TSTP Solution File: RNG047+2 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : RNG047+2 : 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 : n019.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 : Mon Mar 25 14:29:49 EDT 2024
% Result : Theorem 26.64s 26.84s
% Output : Proof 26.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : RNG047+2 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Mar 21 00:07:48 EDT 2024
% 0.13/0.34 % CPUTime :
% 26.64/26.84 % SZS status Theorem for theBenchmark
% 26.64/26.84 % SZS output start Proof for theBenchmark
% 26.64/26.84
% 26.64/26.84 % Formula: mNatSort ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mNatSort, axiom, $true).
% 26.64/26.84
% 26.64/26.84 % Formula: mZeroNat ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mZeroNat-1, axiom, ( aNaturalNumber0(sz00) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mSuccNat ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mSuccNat-1, axiom, ( ~aNaturalNumber0(_u1) | aNaturalNumber0(szszuzczcdt0(_u1)) )).
% 26.64/26.84 cnf(mSuccNat-2, axiom, ( ~aNaturalNumber0(_u1) | ( szszuzczcdt0(_u1) != sz00) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mNatExtr ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mNatExtr-1, axiom, ( ~aNaturalNumber0(_u3) | ( _u3 = sz00) | aNaturalNumber0(skolem1(_u3)) )).
% 26.64/26.84 cnf(mNatExtr-2, axiom, ( ~aNaturalNumber0(_u3) | ( _u3 = sz00) | ( _u3 = szszuzczcdt0(skolem1(_u3))) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mSuccEqu ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mSuccEqu-1, axiom, ( ~aNaturalNumber0(_u5) | ~aNaturalNumber0(_u4) | ( szszuzczcdt0(_u5) != szszuzczcdt0(_u4)) | ( _u5 = _u4) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mIHOrd ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mIHOrd, axiom, $true).
% 26.64/26.84
% 26.64/26.84 % Formula: mIH ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mIH-1, axiom, ( ~aNaturalNumber0(_u8) | iLess0(_u8, szszuzczcdt0(_u8)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mScSort ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mScSort, axiom, $true).
% 26.64/26.84
% 26.64/26.84 % Formula: mSZeroSc ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mSZeroSc-1, axiom, ( aScalar0(sz0z00) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mSumSc ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mSumSc-1, axiom, ( ~aScalar0(_u11) | ~aScalar0(_u10) | aScalar0(sdtpldt0(_u11, _u10)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mMulSc ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mMulSc-1, axiom, ( ~aScalar0(_u13) | ~aScalar0(_u12) | aScalar0(sdtasdt0(_u13, _u12)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mNegSc ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mNegSc-1, axiom, ( ~aScalar0(_u14) | aScalar0(smndt0(_u14)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mScZero ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mScZero-1, axiom, ( ~aScalar0(_u15) | ( sdtpldt0(_u15, sz0z00) = _u15) )).
% 26.64/26.84 cnf(mScZero-2, axiom, ( ~aScalar0(_u15) | ( sdtpldt0(sz0z00, _u15) = _u15) )).
% 26.64/26.84 cnf(mScZero-3, axiom, ( ~aScalar0(_u15) | ( sdtasdt0(_u15, sz0z00) = sz0z00) )).
% 26.64/26.84 cnf(mScZero-4, axiom, ( ~aScalar0(_u15) | ( sdtasdt0(sz0z00, _u15) = sz0z00) )).
% 26.64/26.84 cnf(mScZero-5, axiom, ( ~aScalar0(_u15) | ( sdtpldt0(_u15, smndt0(_u15)) = sz0z00) )).
% 26.64/26.84 cnf(mScZero-6, axiom, ( ~aScalar0(_u15) | ( sdtpldt0(smndt0(_u15), _u15) = sz0z00) )).
% 26.64/26.84 cnf(mScZero-7, axiom, ( ~aScalar0(_u15) | ( smndt0(smndt0(_u15)) = _u15) )).
% 26.64/26.84 cnf(mScZero-8, axiom, ( ~aScalar0(_u15) | ( smndt0(sz0z00) = sz0z00) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mArith ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mArith-1, axiom, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtpldt0(sdtpldt0(_u18, _u17), _u16) = sdtpldt0(_u18, sdtpldt0(_u17, _u16))) )).
% 26.64/26.84 cnf(mArith-2, axiom, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtpldt0(_u18, _u17) = sdtpldt0(_u17, _u18)) )).
% 26.64/26.84 cnf(mArith-3, axiom, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtasdt0(sdtasdt0(_u18, _u17), _u16) = sdtasdt0(_u18, sdtasdt0(_u17, _u16))) )).
% 26.64/26.84 cnf(mArith-4, axiom, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtasdt0(_u18, _u17) = sdtasdt0(_u17, _u18)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mDistr ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mDistr-1, axiom, ( ~aScalar0(_u21) | ~aScalar0(_u20) | ~aScalar0(_u19) | ( sdtasdt0(_u21, sdtpldt0(_u20, _u19)) = sdtpldt0(sdtasdt0(_u21, _u20), sdtasdt0(_u21, _u19))) )).
% 26.64/26.84 cnf(mDistr-2, axiom, ( ~aScalar0(_u21) | ~aScalar0(_u20) | ~aScalar0(_u19) | ( sdtasdt0(sdtpldt0(_u21, _u20), _u19) = sdtpldt0(sdtasdt0(_u21, _u19), sdtasdt0(_u20, _u19))) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mDistr2 ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mDistr2-1, axiom, ( ~aScalar0(_u25) | ~aScalar0(_u24) | ~aScalar0(_u23) | ~aScalar0(_u22) | ( sdtasdt0(sdtpldt0(_u25, _u24), sdtpldt0(_u23, _u22)) = sdtpldt0(sdtpldt0(sdtasdt0(_u25, _u23), sdtasdt0(_u25, _u22)), sdtpldt0(sdtasdt0(_u24, _u23), sdtasdt0(_u24, _u22)))) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mMNeg ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mMNeg-1, axiom, ( ~aScalar0(_u27) | ~aScalar0(_u26) | ( sdtasdt0(_u27, smndt0(_u26)) = smndt0(sdtasdt0(_u27, _u26))) )).
% 26.64/26.84 cnf(mMNeg-2, axiom, ( ~aScalar0(_u27) | ~aScalar0(_u26) | ( sdtasdt0(smndt0(_u27), _u26) = smndt0(sdtasdt0(_u27, _u26))) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mMDNeg ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mMDNeg-1, axiom, ( ~aScalar0(_u29) | ~aScalar0(_u28) | ( sdtasdt0(smndt0(_u29), smndt0(_u28)) = sdtasdt0(_u29, _u28)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mLess ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLess, axiom, $true).
% 26.64/26.84
% 26.64/26.84 % Formula: mLERef ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLERef-1, axiom, ( ~aScalar0(_u32) | sdtlseqdt0(_u32, _u32) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mLEASm ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLEASm-1, axiom, ( ~aScalar0(_u34) | ~aScalar0(_u33) | ~sdtlseqdt0(_u34, _u33) | ~sdtlseqdt0(_u33, _u34) | ( _u34 = _u33) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mLETrn ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLETrn-1, axiom, ( ~aScalar0(_u37) | ~aScalar0(_u36) | ~aScalar0(_u35) | ~sdtlseqdt0(_u37, _u36) | ~sdtlseqdt0(_u36, _u35) | sdtlseqdt0(_u37, _u35) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mLEMon ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLEMon-1, axiom, ( ~aScalar0(_u41) | ~aScalar0(_u40) | ~aScalar0(_u39) | ~aScalar0(_u38) | ~sdtlseqdt0(_u41, _u40) | ~sdtlseqdt0(_u39, _u38) | sdtlseqdt0(sdtpldt0(_u41, _u39), sdtpldt0(_u40, _u38)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mLEMonM ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLEMonM-1, axiom, ( ~aScalar0(_u45) | ~aScalar0(_u44) | ~aScalar0(_u43) | ~aScalar0(_u42) | ~sdtlseqdt0(_u45, _u44) | ~sdtlseqdt0(sz0z00, _u43) | ~sdtlseqdt0(_u43, _u42) | sdtlseqdt0(sdtasdt0(_u45, _u43), sdtasdt0(_u44, _u42)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mLETot ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mLETot-1, axiom, ( ~aScalar0(_u47) | ~aScalar0(_u46) | sdtlseqdt0(_u47, _u46) | sdtlseqdt0(_u46, _u47) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mPosMon ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mPosMon-1, axiom, ( ~aScalar0(_u49) | ~aScalar0(_u48) | ~sdtlseqdt0(sz0z00, _u49) | ~sdtlseqdt0(sz0z00, _u48) | sdtlseqdt0(sz0z00, sdtpldt0(_u49, _u48)) )).
% 26.64/26.84 cnf(mPosMon-2, axiom, ( ~aScalar0(_u49) | ~aScalar0(_u48) | ~sdtlseqdt0(sz0z00, _u49) | ~sdtlseqdt0(sz0z00, _u48) | sdtlseqdt0(sz0z00, sdtasdt0(_u49, _u48)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mSqPos ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mSqPos-1, axiom, ( ~aScalar0(_u50) | sdtlseqdt0(sz0z00, sdtasdt0(_u50, _u50)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mSqrt ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mSqrt-1, axiom, ( ~aScalar0(_u52) | ~aScalar0(_u51) | ~sdtlseqdt0(sz0z00, _u52) | ~sdtlseqdt0(sz0z00, _u51) | ( sdtasdt0(_u52, _u52) != sdtasdt0(_u51, _u51)) | ( _u52 = _u51) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mVcSort ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mVcSort, axiom, $true).
% 26.64/26.84
% 26.64/26.84 % Formula: mDimNat ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mDimNat-1, axiom, ( ~aVector0(_u54) | aNaturalNumber0(aDimensionOf0(_u54)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mElmSc ( axiom ) converted to clauses:
% 26.64/26.84 cnf(mElmSc-1, axiom, ( ~aVector0(_u56) | ~aNaturalNumber0(_u55) | aScalar0(sdtlbdtrb0(_u56, _u55)) )).
% 26.64/26.84
% 26.64/26.84 % Formula: mDefInit ( definition ) converted to clauses:
% 26.64/26.84 cnf(mDefInit-1, definition, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u61 != sziznziztdt0(_u60)) | aVector0(_u61) )).
% 26.64/26.84 cnf(mDefInit-2, definition, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u61 != sziznziztdt0(_u60)) | ( szszuzczcdt0(aDimensionOf0(_u61)) = aDimensionOf0(_u60)) )).
% 26.64/26.84 cnf(mDefInit-3, definition, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u61 != sziznziztdt0(_u60)) | ~aNaturalNumber0(_u57) | ( sdtlbdtrb0(_u61, _u57) = sdtlbdtrb0(_u60, _u57)) )).
% 26.64/26.84 cnf(mDefInit-4, definition, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u62 = sziznziztdt0(_u60)) | ~aVector0(_u62) | ( szszuzczcdt0(aDimensionOf0(_u62)) != aDimensionOf0(_u60)) | aNaturalNumber0(skolem2(_u60, _u62)) )).
% 26.64/26.84 cnf(mDefInit-5, definition, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u62 = sziznziztdt0(_u60)) | ~aVector0(_u62) | ( szszuzczcdt0(aDimensionOf0(_u62)) != aDimensionOf0(_u60)) | ( sdtlbdtrb0(_u62, skolem2(_u60, _u62)) != sdtlbdtrb0(_u60, skolem2(_u60, _u62))) )).
% 26.64/26.84
% 26.64/26.84 % Formula: m__1329 ( hypothesis ) converted to clauses:
% 26.64/26.84 cnf(m__1329-1, hypothesis, ( aVector0(xs) )).
% 26.64/26.84 cnf(m__1329-2, hypothesis, ( aVector0(xt) )).
% 26.64/26.84
% 26.64/26.84 % Formula: m__1329_01 ( hypothesis ) converted to clauses:
% 26.64/26.84 cnf(m__1329_01-1, hypothesis, ( ( aDimensionOf0(xs) = aDimensionOf0(xt)) )).
% 26.64/26.84 cnf(m__1329_01-2, hypothesis, ( ( aDimensionOf0(xt) != sz00) )).
% 26.64/26.84
% 26.64/26.84 % Formula: m__ ( conjecture ) (definitionally) converted to clauses:
% 26.64/26.84 cnf(m__-1, negated_conjecture, ( aVector0(sziznziztdt0(xs)) )).
% 26.64/26.84 cnf(m__-2, negated_conjecture, ( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)) )).
% 26.64/26.84 cnf(m__-3, negated_conjecture, ( ~aNaturalNumber0(_u63) | ( sdtlbdtrb0(sziznziztdt0(xs), _u63) = sdtlbdtrb0(xs, _u63)) )).
% 26.64/26.84 cnf(m__-4, negated_conjecture, ( aVector0(sziznziztdt0(xt)) )).
% 26.64/26.84 cnf(m__-5, negated_conjecture, ( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)) )).
% 26.64/26.84 cnf(m__-6, negated_conjecture, ( ~aNaturalNumber0(_u64) | ( sdtlbdtrb0(sziznziztdt0(xt), _u64) = sdtlbdtrb0(xt, _u64)) )).
% 26.64/26.84 cnf(m__-7, negated_conjecture, ( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))) )).
% 26.64/26.84
% 26.64/26.84 % Problem matrix:
% 26.64/26.84 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 26.64/26.84 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 26.64/26.84 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 26.64/26.84 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( szszuzczcdt0(__eqx_0) = szszuzczcdt0(__eqy_0)) )).
% 26.64/26.84 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtpldt0(__eqx_0, __eqx_1) = sdtpldt0(__eqy_0, __eqy_1)) )).
% 26.64/26.84 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtasdt0(__eqx_0, __eqx_1) = sdtasdt0(__eqy_0, __eqy_1)) )).
% 26.64/26.84 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( smndt0(__eqx_0) = smndt0(__eqy_0)) )).
% 26.64/26.84 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( aDimensionOf0(__eqx_0) = aDimensionOf0(__eqy_0)) )).
% 26.64/26.84 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtlbdtrb0(__eqx_0, __eqx_1) = sdtlbdtrb0(__eqy_0, __eqy_1)) )).
% 26.64/26.84 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( sziznziztdt0(__eqx_0) = sziznziztdt0(__eqy_0)) )).
% 26.64/26.84 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem1(__eqx_0) = skolem1(__eqy_0)) )).
% 26.64/26.84 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 26.64/26.84 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ~aNaturalNumber0(__eqx_0) | aNaturalNumber0(__eqy_0) )).
% 26.64/26.84 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~iLess0(__eqx_0, __eqx_1) | iLess0(__eqy_0, __eqy_1) )).
% 26.64/26.84 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ~aScalar0(__eqx_0) | aScalar0(__eqy_0) )).
% 26.64/26.84 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~sdtlseqdt0(__eqx_0, __eqx_1) | sdtlseqdt0(__eqy_0, __eqy_1) )).
% 26.64/26.84 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ~aVector0(__eqx_0) | aVector0(__eqy_0) )).
% 26.64/26.84 cnf(matrix-17, plain, ( aNaturalNumber0(sz00) )).
% 26.64/26.84 cnf(matrix-18, plain, ( ~aNaturalNumber0(_u1) | aNaturalNumber0(szszuzczcdt0(_u1)) )).
% 26.64/26.84 cnf(matrix-19, plain, ( ~aNaturalNumber0(_u1) | ( szszuzczcdt0(_u1) != sz00) )).
% 26.64/26.84 cnf(matrix-20, plain, ( ~aNaturalNumber0(_u3) | ( _u3 = sz00) | aNaturalNumber0(skolem1(_u3)) )).
% 26.64/26.84 cnf(matrix-21, plain, ( ~aNaturalNumber0(_u3) | ( _u3 = sz00) | ( _u3 = szszuzczcdt0(skolem1(_u3))) )).
% 26.64/26.84 cnf(matrix-22, plain, ( ~aNaturalNumber0(_u5) | ~aNaturalNumber0(_u4) | ( szszuzczcdt0(_u5) != szszuzczcdt0(_u4)) | ( _u5 = _u4) )).
% 26.64/26.84 cnf(matrix-23, plain, ( ~aNaturalNumber0(_u8) | iLess0(_u8, szszuzczcdt0(_u8)) )).
% 26.64/26.84 cnf(matrix-24, plain, ( aScalar0(sz0z00) )).
% 26.64/26.84 cnf(matrix-25, plain, ( ~aScalar0(_u11) | ~aScalar0(_u10) | aScalar0(sdtpldt0(_u11, _u10)) )).
% 26.64/26.84 cnf(matrix-26, plain, ( ~aScalar0(_u13) | ~aScalar0(_u12) | aScalar0(sdtasdt0(_u13, _u12)) )).
% 26.64/26.84 cnf(matrix-27, plain, ( ~aScalar0(_u14) | aScalar0(smndt0(_u14)) )).
% 26.64/26.84 cnf(matrix-28, plain, ( ~aScalar0(_u15) | ( sdtpldt0(_u15, sz0z00) = _u15) )).
% 26.64/26.84 cnf(matrix-29, plain, ( ~aScalar0(_u15) | ( sdtpldt0(sz0z00, _u15) = _u15) )).
% 26.64/26.84 cnf(matrix-30, plain, ( ~aScalar0(_u15) | ( sdtasdt0(_u15, sz0z00) = sz0z00) )).
% 26.64/26.84 cnf(matrix-31, plain, ( ~aScalar0(_u15) | ( sdtasdt0(sz0z00, _u15) = sz0z00) )).
% 26.64/26.84 cnf(matrix-32, plain, ( ~aScalar0(_u15) | ( sdtpldt0(_u15, smndt0(_u15)) = sz0z00) )).
% 26.64/26.84 cnf(matrix-33, plain, ( ~aScalar0(_u15) | ( sdtpldt0(smndt0(_u15), _u15) = sz0z00) )).
% 26.64/26.84 cnf(matrix-34, plain, ( ~aScalar0(_u15) | ( smndt0(smndt0(_u15)) = _u15) )).
% 26.64/26.84 cnf(matrix-35, plain, ( ~aScalar0(_u15) | ( smndt0(sz0z00) = sz0z00) )).
% 26.64/26.84 cnf(matrix-36, plain, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtpldt0(sdtpldt0(_u18, _u17), _u16) = sdtpldt0(_u18, sdtpldt0(_u17, _u16))) )).
% 26.64/26.84 cnf(matrix-37, plain, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtpldt0(_u18, _u17) = sdtpldt0(_u17, _u18)) )).
% 26.64/26.84 cnf(matrix-38, plain, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtasdt0(sdtasdt0(_u18, _u17), _u16) = sdtasdt0(_u18, sdtasdt0(_u17, _u16))) )).
% 26.64/26.84 cnf(matrix-39, plain, ( ~aScalar0(_u18) | ~aScalar0(_u17) | ~aScalar0(_u16) | ( sdtasdt0(_u18, _u17) = sdtasdt0(_u17, _u18)) )).
% 26.64/26.84 cnf(matrix-40, plain, ( ~aScalar0(_u21) | ~aScalar0(_u20) | ~aScalar0(_u19) | ( sdtasdt0(_u21, sdtpldt0(_u20, _u19)) = sdtpldt0(sdtasdt0(_u21, _u20), sdtasdt0(_u21, _u19))) )).
% 26.64/26.84 cnf(matrix-41, plain, ( ~aScalar0(_u21) | ~aScalar0(_u20) | ~aScalar0(_u19) | ( sdtasdt0(sdtpldt0(_u21, _u20), _u19) = sdtpldt0(sdtasdt0(_u21, _u19), sdtasdt0(_u20, _u19))) )).
% 26.64/26.84 cnf(matrix-42, plain, ( ~aScalar0(_u25) | ~aScalar0(_u24) | ~aScalar0(_u23) | ~aScalar0(_u22) | ( sdtasdt0(sdtpldt0(_u25, _u24), sdtpldt0(_u23, _u22)) = sdtpldt0(sdtpldt0(sdtasdt0(_u25, _u23), sdtasdt0(_u25, _u22)), sdtpldt0(sdtasdt0(_u24, _u23), sdtasdt0(_u24, _u22)))) )).
% 26.64/26.84 cnf(matrix-43, plain, ( ~aScalar0(_u27) | ~aScalar0(_u26) | ( sdtasdt0(_u27, smndt0(_u26)) = smndt0(sdtasdt0(_u27, _u26))) )).
% 26.64/26.84 cnf(matrix-44, plain, ( ~aScalar0(_u27) | ~aScalar0(_u26) | ( sdtasdt0(smndt0(_u27), _u26) = smndt0(sdtasdt0(_u27, _u26))) )).
% 26.64/26.84 cnf(matrix-45, plain, ( ~aScalar0(_u29) | ~aScalar0(_u28) | ( sdtasdt0(smndt0(_u29), smndt0(_u28)) = sdtasdt0(_u29, _u28)) )).
% 26.64/26.84 cnf(matrix-46, plain, ( ~aScalar0(_u32) | sdtlseqdt0(_u32, _u32) )).
% 26.64/26.84 cnf(matrix-47, plain, ( ~aScalar0(_u34) | ~aScalar0(_u33) | ~sdtlseqdt0(_u34, _u33) | ~sdtlseqdt0(_u33, _u34) | ( _u34 = _u33) )).
% 26.64/26.84 cnf(matrix-48, plain, ( ~aScalar0(_u37) | ~aScalar0(_u36) | ~aScalar0(_u35) | ~sdtlseqdt0(_u37, _u36) | ~sdtlseqdt0(_u36, _u35) | sdtlseqdt0(_u37, _u35) )).
% 26.64/26.84 cnf(matrix-49, plain, ( ~aScalar0(_u41) | ~aScalar0(_u40) | ~aScalar0(_u39) | ~aScalar0(_u38) | ~sdtlseqdt0(_u41, _u40) | ~sdtlseqdt0(_u39, _u38) | sdtlseqdt0(sdtpldt0(_u41, _u39), sdtpldt0(_u40, _u38)) )).
% 26.64/26.84 cnf(matrix-50, plain, ( ~aScalar0(_u45) | ~aScalar0(_u44) | ~aScalar0(_u43) | ~aScalar0(_u42) | ~sdtlseqdt0(_u45, _u44) | ~sdtlseqdt0(sz0z00, _u43) | ~sdtlseqdt0(_u43, _u42) | sdtlseqdt0(sdtasdt0(_u45, _u43), sdtasdt0(_u44, _u42)) )).
% 26.64/26.84 cnf(matrix-51, plain, ( ~aScalar0(_u47) | ~aScalar0(_u46) | sdtlseqdt0(_u47, _u46) | sdtlseqdt0(_u46, _u47) )).
% 26.64/26.84 cnf(matrix-52, plain, ( ~aScalar0(_u49) | ~aScalar0(_u48) | ~sdtlseqdt0(sz0z00, _u49) | ~sdtlseqdt0(sz0z00, _u48) | sdtlseqdt0(sz0z00, sdtpldt0(_u49, _u48)) )).
% 26.64/26.84 cnf(matrix-53, plain, ( ~aScalar0(_u49) | ~aScalar0(_u48) | ~sdtlseqdt0(sz0z00, _u49) | ~sdtlseqdt0(sz0z00, _u48) | sdtlseqdt0(sz0z00, sdtasdt0(_u49, _u48)) )).
% 26.64/26.84 cnf(matrix-54, plain, ( ~aScalar0(_u50) | sdtlseqdt0(sz0z00, sdtasdt0(_u50, _u50)) )).
% 26.64/26.84 cnf(matrix-55, plain, ( ~aScalar0(_u52) | ~aScalar0(_u51) | ~sdtlseqdt0(sz0z00, _u52) | ~sdtlseqdt0(sz0z00, _u51) | ( sdtasdt0(_u52, _u52) != sdtasdt0(_u51, _u51)) | ( _u52 = _u51) )).
% 26.64/26.84 cnf(matrix-56, plain, ( ~aVector0(_u54) | aNaturalNumber0(aDimensionOf0(_u54)) )).
% 26.64/26.84 cnf(matrix-57, plain, ( ~aVector0(_u56) | ~aNaturalNumber0(_u55) | aScalar0(sdtlbdtrb0(_u56, _u55)) )).
% 26.64/26.84 cnf(matrix-58, plain, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u61 != sziznziztdt0(_u60)) | aVector0(_u61) )).
% 26.64/26.84 cnf(matrix-59, plain, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u61 != sziznziztdt0(_u60)) | ( szszuzczcdt0(aDimensionOf0(_u61)) = aDimensionOf0(_u60)) )).
% 26.64/26.84 cnf(matrix-60, plain, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u61 != sziznziztdt0(_u60)) | ~aNaturalNumber0(_u57) | ( sdtlbdtrb0(_u61, _u57) = sdtlbdtrb0(_u60, _u57)) )).
% 26.64/26.84 cnf(matrix-61, plain, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u62 = sziznziztdt0(_u60)) | ~aVector0(_u62) | ( szszuzczcdt0(aDimensionOf0(_u62)) != aDimensionOf0(_u60)) | aNaturalNumber0(skolem2(_u60, _u62)) )).
% 26.64/26.84 cnf(matrix-62, plain, ( ~aVector0(_u60) | ( aDimensionOf0(_u60) = sz00) | ( _u62 = sziznziztdt0(_u60)) | ~aVector0(_u62) | ( szszuzczcdt0(aDimensionOf0(_u62)) != aDimensionOf0(_u60)) | ( sdtlbdtrb0(_u62, skolem2(_u60, _u62)) != sdtlbdtrb0(_u60, skolem2(_u60, _u62))) )).
% 26.64/26.84 cnf(matrix-63, plain, ( aVector0(xs) )).
% 26.64/26.84 cnf(matrix-64, plain, ( aVector0(xt) )).
% 26.64/26.84 cnf(matrix-65, plain, ( ( aDimensionOf0(xs) = aDimensionOf0(xt)) )).
% 26.64/26.84 cnf(matrix-66, plain, ( ( aDimensionOf0(xt) != sz00) )).
% 26.64/26.84 cnf(matrix-67, plain, ( aVector0(sziznziztdt0(xs)) )).
% 26.64/26.84 cnf(matrix-68, plain, ( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)) )).
% 26.64/26.84 cnf(matrix-69, plain, ( ~aNaturalNumber0(_u63) | ( sdtlbdtrb0(sziznziztdt0(xs), _u63) = sdtlbdtrb0(xs, _u63)) )).
% 26.64/26.84 cnf(matrix-70, plain, ( aVector0(sziznziztdt0(xt)) )).
% 26.64/26.84 cnf(matrix-71, plain, ( ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)) )).
% 26.64/26.84 cnf(matrix-72, plain, ( ~aNaturalNumber0(_u64) | ( sdtlbdtrb0(sziznziztdt0(xt), _u64) = sdtlbdtrb0(xt, _u64)) )).
% 26.64/26.84 cnf(matrix-73, plain, ( ( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))) )).
% 26.64/26.84
% 26.64/26.84 % Proof stack:
% 26.64/26.84 cnf(proof-stack, plain,
% 26.64/26.84 proof_stack(
% 26.64/26.84 start(68),
% 26.64/26.84 left_branch(0, 2, 0, 2),
% 26.64/26.84 left_branch(0, 22, 2, 3),
% 26.64/26.84 left_branch(0, 56, 1, 4),
% 26.64/26.84 left_branch(0, 67, 0, 5),
% 26.64/26.84 right_branch(5),
% 26.64/26.84 right_branch(4),
% 26.64/26.84 left_branch(0, 73, 0, 5),
% 26.64/26.84 right_branch(5),
% 26.64/26.84 left_branch(0, 56, 1, 6),
% 26.64/26.84 left_branch(0, 70, 0, 7),
% 26.64/26.84 right_branch(7),
% 26.64/26.84 right_branch(6),
% 26.64/26.84 right_branch(3),
% 26.64/26.84 left_branch(0, 2, 2, 4),
% 26.64/26.84 left_branch(0, 65, 0, 5),
% 26.64/26.84 right_branch(5),
% 26.64/26.84 left_branch(0, 1, 1, 6),
% 26.64/26.84 left_branch(0, 71, 0, 7),
% 26.64/26.84 right_branch(7),
% 26.64/26.84 right_branch(6),
% 26.64/26.84 right_branch(4),
% 26.64/26.84 right_branch(2)
% 26.64/26.84 )).
% 26.64/26.84 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------