TSTP Solution File: COM018+1 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n009.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 : Wed Mar 6 08:54:00 EST 2024
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM018+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n009.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 : Mon Mar 4 11:25:02 EST 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start Proof for theBenchmark
% 0.12/0.35
% 0.12/0.35 % Formula: mElmSort ( axiom ) converted to clauses:
% 0.12/0.35
% 0.12/0.35 % Formula: mRelSort ( axiom ) converted to clauses:
% 0.12/0.35
% 0.12/0.35 % Formula: mReduct ( axiom ) converted to clauses:
% 0.12/0.35 cnf(mReduct-1, axiom, ( ~aElement0(_u4) | ~aRewritingSystem0(_u3) | ~aReductOfIn0(_u2, _u4, _u3) | aElement0(_u2) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mWFOrd ( axiom ) converted to clauses:
% 0.12/0.35
% 0.12/0.35 % Formula: mTCbr ( axiom ) converted to clauses:
% 0.12/0.35
% 0.12/0.35 % Formula: mTCDef ( definition ) converted to clauses:
% 0.12/0.35 cnf(mTCDef-1, definition, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | ~sdtmndtplgtdt0(_u14, _u13, _u12) | aReductOfIn0(_u12, _u14, _u13) | aElement0(skolem1(_u14, _u13, _u12)) )).
% 0.12/0.35 cnf(mTCDef-2, definition, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | ~sdtmndtplgtdt0(_u14, _u13, _u12) | aReductOfIn0(_u12, _u14, _u13) | aReductOfIn0(skolem1(_u14, _u13, _u12), _u14, _u13) )).
% 0.12/0.35 cnf(mTCDef-3, definition, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | ~sdtmndtplgtdt0(_u14, _u13, _u12) | aReductOfIn0(_u12, _u14, _u13) | sdtmndtplgtdt0(skolem1(_u14, _u13, _u12), _u13, _u12) )).
% 0.12/0.35 cnf(mTCDef-4, definition, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | sdtmndtplgtdt0(_u14, _u13, _u12) | ~aReductOfIn0(_u12, _u14, _u13) )).
% 0.12/0.35 cnf(mTCDef-5, definition, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | sdtmndtplgtdt0(_u14, _u13, _u12) | ~aElement0(_u11) | ~aReductOfIn0(_u11, _u14, _u13) | ~sdtmndtplgtdt0(_u11, _u13, _u12) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mTCTrans ( axiom ) converted to clauses:
% 0.12/0.35 cnf(mTCTrans-1, axiom, ( ~aElement0(_u18) | ~aRewritingSystem0(_u17) | ~aElement0(_u16) | ~aElement0(_u15) | ~sdtmndtplgtdt0(_u18, _u17, _u16) | ~sdtmndtplgtdt0(_u16, _u17, _u15) | sdtmndtplgtdt0(_u18, _u17, _u15) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mTCRDef ( definition ) converted to clauses:
% 0.12/0.35 cnf(mTCRDef-1, definition, ( ~aElement0(_u21) | ~aRewritingSystem0(_u20) | ~aElement0(_u19) | ~sdtmndtasgtdt0(_u21, _u20, _u19) | ( _u21 = _u19) | sdtmndtplgtdt0(_u21, _u20, _u19) )).
% 0.12/0.35 cnf(mTCRDef-2, definition, ( ~aElement0(_u21) | ~aRewritingSystem0(_u20) | ~aElement0(_u19) | sdtmndtasgtdt0(_u21, _u20, _u19) | ( _u21 != _u19) )).
% 0.12/0.35 cnf(mTCRDef-3, definition, ( ~aElement0(_u21) | ~aRewritingSystem0(_u20) | ~aElement0(_u19) | sdtmndtasgtdt0(_u21, _u20, _u19) | ~sdtmndtplgtdt0(_u21, _u20, _u19) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mTCRTrans ( axiom ) converted to clauses:
% 0.12/0.35 cnf(mTCRTrans-1, axiom, ( ~aElement0(_u25) | ~aRewritingSystem0(_u24) | ~aElement0(_u23) | ~aElement0(_u22) | ~sdtmndtasgtdt0(_u25, _u24, _u23) | ~sdtmndtasgtdt0(_u23, _u24, _u22) | sdtmndtasgtdt0(_u25, _u24, _u22) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mCRDef ( definition ) converted to clauses:
% 0.12/0.35 cnf(mCRDef-1, definition, ( ~aRewritingSystem0(_u34) | ~isConfluent0(_u34) | ~aElement0(_u29) | ~aElement0(_u28) | ~aElement0(_u27) | ~sdtmndtasgtdt0(_u29, _u34, _u28) | ~sdtmndtasgtdt0(_u29, _u34, _u27) | aElement0(skolem2(_u34, _u29, _u28, _u27)) )).
% 0.12/0.35 cnf(mCRDef-2, definition, ( ~aRewritingSystem0(_u34) | ~isConfluent0(_u34) | ~aElement0(_u29) | ~aElement0(_u28) | ~aElement0(_u27) | ~sdtmndtasgtdt0(_u29, _u34, _u28) | ~sdtmndtasgtdt0(_u29, _u34, _u27) | sdtmndtasgtdt0(_u28, _u34, skolem2(_u34, _u29, _u28, _u27)) )).
% 0.12/0.35 cnf(mCRDef-3, definition, ( ~aRewritingSystem0(_u34) | ~isConfluent0(_u34) | ~aElement0(_u29) | ~aElement0(_u28) | ~aElement0(_u27) | ~sdtmndtasgtdt0(_u29, _u34, _u28) | ~sdtmndtasgtdt0(_u29, _u34, _u27) | sdtmndtasgtdt0(_u27, _u34, skolem2(_u34, _u29, _u28, _u27)) )).
% 0.12/0.35 cnf(mCRDef-4, definition, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | aElement0(skolem3(_u34)) )).
% 0.12/0.35 cnf(mCRDef-5, definition, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | aElement0(skolem4(_u34)) )).
% 0.12/0.35 cnf(mCRDef-6, definition, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | aElement0(skolem5(_u34)) )).
% 0.12/0.35 cnf(mCRDef-7, definition, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | sdtmndtasgtdt0(skolem3(_u34), _u34, skolem4(_u34)) )).
% 0.12/0.35 cnf(mCRDef-8, definition, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | sdtmndtasgtdt0(skolem3(_u34), _u34, skolem5(_u34)) )).
% 0.12/0.35 cnf(mCRDef-9, definition, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | ~aElement0(_u30) | ~sdtmndtasgtdt0(skolem4(_u34), _u34, _u30) | ~sdtmndtasgtdt0(skolem5(_u34), _u34, _u30) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mWCRDef ( definition ) converted to clauses:
% 0.12/0.35 cnf(mWCRDef-1, definition, ( ~aRewritingSystem0(_u43) | ~isLocallyConfluent0(_u43) | ~aElement0(_u38) | ~aElement0(_u37) | ~aElement0(_u36) | ~aReductOfIn0(_u37, _u38, _u43) | ~aReductOfIn0(_u36, _u38, _u43) | aElement0(skolem6(_u43, _u38, _u37, _u36)) )).
% 0.12/0.35 cnf(mWCRDef-2, definition, ( ~aRewritingSystem0(_u43) | ~isLocallyConfluent0(_u43) | ~aElement0(_u38) | ~aElement0(_u37) | ~aElement0(_u36) | ~aReductOfIn0(_u37, _u38, _u43) | ~aReductOfIn0(_u36, _u38, _u43) | sdtmndtasgtdt0(_u37, _u43, skolem6(_u43, _u38, _u37, _u36)) )).
% 0.12/0.35 cnf(mWCRDef-3, definition, ( ~aRewritingSystem0(_u43) | ~isLocallyConfluent0(_u43) | ~aElement0(_u38) | ~aElement0(_u37) | ~aElement0(_u36) | ~aReductOfIn0(_u37, _u38, _u43) | ~aReductOfIn0(_u36, _u38, _u43) | sdtmndtasgtdt0(_u36, _u43, skolem6(_u43, _u38, _u37, _u36)) )).
% 0.12/0.35 cnf(mWCRDef-4, definition, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aElement0(skolem7(_u43)) )).
% 0.12/0.35 cnf(mWCRDef-5, definition, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aElement0(skolem8(_u43)) )).
% 0.12/0.35 cnf(mWCRDef-6, definition, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aElement0(skolem9(_u43)) )).
% 0.12/0.35 cnf(mWCRDef-7, definition, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aReductOfIn0(skolem8(_u43), skolem7(_u43), _u43) )).
% 0.12/0.35 cnf(mWCRDef-8, definition, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aReductOfIn0(skolem9(_u43), skolem7(_u43), _u43) )).
% 0.12/0.35 cnf(mWCRDef-9, definition, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | ~aElement0(_u39) | ~sdtmndtasgtdt0(skolem8(_u43), _u43, _u39) | ~sdtmndtasgtdt0(skolem9(_u43), _u43, _u39) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mTermin ( definition ) converted to clauses:
% 0.12/0.35 cnf(mTermin-1, definition, ( ~aRewritingSystem0(_u48) | ~isTerminating0(_u48) | ~aElement0(_u45) | ~aElement0(_u44) | ~sdtmndtplgtdt0(_u45, _u48, _u44) | iLess0(_u44, _u45) )).
% 0.12/0.35 cnf(mTermin-2, definition, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | aElement0(skolem10(_u48)) )).
% 0.12/0.35 cnf(mTermin-3, definition, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | aElement0(skolem11(_u48)) )).
% 0.12/0.35 cnf(mTermin-4, definition, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | sdtmndtplgtdt0(skolem10(_u48), _u48, skolem11(_u48)) )).
% 0.12/0.35 cnf(mTermin-5, definition, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | ~iLess0(skolem11(_u48), skolem10(_u48)) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mNFRDef ( definition ) converted to clauses:
% 0.12/0.35 cnf(mNFRDef-1, definition, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aNormalFormOfIn0(_u54, _u53, _u52) | aElement0(_u54) )).
% 0.12/0.35 cnf(mNFRDef-2, definition, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aNormalFormOfIn0(_u54, _u53, _u52) | sdtmndtasgtdt0(_u53, _u52, _u54) )).
% 0.12/0.35 cnf(mNFRDef-3, definition, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aNormalFormOfIn0(_u54, _u53, _u52) | ~aReductOfIn0(_u49, _u54, _u52) )).
% 0.12/0.35 cnf(mNFRDef-4, definition, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aElement0(_u55) | ~sdtmndtasgtdt0(_u53, _u52, _u55) | aReductOfIn0(skolem12(_u53, _u52, _u55), _u55, _u52) | aNormalFormOfIn0(_u55, _u53, _u52) )).
% 0.12/0.35
% 0.12/0.35 % Formula: mTermNF ( axiom ) converted to clauses:
% 0.12/0.35 cnf(mTermNF-1, axiom, ( ~aRewritingSystem0(_u58) | ~isTerminating0(_u58) | ~aElement0(_u57) | aNormalFormOfIn0(skolem13(_u58, _u57), _u57, _u58) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__656 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__656-1, hypothesis, ( aRewritingSystem0(xR) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__656_01 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__656_01-1, hypothesis, ( isLocallyConfluent0(xR) )).
% 0.12/0.35 cnf(m__656_01-2, hypothesis, ( isTerminating0(xR) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__731 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__731-1, hypothesis, ( aElement0(xa) )).
% 0.12/0.35 cnf(m__731-2, hypothesis, ( aElement0(xb) )).
% 0.12/0.35 cnf(m__731-3, hypothesis, ( aElement0(xc) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__715 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__715-1, hypothesis, ( ~aElement0(_u62) | ~aElement0(_u61) | ~aElement0(_u60) | ~sdtmndtasgtdt0(_u62, xR, _u61) | ~sdtmndtasgtdt0(_u62, xR, _u60) | ~iLess0(_u62, xa) | aElement0(skolem14(_u62, _u61, _u60)) )).
% 0.12/0.35 cnf(m__715-2, hypothesis, ( ~aElement0(_u62) | ~aElement0(_u61) | ~aElement0(_u60) | ~sdtmndtasgtdt0(_u62, xR, _u61) | ~sdtmndtasgtdt0(_u62, xR, _u60) | ~iLess0(_u62, xa) | sdtmndtasgtdt0(_u61, xR, skolem14(_u62, _u61, _u60)) )).
% 0.12/0.35 cnf(m__715-3, hypothesis, ( ~aElement0(_u62) | ~aElement0(_u61) | ~aElement0(_u60) | ~sdtmndtasgtdt0(_u62, xR, _u61) | ~sdtmndtasgtdt0(_u62, xR, _u60) | ~iLess0(_u62, xa) | sdtmndtasgtdt0(_u60, xR, skolem14(_u62, _u61, _u60)) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__731_02 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__731_02-1, hypothesis, ( sdtmndtplgtdt0(xa, xR, xb) )).
% 0.12/0.35 cnf(m__731_02-2, hypothesis, ( sdtmndtplgtdt0(xa, xR, xc) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__755 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__755-1, hypothesis, ( aElement0(xu) )).
% 0.12/0.35 cnf(m__755-2, hypothesis, ( aReductOfIn0(xu, xa, xR) )).
% 0.12/0.35 cnf(m__755-3, hypothesis, ( sdtmndtasgtdt0(xu, xR, xb) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__779 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__779-1, hypothesis, ( aElement0(xv) )).
% 0.12/0.35 cnf(m__779-2, hypothesis, ( aReductOfIn0(xv, xa, xR) )).
% 0.12/0.35 cnf(m__779-3, hypothesis, ( sdtmndtasgtdt0(xv, xR, xc) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__799 ( hypothesis ) converted to clauses:
% 0.12/0.35 cnf(m__799-1, hypothesis, ( aElement0(xw) )).
% 0.12/0.35 cnf(m__799-2, hypothesis, ( sdtmndtasgtdt0(xu, xR, xw) )).
% 0.12/0.35 cnf(m__799-3, hypothesis, ( sdtmndtasgtdt0(xv, xR, xw) )).
% 0.12/0.35
% 0.12/0.35 % Formula: m__ ( conjecture ) converted to clauses:
% 0.12/0.35 cnf(m__-1, negated_conjecture, ( ~aNormalFormOfIn0(_u63, xw, xR) )).
% 0.12/0.35
% 0.12/0.35 % Problem matrix:
% 0.12/0.35 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.12/0.35 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.12/0.35 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.12/0.35 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem1(__eqx_0, __eqx_1, __eqx_2) = skolem1(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.12/0.35 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem2(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem2(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 0.12/0.35 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( skolem3(__eqx_0) = skolem3(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( skolem5(__eqx_0) = skolem5(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem6(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem6(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 0.12/0.35 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem8(__eqx_0) = skolem8(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem10(__eqx_0) = skolem10(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( skolem11(__eqx_0) = skolem11(__eqy_0)) )).
% 0.12/0.35 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem12(__eqx_0, __eqx_1, __eqx_2) = skolem12(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.12/0.35 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem13(__eqx_0, __eqx_1) = skolem13(__eqy_0, __eqy_1)) )).
% 0.12/0.35 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem14(__eqx_0, __eqx_1, __eqx_2) = skolem14(__eqy_0, __eqy_1, __eqy_2)) )).
% 0.12/0.35 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ~aElement0(__eqx_0) | aElement0(__eqy_0) )).
% 0.12/0.35 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ~aRewritingSystem0(__eqx_0) | aRewritingSystem0(__eqy_0) )).
% 0.12/0.35 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~aReductOfIn0(__eqx_0, __eqx_1, __eqx_2) | aReductOfIn0(__eqy_0, __eqy_1, __eqy_2) )).
% 0.12/0.35 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~iLess0(__eqx_0, __eqx_1) | iLess0(__eqy_0, __eqy_1) )).
% 0.12/0.35 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~sdtmndtplgtdt0(__eqx_0, __eqx_1, __eqx_2) | sdtmndtplgtdt0(__eqy_0, __eqy_1, __eqy_2) )).
% 0.12/0.35 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~sdtmndtasgtdt0(__eqx_0, __eqx_1, __eqx_2) | sdtmndtasgtdt0(__eqy_0, __eqy_1, __eqy_2) )).
% 0.12/0.35 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ~isConfluent0(__eqx_0) | isConfluent0(__eqy_0) )).
% 0.12/0.35 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ~isLocallyConfluent0(__eqx_0) | isLocallyConfluent0(__eqy_0) )).
% 0.12/0.35 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~isTerminating0(__eqx_0) | isTerminating0(__eqy_0) )).
% 0.12/0.35 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~aNormalFormOfIn0(__eqx_0, __eqx_1, __eqx_2) | aNormalFormOfIn0(__eqy_0, __eqy_1, __eqy_2) )).
% 0.12/0.35 cnf(matrix-27, plain, ( ~aElement0(_u4) | ~aRewritingSystem0(_u3) | ~aReductOfIn0(_u2, _u4, _u3) | aElement0(_u2) )).
% 0.12/0.35 cnf(matrix-28, plain, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | ~sdtmndtplgtdt0(_u14, _u13, _u12) | aReductOfIn0(_u12, _u14, _u13) | aElement0(skolem1(_u14, _u13, _u12)) )).
% 0.12/0.35 cnf(matrix-29, plain, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | ~sdtmndtplgtdt0(_u14, _u13, _u12) | aReductOfIn0(_u12, _u14, _u13) | aReductOfIn0(skolem1(_u14, _u13, _u12), _u14, _u13) )).
% 0.12/0.35 cnf(matrix-30, plain, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | ~sdtmndtplgtdt0(_u14, _u13, _u12) | aReductOfIn0(_u12, _u14, _u13) | sdtmndtplgtdt0(skolem1(_u14, _u13, _u12), _u13, _u12) )).
% 0.12/0.35 cnf(matrix-31, plain, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | sdtmndtplgtdt0(_u14, _u13, _u12) | ~aReductOfIn0(_u12, _u14, _u13) )).
% 0.12/0.35 cnf(matrix-32, plain, ( ~aElement0(_u14) | ~aRewritingSystem0(_u13) | ~aElement0(_u12) | sdtmndtplgtdt0(_u14, _u13, _u12) | ~aElement0(_u11) | ~aReductOfIn0(_u11, _u14, _u13) | ~sdtmndtplgtdt0(_u11, _u13, _u12) )).
% 0.12/0.35 cnf(matrix-33, plain, ( ~aElement0(_u18) | ~aRewritingSystem0(_u17) | ~aElement0(_u16) | ~aElement0(_u15) | ~sdtmndtplgtdt0(_u18, _u17, _u16) | ~sdtmndtplgtdt0(_u16, _u17, _u15) | sdtmndtplgtdt0(_u18, _u17, _u15) )).
% 0.12/0.35 cnf(matrix-34, plain, ( ~aElement0(_u21) | ~aRewritingSystem0(_u20) | ~aElement0(_u19) | ~sdtmndtasgtdt0(_u21, _u20, _u19) | ( _u21 = _u19) | sdtmndtplgtdt0(_u21, _u20, _u19) )).
% 0.12/0.35 cnf(matrix-35, plain, ( ~aElement0(_u21) | ~aRewritingSystem0(_u20) | ~aElement0(_u19) | sdtmndtasgtdt0(_u21, _u20, _u19) | ( _u21 != _u19) )).
% 0.12/0.35 cnf(matrix-36, plain, ( ~aElement0(_u21) | ~aRewritingSystem0(_u20) | ~aElement0(_u19) | sdtmndtasgtdt0(_u21, _u20, _u19) | ~sdtmndtplgtdt0(_u21, _u20, _u19) )).
% 0.12/0.35 cnf(matrix-37, plain, ( ~aElement0(_u25) | ~aRewritingSystem0(_u24) | ~aElement0(_u23) | ~aElement0(_u22) | ~sdtmndtasgtdt0(_u25, _u24, _u23) | ~sdtmndtasgtdt0(_u23, _u24, _u22) | sdtmndtasgtdt0(_u25, _u24, _u22) )).
% 0.12/0.35 cnf(matrix-38, plain, ( ~aRewritingSystem0(_u34) | ~isConfluent0(_u34) | ~aElement0(_u29) | ~aElement0(_u28) | ~aElement0(_u27) | ~sdtmndtasgtdt0(_u29, _u34, _u28) | ~sdtmndtasgtdt0(_u29, _u34, _u27) | aElement0(skolem2(_u34, _u29, _u28, _u27)) )).
% 0.12/0.35 cnf(matrix-39, plain, ( ~aRewritingSystem0(_u34) | ~isConfluent0(_u34) | ~aElement0(_u29) | ~aElement0(_u28) | ~aElement0(_u27) | ~sdtmndtasgtdt0(_u29, _u34, _u28) | ~sdtmndtasgtdt0(_u29, _u34, _u27) | sdtmndtasgtdt0(_u28, _u34, skolem2(_u34, _u29, _u28, _u27)) )).
% 0.12/0.35 cnf(matrix-40, plain, ( ~aRewritingSystem0(_u34) | ~isConfluent0(_u34) | ~aElement0(_u29) | ~aElement0(_u28) | ~aElement0(_u27) | ~sdtmndtasgtdt0(_u29, _u34, _u28) | ~sdtmndtasgtdt0(_u29, _u34, _u27) | sdtmndtasgtdt0(_u27, _u34, skolem2(_u34, _u29, _u28, _u27)) )).
% 0.12/0.35 cnf(matrix-41, plain, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | aElement0(skolem3(_u34)) )).
% 0.12/0.35 cnf(matrix-42, plain, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | aElement0(skolem4(_u34)) )).
% 0.12/0.35 cnf(matrix-43, plain, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | aElement0(skolem5(_u34)) )).
% 0.12/0.35 cnf(matrix-44, plain, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | sdtmndtasgtdt0(skolem3(_u34), _u34, skolem4(_u34)) )).
% 0.12/0.35 cnf(matrix-45, plain, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | sdtmndtasgtdt0(skolem3(_u34), _u34, skolem5(_u34)) )).
% 0.12/0.35 cnf(matrix-46, plain, ( ~aRewritingSystem0(_u34) | isConfluent0(_u34) | ~aElement0(_u30) | ~sdtmndtasgtdt0(skolem4(_u34), _u34, _u30) | ~sdtmndtasgtdt0(skolem5(_u34), _u34, _u30) )).
% 0.12/0.35 cnf(matrix-47, plain, ( ~aRewritingSystem0(_u43) | ~isLocallyConfluent0(_u43) | ~aElement0(_u38) | ~aElement0(_u37) | ~aElement0(_u36) | ~aReductOfIn0(_u37, _u38, _u43) | ~aReductOfIn0(_u36, _u38, _u43) | aElement0(skolem6(_u43, _u38, _u37, _u36)) )).
% 0.12/0.35 cnf(matrix-48, plain, ( ~aRewritingSystem0(_u43) | ~isLocallyConfluent0(_u43) | ~aElement0(_u38) | ~aElement0(_u37) | ~aElement0(_u36) | ~aReductOfIn0(_u37, _u38, _u43) | ~aReductOfIn0(_u36, _u38, _u43) | sdtmndtasgtdt0(_u37, _u43, skolem6(_u43, _u38, _u37, _u36)) )).
% 0.12/0.35 cnf(matrix-49, plain, ( ~aRewritingSystem0(_u43) | ~isLocallyConfluent0(_u43) | ~aElement0(_u38) | ~aElement0(_u37) | ~aElement0(_u36) | ~aReductOfIn0(_u37, _u38, _u43) | ~aReductOfIn0(_u36, _u38, _u43) | sdtmndtasgtdt0(_u36, _u43, skolem6(_u43, _u38, _u37, _u36)) )).
% 0.12/0.35 cnf(matrix-50, plain, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aElement0(skolem7(_u43)) )).
% 0.12/0.35 cnf(matrix-51, plain, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aElement0(skolem8(_u43)) )).
% 0.12/0.35 cnf(matrix-52, plain, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aElement0(skolem9(_u43)) )).
% 0.12/0.35 cnf(matrix-53, plain, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aReductOfIn0(skolem8(_u43), skolem7(_u43), _u43) )).
% 0.12/0.35 cnf(matrix-54, plain, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | aReductOfIn0(skolem9(_u43), skolem7(_u43), _u43) )).
% 0.12/0.35 cnf(matrix-55, plain, ( ~aRewritingSystem0(_u43) | isLocallyConfluent0(_u43) | ~aElement0(_u39) | ~sdtmndtasgtdt0(skolem8(_u43), _u43, _u39) | ~sdtmndtasgtdt0(skolem9(_u43), _u43, _u39) )).
% 0.12/0.35 cnf(matrix-56, plain, ( ~aRewritingSystem0(_u48) | ~isTerminating0(_u48) | ~aElement0(_u45) | ~aElement0(_u44) | ~sdtmndtplgtdt0(_u45, _u48, _u44) | iLess0(_u44, _u45) )).
% 0.12/0.35 cnf(matrix-57, plain, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | aElement0(skolem10(_u48)) )).
% 0.12/0.35 cnf(matrix-58, plain, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | aElement0(skolem11(_u48)) )).
% 0.12/0.35 cnf(matrix-59, plain, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | sdtmndtplgtdt0(skolem10(_u48), _u48, skolem11(_u48)) )).
% 0.12/0.35 cnf(matrix-60, plain, ( ~aRewritingSystem0(_u48) | isTerminating0(_u48) | ~iLess0(skolem11(_u48), skolem10(_u48)) )).
% 0.12/0.35 cnf(matrix-61, plain, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aNormalFormOfIn0(_u54, _u53, _u52) | aElement0(_u54) )).
% 0.12/0.35 cnf(matrix-62, plain, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aNormalFormOfIn0(_u54, _u53, _u52) | sdtmndtasgtdt0(_u53, _u52, _u54) )).
% 0.12/0.35 cnf(matrix-63, plain, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aNormalFormOfIn0(_u54, _u53, _u52) | ~aReductOfIn0(_u49, _u54, _u52) )).
% 0.12/0.35 cnf(matrix-64, plain, ( ~aElement0(_u53) | ~aRewritingSystem0(_u52) | ~aElement0(_u55) | ~sdtmndtasgtdt0(_u53, _u52, _u55) | aReductOfIn0(skolem12(_u53, _u52, _u55), _u55, _u52) | aNormalFormOfIn0(_u55, _u53, _u52) )).
% 0.12/0.35 cnf(matrix-65, plain, ( ~aRewritingSystem0(_u58) | ~isTerminating0(_u58) | ~aElement0(_u57) | aNormalFormOfIn0(skolem13(_u58, _u57), _u57, _u58) )).
% 0.12/0.35 cnf(matrix-66, plain, ( aRewritingSystem0(xR) )).
% 0.12/0.35 cnf(matrix-67, plain, ( isLocallyConfluent0(xR) )).
% 0.12/0.35 cnf(matrix-68, plain, ( isTerminating0(xR) )).
% 0.12/0.35 cnf(matrix-69, plain, ( aElement0(xa) )).
% 0.12/0.35 cnf(matrix-70, plain, ( aElement0(xb) )).
% 0.12/0.35 cnf(matrix-71, plain, ( aElement0(xc) )).
% 0.12/0.35 cnf(matrix-72, plain, ( ~aElement0(_u62) | ~aElement0(_u61) | ~aElement0(_u60) | ~sdtmndtasgtdt0(_u62, xR, _u61) | ~sdtmndtasgtdt0(_u62, xR, _u60) | ~iLess0(_u62, xa) | aElement0(skolem14(_u62, _u61, _u60)) )).
% 0.12/0.35 cnf(matrix-73, plain, ( ~aElement0(_u62) | ~aElement0(_u61) | ~aElement0(_u60) | ~sdtmndtasgtdt0(_u62, xR, _u61) | ~sdtmndtasgtdt0(_u62, xR, _u60) | ~iLess0(_u62, xa) | sdtmndtasgtdt0(_u61, xR, skolem14(_u62, _u61, _u60)) )).
% 0.12/0.35 cnf(matrix-74, plain, ( ~aElement0(_u62) | ~aElement0(_u61) | ~aElement0(_u60) | ~sdtmndtasgtdt0(_u62, xR, _u61) | ~sdtmndtasgtdt0(_u62, xR, _u60) | ~iLess0(_u62, xa) | sdtmndtasgtdt0(_u60, xR, skolem14(_u62, _u61, _u60)) )).
% 0.12/0.35 cnf(matrix-75, plain, ( sdtmndtplgtdt0(xa, xR, xb) )).
% 0.12/0.35 cnf(matrix-76, plain, ( sdtmndtplgtdt0(xa, xR, xc) )).
% 0.12/0.35 cnf(matrix-77, plain, ( aElement0(xu) )).
% 0.12/0.35 cnf(matrix-78, plain, ( aReductOfIn0(xu, xa, xR) )).
% 0.12/0.35 cnf(matrix-79, plain, ( sdtmndtasgtdt0(xu, xR, xb) )).
% 0.12/0.35 cnf(matrix-80, plain, ( aElement0(xv) )).
% 0.12/0.35 cnf(matrix-81, plain, ( aReductOfIn0(xv, xa, xR) )).
% 0.12/0.35 cnf(matrix-82, plain, ( sdtmndtasgtdt0(xv, xR, xc) )).
% 0.12/0.35 cnf(matrix-83, plain, ( aElement0(xw) )).
% 0.12/0.35 cnf(matrix-84, plain, ( sdtmndtasgtdt0(xu, xR, xw) )).
% 0.12/0.35 cnf(matrix-85, plain, ( sdtmndtasgtdt0(xv, xR, xw) )).
% 0.12/0.35 cnf(matrix-86, plain, ( ~aNormalFormOfIn0(_u63, xw, xR) )).
% 0.12/0.35
% 0.12/0.35 % Proof stack:
% 0.12/0.35 cnf(proof-stack, plain,
% 0.12/0.35 proof_stack(
% 0.12/0.35 start(86),
% 0.12/0.35 left_branch(0, 65, 3, 2),
% 0.12/0.35 left_branch(0, 66, 0, 3),
% 0.12/0.35 right_branch(3),
% 0.12/0.35 left_branch(0, 83, 0, 4),
% 0.12/0.35 right_branch(4),
% 0.12/0.35 left_branch(0, 68, 0, 5),
% 0.12/0.35 right_branch(5),
% 0.12/0.35 right_branch(2)
% 0.12/0.35 )).
% 0.12/0.35 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------