%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM012+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:00:58 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COM012+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 12:22:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(sdtmndtasgtdt0_type, type, (
% 0.12/0.37 sdtmndtasgtdt0: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(xy_type, type, (
% 0.12/0.37 xy: $i)).
% 0.12/0.37 tff(xR_type, type, (
% 0.12/0.37 xR: $i)).
% 0.12/0.37 tff(xx_type, type, (
% 0.12/0.37 xx: $i)).
% 0.12/0.37 tff(xz_type, type, (
% 0.12/0.37 xz: $i)).
% 0.12/0.37 tff(sdtmndtplgtdt0_type, type, (
% 0.12/0.37 sdtmndtplgtdt0: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(aReductOfIn0_type, type, (
% 0.12/0.37 aReductOfIn0: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(aElement0_type, type, (
% 0.12/0.37 aElement0: $i > $o)).
% 0.12/0.37 tff(aRewritingSystem0_type, type, (
% 0.12/0.37 aRewritingSystem0: $i > $o)).
% 0.12/0.37 tff(1,assumption,(sdtmndtplgtdt0(xy, xR, xz)), introduced(assumption)).
% 0.12/0.37 tff(2,assumption,(sdtmndtplgtdt0(xx, xR, xy)), introduced(assumption)).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~sdtmndtplgtdt0(xx, xR, xz)) <=> (~sdtmndtplgtdt0(xx, xR, xz))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~((((((xx = xy) | ((aReductOfIn0(xy, xx, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xx, xR)) & sdtmndtplgtdt0(W0, xR, xy))) & sdtmndtplgtdt0(xx, xR, xy))) & sdtmndtasgtdt0(xx, xR, xy)) & ((xy = xz) | ((aReductOfIn0(xz, xy, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xy, xR)) & sdtmndtplgtdt0(W0, xR, xz))) & sdtmndtplgtdt0(xy, xR, xz)))) & sdtmndtasgtdt0(xy, xR, xz)) => (((((xx = xz) | aReductOfIn0(xz, xx, xR)) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xx, xR)) & sdtmndtplgtdt0(W0, xR, xz))) | sdtmndtplgtdt0(xx, xR, xz)) | sdtmndtasgtdt0(xx, xR, xz)))) <=> (~((xx = xz) | aReductOfIn0(xz, xx, xR) | sdtmndtplgtdt0(xx, xR, xz) | sdtmndtasgtdt0(xx, xR, xz) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xx, xR) & sdtmndtplgtdt0(W0, xR, xz)) | (~(((xx = xy) | ((aReductOfIn0(xy, xx, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xx, xR) & sdtmndtplgtdt0(W0, xR, xy))) & sdtmndtplgtdt0(xx, xR, xy))) & sdtmndtasgtdt0(xx, xR, xy) & ((xy = xz) | ((aReductOfIn0(xz, xy, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xy, xR) & sdtmndtplgtdt0(W0, xR, xz))) & sdtmndtplgtdt0(xy, xR, xz))) & sdtmndtasgtdt0(xy, xR, xz)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(~((((((xx = xy) | ((aReductOfIn0(xy, xx, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xx, xR)) & sdtmndtplgtdt0(W0, xR, xy))) & sdtmndtplgtdt0(xx, xR, xy))) & sdtmndtasgtdt0(xx, xR, xy)) & ((xy = xz) | ((aReductOfIn0(xz, xy, xR) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xy, xR)) & sdtmndtplgtdt0(W0, xR, xz))) & sdtmndtplgtdt0(xy, xR, xz)))) & sdtmndtasgtdt0(xy, xR, xz)) => (((((xx = xz) | aReductOfIn0(xz, xx, xR)) | ?[W0: $i] : ((aElement0(W0) & aReductOfIn0(W0, xx, xR)) & sdtmndtplgtdt0(W0, xR, xz))) | sdtmndtplgtdt0(xx, xR, xz)) | sdtmndtasgtdt0(xx, xR, xz)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~((xx = xz) | aReductOfIn0(xz, xx, xR) | sdtmndtplgtdt0(xx, xR, xz) | sdtmndtasgtdt0(xx, xR, xz) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xx, xR) & sdtmndtplgtdt0(W0, xR, xz)) | (~(((xx = xy) | ((aReductOfIn0(xy, xx, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xx, xR) & sdtmndtplgtdt0(W0, xR, xy))) & sdtmndtplgtdt0(xx, xR, xy))) & sdtmndtasgtdt0(xx, xR, xy) & ((xy = xz) | ((aReductOfIn0(xz, xy, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xy, xR) & sdtmndtplgtdt0(W0, xR, xz))) & sdtmndtplgtdt0(xy, xR, xz))) & sdtmndtasgtdt0(xy, xR, xz))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~sdtmndtplgtdt0(xx, xR, xz)),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~sdtmndtplgtdt0(xx, xR, xz)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (aElement0(xz) <=> aElement0(xz)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(10,axiom,(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__349')).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (aElement0(xz)),
% 0.12/0.37 inference(and_elim,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (aElement0(xz)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (aElement0(xy) <=> aElement0(xy)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 ((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)),
% 0.12/0.38 inference(and_elim,[status(thm)],[10])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (aElement0(xy)),
% 0.12/0.38 inference(and_elim,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (aElement0(xy)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (aRewritingSystem0(xR) <=> aRewritingSystem0(xR)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (aElement0(xx) & aRewritingSystem0(xR)),
% 0.12/0.38 inference(and_elim,[status(thm)],[14])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (aRewritingSystem0(xR)),
% 0.12/0.38 inference(and_elim,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (aRewritingSystem0(xR)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (aElement0(xx) <=> aElement0(xx)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (aElement0(xx)),
% 0.12/0.38 inference(and_elim,[status(thm)],[18])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (aElement0(xx)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (^[W0: $i, W1: $i, W2: $i, W3: $i] : refl((sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite((sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3)) <=> (~((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3))))), ((~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) <=> (~(~((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3))))))), rewrite((~(~((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3))))) <=> ((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)))), ((~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) <=> ((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3))))), trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) <=> (~((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> (~(~((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> ((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))) <=> (sdtmndtplgtdt0(W0, W1, W3) | ((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3))) | ((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))))), rewrite((sdtmndtplgtdt0(W0, W1, W3) | ((~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3))) | ((~aElement0(W2)) | (~aElement0(W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) <=> (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))) <=> (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (^[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(((sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3)) => sdtmndtplgtdt0(W0, W1, W3)) <=> ((~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | sdtmndtplgtdt0(W0, W1, W3))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3)) => sdtmndtplgtdt0(W0, W1, W3))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | sdtmndtplgtdt0(W0, W1, W3))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | sdtmndtplgtdt0(W0, W1, W3))) <=> (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3)) => sdtmndtplgtdt0(W0, W1, W3))) <=> (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3)) => sdtmndtplgtdt0(W0, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.38 tff(31,axiom,(![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3)) => sdtmndtplgtdt0(W0, W1, W3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mTCTrans')).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.38 tff(34,plain,(
% 0.12/0.38 ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~(sdtmndtplgtdt0(W0, W1, W2) & sdtmndtplgtdt0(W2, W1, W3))) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[33])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (sdtmndtplgtdt0(xx, xR, xz) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (~aElement0(xz)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | sdtmndtplgtdt0(xx, xR, xz) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (~aElement0(xz)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((sdtmndtplgtdt0(xx, xR, xz) | (~aElement0(xy)) | (~aElement0(xz)) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aElement0(xx)) | (~aRewritingSystem0(xR))) <=> (sdtmndtplgtdt0(xx, xR, xz) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (~aElement0(xz)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (sdtmndtplgtdt0(xx, xR, xz) | (~aElement0(xy)) | (~aElement0(xz)) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aElement0(xx)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (sdtmndtplgtdt0(xx, xR, xz) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (~aElement0(xz))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (sdtmndtplgtdt0(xx, xR, xz) | (~aElement0(xy)) | (~aElement0(xz)) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aElement0(xx)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | sdtmndtplgtdt0(xx, xR, xz) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (~aElement0(xz)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[39, 37])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (sdtmndtplgtdt0(xx, xR, xz) | (~aElement0(xy)) | (~aElement0(xz)) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aElement0(xx)) | (~aRewritingSystem0(xR)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtplgtdt0(W0, W1, W3) | (~aElement0(W2)) | (~aElement0(W3)) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~sdtmndtplgtdt0(W2, W1, W3)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | sdtmndtplgtdt0(xx, xR, xz) | (~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz)) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (~aElement0(xz))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 36, 23, 20, 16, 12, 8, 2, 1])).
% 0.12/0.38 tff(44,plain,((~sdtmndtplgtdt0(xx, xR, xy)) | (~sdtmndtplgtdt0(xy, xR, xz))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (~sdtmndtplgtdt0(xx, xR, xy)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 1])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[W0: $i, W1: $i, W2: $i] : refl(((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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (^[W0: $i, W1: $i, W2: $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(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2))))))), rewrite((~(~((~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2))))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))), ((~(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)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))), (((~(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(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![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(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.38 tff(53,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/sandbox/benchmark/theBenchmark.p','mTCRDef')).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.38 tff(56,plain,(
% 0.12/0.38 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[55])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (((sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))) | (~aElement0(xx)) | (~aRewritingSystem0(xR)) | (~aElement0(xy))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))) | (~aElement0(xx)) | (~aRewritingSystem0(xR)) | (~aElement0(xy)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))) | (~aElement0(xx)) | (~aRewritingSystem0(xR)) | (~aElement0(xy)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[61, 59])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))) | (~aElement0(xx)) | (~aRewritingSystem0(xR)) | (~aElement0(xy)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | (~aRewritingSystem0(xR)) | (~aElement0(xx)) | (~aElement0(xy)) | (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 58, 23, 20, 16])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xx, xR, xy) <=> sdtmndtasgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (((xx = xy) | ((aReductOfIn0(xy, xx, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xx, xR) & sdtmndtplgtdt0(W0, xR, xy))) & sdtmndtplgtdt0(xx, xR, xy))) & sdtmndtasgtdt0(xx, xR, xy) & ((xy = xz) | ((aReductOfIn0(xz, xy, xR) | ?[W0: $i] : (aElement0(W0) & aReductOfIn0(W0, xy, xR) & sdtmndtplgtdt0(W0, xR, xz))) & sdtmndtplgtdt0(xy, xR, xz))) & sdtmndtasgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(or_elim,[status(thm)],[6])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(and_elim,[status(thm)],[67])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~(sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy)))) | (~sdtmndtasgtdt0(xx, xR, xy)) | ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~(sdtmndtasgtdt0(xx, xR, xy) <=> ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy)))) | ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~((xx = xy) | sdtmndtplgtdt0(xx, xR, xy))) | (xx = xy) | sdtmndtplgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((xx = xy) | sdtmndtplgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (xx = xy),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 45])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (sdtmndtplgtdt0(xx, xR, xz) <=> sdtmndtplgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[75])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (sdtmndtplgtdt0(xy, xR, xz) <=> sdtmndtplgtdt0(xx, xR, xz)),
% 0.12/0.39 inference(symmetry,[status(thm)],[76])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (sdtmndtplgtdt0(xx, xR, xz)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[1, 77])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 78])).
% 0.12/0.39 tff(80,plain,(~sdtmndtplgtdt0(xy, xR, xz)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xy)) | (~aElement0(xz)) | (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | (~aRewritingSystem0(xR)) | (~aElement0(xy)) | (~aElement0(xz)) | (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (((sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))) | (~aElement0(xy)) | (~aRewritingSystem0(xR)) | (~aElement0(xz))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(xy)) | (~aElement0(xz)) | (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))) | (~aElement0(xy)) | (~aRewritingSystem0(xR)) | (~aElement0(xz)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((~aRewritingSystem0(xR)) | (~aElement0(xy)) | (~aElement0(xz)) | (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[82])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))) | (~aElement0(xy)) | (~aRewritingSystem0(xR)) | (~aElement0(xz)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | (~aRewritingSystem0(xR)) | (~aElement0(xy)) | (~aElement0(xz)) | (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[83, 81])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | ((sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))) | (~aElement0(xy)) | (~aRewritingSystem0(xR)) | (~aElement0(xz)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~aElement0(W2)))) | (~aRewritingSystem0(xR)) | (~aElement0(xy)) | (~aElement0(xz)) | (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[86, 58, 20, 16, 12])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xy, xR, xz) <=> sdtmndtasgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(and_elim,[status(thm)],[67])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 ((~(sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz)))) | (~sdtmndtasgtdt0(xy, xR, xz)) | ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 ((~(sdtmndtasgtdt0(xy, xR, xz) <=> ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz)))) | ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[92, 87])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 ((~((xy = xz) | sdtmndtplgtdt0(xy, xR, xz))) | (xy = xz) | sdtmndtplgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 ((xy = xz) | sdtmndtplgtdt0(xy, xR, xz)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 (xy = xz),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[95, 80])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xx, xR, xy) <=> sdtmndtasgtdt0(xx, xR, xz)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[96])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (sdtmndtasgtdt0(xx, xR, xz) <=> sdtmndtasgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(symmetry,[status(thm)],[97])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 ((~sdtmndtasgtdt0(xx, xR, xz)) <=> (~sdtmndtasgtdt0(xx, xR, xy))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[98])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 ((~sdtmndtasgtdt0(xx, xR, xz)) <=> (~sdtmndtasgtdt0(xx, xR, xz))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (~sdtmndtasgtdt0(xx, xR, xz)),
% 0.12/0.39 inference(or_elim,[status(thm)],[6])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 (~sdtmndtasgtdt0(xx, xR, xz)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (~sdtmndtasgtdt0(xx, xR, xy)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[69, 103])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------