(1,plain,
% 0.67/0.86 (aElement0(xw) <=> aElement0(xw)),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(2,axiom,((((aElement0(xw) & ((xu = xw) | ((aReductOfIn0(xw, xu, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xu, xR)) & sdtmndtplgtdt0(W0, xR, xw))) & sdtmndtplgtdt0(xu, xR, xw)))) & sdtmndtasgtdt0(xu, xR, xw)) & ((xv = xw) | ((aReductOfIn0(xw, xv, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xv, xR)) & sdtmndtplgtdt0(W0, xR, xw))) & sdtmndtplgtdt0(xv, xR, xw)))) & sdtmndtasgtdt0(xv, xR, xw)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__799')).
% 0.67/0.86 tff(3,plain,
% 0.67/0.86 (((aElement0(xw) & ((xu = xw) | ((aReductOfIn0(xw, xu, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xu, xR)) & sdtmndtplgtdt0(W0, xR, xw))) & sdtmndtplgtdt0(xu, xR, xw)))) & sdtmndtasgtdt0(xu, xR, xw)) & ((xv = xw) | ((aReductOfIn0(xw, xv, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xv, xR)) & sdtmndtplgtdt0(W0, xR, xw))) & sdtmndtplgtdt0(xv, xR, xw)))),
% 0.67/0.86 inference(and_elim,[status(thm)],[2])).
% 0.67/0.86 tff(4,plain,
% 0.67/0.86 ((aElement0(xw) & ((xu = xw) | ((aReductOfIn0(xw, xu, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xu, xR)) & sdtmndtplgtdt0(W0, xR, xw))) & sdtmndtplgtdt0(xu, xR, xw)))) & sdtmndtasgtdt0(xu, xR, xw)),
% 0.67/0.86 inference(and_elim,[status(thm)],[3])).
% 0.67/0.86 tff(5,plain,
% 0.67/0.86 (aElement0(xw) & ((xu = xw) | ((aReductOfIn0(xw, xu, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xu, xR)) & sdtmndtplgtdt0(W0, xR, xw))) & sdtmndtplgtdt0(xu, xR, xw)))),
% 0.67/0.86 inference(and_elim,[status(thm)],[4])).
% 0.67/0.86 tff(6,plain,
% 0.67/0.86 (aElement0(xw)),
% 0.67/0.86 inference(and_elim,[status(thm)],[5])).
% 0.67/0.86 tff(7,plain,
% 0.67/0.86 (aElement0(xw)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.67/0.86 tff(8,plain,
% 0.67/0.86 (aRewritingSystem0(xR) <=> aRewritingSystem0(xR)),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(9,axiom,(aRewritingSystem0(xR)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__656')).
% 0.67/0.86 tff(10,plain,
% 0.67/0.86 (aRewritingSystem0(xR)),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.67/0.86 tff(11,plain,
% 0.67/0.86 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))))))))), rewrite(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(12,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[11])).
% 0.67/0.86 tff(13,plain,
% 0.67/0.86 (^[W0: $i, W1: $i] : refl(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(14,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[13])).
% 0.67/0.86 tff(15,plain,
% 0.67/0.86 (^[W0: $i, W1: $i] : rewrite(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(16,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[15])).
% 0.67/0.86 tff(17,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.67/0.86 inference(transitivity,[status(thm)],[16, 14])).
% 0.67/0.86 tff(18,plain,
% 0.67/0.86 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1)) <=> (~((~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> (~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) <=> ((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))), rewrite((aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)) <=> (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))), ((((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))), rewrite((((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))), ((((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))), (![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> (((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))), rewrite((((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(19,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[18])).
% 0.67/0.86 tff(20,plain,
% 0.67/0.86 (^[W0: $i, W1: $i] : rewrite(((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(21,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[20])).
% 0.67/0.86 tff(22,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(23,plain,
% 0.67/0.86 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))) <=> (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))) <=> ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))))),
% 0.67/0.86 inference(bind,[status(th)],[])).
% 0.67/0.86 tff(24,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.67/0.86 inference(quant_intro,[status(thm)],[23])).
% 0.67/0.86 tff(25,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mNFRDef')).
% 0.67/0.86 tff(26,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.67/0.86 tff(27,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.67/0.86 tff(28,plain,(
% 0.67/0.86 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))),
% 0.67/0.86 inference(skolemize,[status(sab)],[27])).
% 0.67/0.86 tff(29,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.67/0.86 tff(30,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.67/0.86 tff(31,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.67/0.86 tff(32,plain,
% 0.67/0.86 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[31, 12])).
% 0.67/0.86 tff(33,plain,
% 0.67/0.86 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(34,plain,
% 0.67/0.87 (((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(35,plain,
% 0.67/0.87 (^[W2: $i] : rewrite((~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(36,plain,
% 0.67/0.87 (![W2: $i] : (~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[35])).
% 0.67/0.87 tff(37,plain,
% 0.67/0.87 (((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[36])).
% 0.67/0.87 tff(38,plain,
% 0.67/0.87 (((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[37, 34])).
% 0.67/0.87 tff(39,plain,
% 0.67/0.87 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[38])).
% 0.67/0.87 tff(40,plain,
% 0.67/0.87 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[39, 33])).
% 0.67/0.87 tff(41,plain,
% 0.67/0.87 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, xw, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(42,plain,
% 0.67/0.87 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(xw)) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.67/0.87 tff(43,plain,
% 0.67/0.87 (![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[42, 32, 10, 7])).
% 0.67/0.87 tff(44,plain,
% 0.67/0.87 (((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(45,plain,
% 0.67/0.87 ((~((~((~aElement0(xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR) | aNormalFormOfIn0(xd, xw, xR) | (~sdtmndtasgtdt0(xw, xR, xd)))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))))) <=> (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(46,plain,
% 0.67/0.87 (((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR) | aNormalFormOfIn0(xd, xw, xR) | (~sdtmndtasgtdt0(xw, xR, xd)))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[45])).
% 0.67/0.87 tff(47,plain,
% 0.67/0.87 (((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR) | aNormalFormOfIn0(xd, xw, xR) | (~sdtmndtasgtdt0(xw, xR, xd)))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[46, 44])).
% 0.67/0.87 tff(48,plain,
% 0.67/0.87 ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR) | aNormalFormOfIn0(xd, xw, xR) | (~sdtmndtasgtdt0(xw, xR, xd)))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(49,plain,
% 0.67/0.87 ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, xw, xR) | (~sdtmndtasgtdt0(xw, xR, W2)))) | (~((~aNormalFormOfIn0(W2, xw, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(xw, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.67/0.87 tff(50,plain,
% 0.67/0.87 (~((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.67/0.87 tff(51,plain,
% 0.67/0.87 (((~(aNormalFormOfIn0(xd, xw, xR) | (~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | aReductOfIn0(tptp_fun_W3_10(xd, xR), xd, xR))) | (~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))))) | ((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))),
% 0.67/0.87 inference(tautology,[status(thm)],[])).
% 0.67/0.87 tff(52,plain,
% 0.67/0.87 ((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.67/0.87 tff(53,plain,
% 0.67/0.87 (aNormalFormOfIn0(xd, xw, xR) <=> aNormalFormOfIn0(xd, xw, xR)),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(54,axiom,((((aElement0(xd) & ((xw = xd) | ((aReductOfIn0(xd, xw, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xw, xR)) & sdtmndtplgtdt0(W0, xR, xd))) & sdtmndtplgtdt0(xw, xR, xd)))) & sdtmndtasgtdt0(xw, xR, xd)) & (~?[W0: $i] : aReductOfIn0(W0, xd, xR))) & aNormalFormOfIn0(xd, xw, xR)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__818')).
% 0.67/0.87 tff(55,plain,
% 0.67/0.87 (aNormalFormOfIn0(xd, xw, xR)),
% 0.67/0.87 inference(and_elim,[status(thm)],[54])).
% 0.67/0.87 tff(56,plain,
% 0.67/0.87 (aNormalFormOfIn0(xd, xw, xR)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.67/0.87 tff(57,plain,
% 0.67/0.87 ((~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))) | (~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))),
% 0.67/0.87 inference(tautology,[status(thm)],[])).
% 0.67/0.87 tff(58,plain,
% 0.67/0.87 ((~((~aNormalFormOfIn0(xd, xw, xR)) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))))) | (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.67/0.87 tff(59,plain,
% 0.67/0.87 (~((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR))))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.67/0.87 tff(60,plain,
% 0.67/0.87 (((~aElement0(xd)) | (~sdtmndtasgtdt0(xw, xR, xd)) | (~![W3: $i] : (~aReductOfIn0(W3, xd, xR)))) | ![W3: $i] : (~aReductOfIn0(W3, xd, xR))),
% 0.67/0.87 inference(tautology,[status(thm)],[])).
% 0.67/0.87 tff(61,plain,
% 0.67/0.87 (![W3: $i] : (~aReductOfIn0(W3, xd, xR))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.67/0.87 tff(62,assumption,(aReductOfIn0(W0!23, xd, xR)), introduced(assumption)).
% 0.67/0.87 tff(63,plain,
% 0.67/0.87 ((~![W3: $i] : (~aReductOfIn0(W3, xd, xR))) | (~aReductOfIn0(W0!23, xd, xR))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(64,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[63, 62, 61])).
% 0.67/0.87 tff(65,plain,(~aReductOfIn0(W0!23, xd, xR)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(66,plain,
% 0.67/0.87 (((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx))) | aReductOfIn0(W0!23, xd, xR)),
% 0.67/0.87 inference(tautology,[status(thm)],[])).
% 0.67/0.87 tff(67,plain,
% 0.67/0.87 ((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.67/0.87 tff(68,plain,
% 0.67/0.87 ((xx = xd) <=> (xd = xx)),
% 0.67/0.87 inference(commutativity,[status(thm)],[])).
% 0.67/0.87 tff(69,plain,
% 0.67/0.87 ((~(xx = xd)) <=> (~(xd = xx))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[68])).
% 0.67/0.87 tff(70,plain,
% 0.67/0.87 (aElement0(xx) <=> aElement0(xx)),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(71,axiom,((((aElement0(xx) & ((xb = xx) | ((aReductOfIn0(xx, xb, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xb, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xb, xR, xx)))) & sdtmndtasgtdt0(xb, xR, xx)) & ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xd, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)))) & sdtmndtasgtdt0(xd, xR, xx)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__850')).
% 0.67/0.87 tff(72,plain,
% 0.67/0.87 (((aElement0(xx) & ((xb = xx) | ((aReductOfIn0(xx, xb, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xb, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xb, xR, xx)))) & sdtmndtasgtdt0(xb, xR, xx)) & ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xd, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)))),
% 0.67/0.87 inference(and_elim,[status(thm)],[71])).
% 0.67/0.87 tff(73,plain,
% 0.67/0.87 ((aElement0(xx) & ((xb = xx) | ((aReductOfIn0(xx, xb, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xb, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xb, xR, xx)))) & sdtmndtasgtdt0(xb, xR, xx)),
% 0.67/0.87 inference(and_elim,[status(thm)],[72])).
% 0.67/0.87 tff(74,plain,
% 0.67/0.87 (aElement0(xx) & ((xb = xx) | ((aReductOfIn0(xx, xb, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xb, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xb, xR, xx)))),
% 0.67/0.87 inference(and_elim,[status(thm)],[73])).
% 0.67/0.87 tff(75,plain,
% 0.67/0.87 (aElement0(xx)),
% 0.67/0.87 inference(and_elim,[status(thm)],[74])).
% 0.67/0.87 tff(76,plain,
% 0.67/0.87 (aElement0(xx)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.67/0.87 tff(77,plain,
% 0.67/0.87 (aElement0(xd) <=> aElement0(xd)),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(78,plain,
% 0.67/0.87 (((aElement0(xd) & ((xw = xd) | ((aReductOfIn0(xd, xw, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xw, xR)) & sdtmndtplgtdt0(W0, xR, xd))) & sdtmndtplgtdt0(xw, xR, xd)))) & sdtmndtasgtdt0(xw, xR, xd)) & (~?[W0: $i] : aReductOfIn0(W0, xd, xR))),
% 0.67/0.87 inference(and_elim,[status(thm)],[54])).
% 0.67/0.87 tff(79,plain,
% 0.67/0.87 ((aElement0(xd) & ((xw = xd) | ((aReductOfIn0(xd, xw, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xw, xR)) & sdtmndtplgtdt0(W0, xR, xd))) & sdtmndtplgtdt0(xw, xR, xd)))) & sdtmndtasgtdt0(xw, xR, xd)),
% 0.67/0.87 inference(and_elim,[status(thm)],[78])).
% 0.67/0.87 tff(80,plain,
% 0.67/0.87 (aElement0(xd) & ((xw = xd) | ((aReductOfIn0(xd, xw, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xw, xR)) & sdtmndtplgtdt0(W0, xR, xd))) & sdtmndtplgtdt0(xw, xR, xd)))),
% 0.67/0.87 inference(and_elim,[status(thm)],[79])).
% 0.67/0.87 tff(81,plain,
% 0.67/0.87 (aElement0(xd)),
% 0.67/0.87 inference(and_elim,[status(thm)],[80])).
% 0.67/0.87 tff(82,plain,
% 0.67/0.87 (aElement0(xd)),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.67/0.87 tff(83,plain,
% 0.67/0.87 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(84,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[83])).
% 0.67/0.87 tff(85,plain,
% 0.67/0.87 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(86,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[85])).
% 0.67/0.87 tff(87,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(88,plain,
% 0.67/0.87 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))))),
% 0.67/0.87 inference(bind,[status(th)],[])).
% 0.67/0.87 tff(89,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.67/0.87 inference(quant_intro,[status(thm)],[88])).
% 0.67/0.87 tff(90,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mTCRDef')).
% 0.67/0.87 tff(91,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.67/0.87 tff(92,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.67/0.87 tff(93,plain,(
% 0.67/0.87 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.67/0.87 inference(skolemize,[status(sab)],[92])).
% 0.67/0.87 tff(94,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.67/0.87 tff(95,plain,
% 0.67/0.87 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.67/0.87 tff(96,plain,
% 0.67/0.87 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xd)) | (~aElement0(xx)) | (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aRewritingSystem0(xR)) | (~aElement0(xd)) | (~aElement0(xx)) | (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(97,plain,
% 0.67/0.87 (((sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))) | (~aElement0(xd)) | (~aElement0(xx)) | (~aRewritingSystem0(xR))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xd)) | (~aElement0(xx)) | (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(98,plain,
% 0.67/0.87 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))) | (~aElement0(xd)) | (~aElement0(xx)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xd)) | (~aElement0(xx)) | (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[97])).
% 0.67/0.87 tff(99,plain,
% 0.67/0.87 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))) | (~aElement0(xd)) | (~aElement0(xx)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aRewritingSystem0(xR)) | (~aElement0(xd)) | (~aElement0(xx)) | (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[98, 96])).
% 0.67/0.88 tff(100,plain,
% 0.67/0.88 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))) | (~aElement0(xd)) | (~aElement0(xx)) | (~aRewritingSystem0(xR)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(101,plain,
% 0.67/0.88 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aRewritingSystem0(xR)) | (~aElement0(xd)) | (~aElement0(xx)) | (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.67/0.88 tff(102,plain,
% 0.67/0.88 (sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[101, 95, 10, 82, 76])).
% 0.67/0.88 tff(103,plain,
% 0.67/0.88 ((~sdtmndtasgtdt0(xb, xR, xd)) <=> (~sdtmndtasgtdt0(xb, xR, xd))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(104,axiom,(~(((((xb = xd) | aReductOfIn0(xd, xb, xR)) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xb, xR)) & sdtmndtplgtdt0(W0, xR, xd))) | sdtmndtplgtdt0(xb, xR, xd)) | sdtmndtasgtdt0(xb, xR, xd))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.67/0.88 tff(105,plain,
% 0.67/0.88 (~sdtmndtasgtdt0(xb, xR, xd)),
% 0.67/0.88 inference(or_elim,[status(thm)],[104])).
% 0.67/0.88 tff(106,plain,
% 0.67/0.88 (~sdtmndtasgtdt0(xb, xR, xd)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[105, 103])).
% 0.67/0.88 tff(107,plain,
% 0.67/0.88 (sdtmndtasgtdt0(xb, xR, xx) <=> sdtmndtasgtdt0(xb, xR, xx)),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(108,plain,
% 0.67/0.88 (sdtmndtasgtdt0(xb, xR, xx)),
% 0.67/0.88 inference(and_elim,[status(thm)],[73])).
% 0.67/0.88 tff(109,plain,
% 0.67/0.88 (sdtmndtasgtdt0(xb, xR, xx)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.67/0.88 tff(110,plain,
% 0.67/0.88 (aElement0(xb) <=> aElement0(xb)),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(111,axiom,((aElement0(xa) & aElement0(xb)) & aElement0(xc)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__731')).
% 0.67/0.88 tff(112,plain,
% 0.67/0.88 (aElement0(xa) & aElement0(xb)),
% 0.67/0.88 inference(and_elim,[status(thm)],[111])).
% 0.67/0.88 tff(113,plain,
% 0.67/0.88 (aElement0(xb)),
% 0.67/0.88 inference(and_elim,[status(thm)],[112])).
% 0.67/0.88 tff(114,plain,
% 0.67/0.88 (aElement0(xb)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.67/0.88 tff(115,plain,
% 0.67/0.88 (^[W0: $i, W1: $i, W2: $i, W3: $i] : refl((sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(116,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[115])).
% 0.67/0.88 tff(117,plain,
% 0.67/0.88 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) <=> (~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> (~(~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), trans(monotonicity(rewrite((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) <=> (~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))), ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) <=> (~(~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))))), rewrite((~(~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))) <=> ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))), ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) <=> ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))), ((sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))))), rewrite((sdtmndtasgtdt0(W0, W1, W3) | ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))), ((sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(118,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[117])).
% 0.67/0.88 tff(119,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(120,plain,
% 0.67/0.88 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) & aElement0(W3)))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) & aElement0(W3)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))), rewrite(((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3)) <=> ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))))),
% 0.67/0.88 inference(bind,[status(th)],[])).
% 0.67/0.88 tff(121,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.67/0.88 inference(quant_intro,[status(thm)],[120])).
% 0.67/0.88 tff(122,axiom,(![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mTCRTrans')).
% 0.67/0.88 tff(123,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.67/0.88 tff(124,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.67/0.88 tff(125,plain,(
% 0.67/0.88 ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.67/0.88 inference(skolemize,[status(sab)],[124])).
% 0.67/0.88 tff(126,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.67/0.88 tff(127,plain,
% 0.67/0.88 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.67/0.88 tff(128,plain,
% 0.67/0.88 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, xd) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xd)) | (~aElement0(xx)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | sdtmndtasgtdt0(xb, xR, xd) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xd)) | (~aElement0(xx)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(129,plain,
% 0.67/0.88 ((sdtmndtasgtdt0(xb, xR, xd) | (~aElement0(xd)) | (~aElement0(xx)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd))) <=> (sdtmndtasgtdt0(xb, xR, xd) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xd)) | (~aElement0(xx)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(130,plain,
% 0.67/0.88 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, xd) | (~aElement0(xd)) | (~aElement0(xx)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, xd) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xd)) | (~aElement0(xx)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[129])).
% 0.67/0.88 tff(131,plain,
% 0.67/0.88 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, xd) | (~aElement0(xd)) | (~aElement0(xx)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | sdtmndtasgtdt0(xb, xR, xd) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xd)) | (~aElement0(xx)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(transitivity,[status(thm)],[130, 128])).
% 0.67/0.88 tff(132,plain,
% 0.67/0.88 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(xb, xR, xd) | (~aElement0(xd)) | (~aElement0(xx)) | (~aElement0(xb)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(quant_inst,[status(thm)],[])).
% 0.67/0.88 tff(133,plain,
% 0.67/0.88 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | sdtmndtasgtdt0(xb, xR, xd) | (~aRewritingSystem0(xR)) | (~aElement0(xb)) | (~aElement0(xd)) | (~aElement0(xx)) | (~sdtmndtasgtdt0(xb, xR, xx)) | (~sdtmndtasgtdt0(xx, xR, xd))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.67/0.88 tff(134,plain,
% 0.67/0.88 (~sdtmndtasgtdt0(xx, xR, xd)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[133, 127, 10, 114, 82, 76, 109, 106])).
% 0.67/0.88 tff(135,plain,
% 0.67/0.88 ((~(sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)))) | sdtmndtasgtdt0(xx, xR, xd) | (~((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(tautology,[status(thm)],[])).
% 0.67/0.88 tff(136,plain,
% 0.67/0.88 ((~(sdtmndtasgtdt0(xx, xR, xd) <=> ((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)))) | (~((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.67/0.88 tff(137,plain,
% 0.67/0.88 (~((xx = xd) | sdtmndtplgtdt0(xx, xR, xd))),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[136, 102])).
% 0.67/0.88 tff(138,plain,
% 0.67/0.88 (((xx = xd) | sdtmndtplgtdt0(xx, xR, xd)) | (~(xx = xd))),
% 0.67/0.88 inference(tautology,[status(thm)],[])).
% 0.67/0.88 tff(139,plain,
% 0.67/0.88 (~(xx = xd)),
% 0.67/0.88 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.67/0.88 tff(140,plain,
% 0.67/0.88 (~(xd = xx)),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[139, 69])).
% 0.67/0.88 tff(141,plain,
% 0.67/0.88 (((xd = xx) | (~((~(aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))) | (~sdtmndtplgtdt0(xd, xR, xx))))) <=> ((xd = xx) | (~((~(aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))) | (~sdtmndtplgtdt0(xd, xR, xx)))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(142,plain,
% 0.67/0.88 (((aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx))))) & sdtmndtplgtdt0(xd, xR, xx)) <=> (~((~(aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))) | (~sdtmndtplgtdt0(xd, xR, xx))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(143,plain,
% 0.67/0.88 ((aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx))))) <=> (aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(144,plain,
% 0.67/0.88 ((aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx)) <=> (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx))))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(145,plain,
% 0.67/0.88 ((aReductOfIn0(xx, xd, xR) | (aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx))) <=> (aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[144])).
% 0.67/0.88 tff(146,plain,
% 0.67/0.88 ((aReductOfIn0(xx, xd, xR) | (aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx))) <=> (aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[145, 143])).
% 0.67/0.88 tff(147,plain,
% 0.67/0.88 (((aReductOfIn0(xx, xd, xR) | (aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)) <=> ((aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx))))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[146])).
% 0.67/0.88 tff(148,plain,
% 0.67/0.88 (((aReductOfIn0(xx, xd, xR) | (aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)) <=> (~((~(aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))) | (~sdtmndtplgtdt0(xd, xR, xx))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[147, 142])).
% 0.67/0.88 tff(149,plain,
% 0.67/0.88 (((xd = xx) | ((aReductOfIn0(xx, xd, xR) | (aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))) <=> ((xd = xx) | (~((~(aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))) | (~sdtmndtplgtdt0(xd, xR, xx)))))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[148])).
% 0.67/0.88 tff(150,plain,
% 0.67/0.88 (((xd = xx) | ((aReductOfIn0(xx, xd, xR) | (aElement0(W0!23) & aReductOfIn0(W0!23, xd, xR) & sdtmndtplgtdt0(W0!23, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))) <=> ((xd = xx) | (~((~(aReductOfIn0(xx, xd, xR) | (~((~aElement0(W0!23)) | (~aReductOfIn0(W0!23, xd, xR)) | (~sdtmndtplgtdt0(W0!23, xR, xx)))))) | (~sdtmndtplgtdt0(xd, xR, xx)))))),
% 0.67/0.88 inference(transitivity,[status(thm)],[149, 141])).
% 0.67/0.88 tff(151,plain,
% 0.67/0.88 ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) <=> (aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(152,plain,
% 0.67/0.88 (((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)) <=> ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[151])).
% 0.67/0.88 tff(153,plain,
% 0.67/0.88 (((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))) <=> ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)))),
% 0.67/0.88 inference(monotonicity,[status(thm)],[152])).
% 0.67/0.88 tff(154,plain,
% 0.67/0.88 (((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))) <=> ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(155,plain,
% 0.67/0.88 (((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xd, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))) <=> ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx)))),
% 0.67/0.88 inference(rewrite,[status(thm)],[])).
% 0.67/0.88 tff(156,plain,
% 0.67/0.88 ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xd, xR)) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(and_elim,[status(thm)],[72])).
% 0.67/0.88 tff(157,plain,
% 0.67/0.88 ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.67/0.88 tff(158,plain,
% 0.67/0.88 ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.67/0.88 tff(159,plain,
% 0.67/0.88 ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.67/0.88 tff(160,plain,
% 0.67/0.88 ((xd = xx) | ((aReductOfIn0(xx, xd, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xd, xR) & sdtmndtplgtdt0(W0, xR, xx))) & sdtmndtplgtdt0(xd, xR, xx))),
% 0.67/0.88 inference(modus_ponens,[status(thm)],[159, 153])).
% 0.67/0.88 Proof display could not be completed: monotonicity rule is not handled
% 0.67/0.89 % E exiting
%------------------------------------------------------------------------------