TSTP Solution File: NUM458+2 by ConnectPP---0.2.2
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%------------------------------------------------------------------------------
% File : ConnectPP---0.2.2
% Problem : NUM458+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 : n006.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 09:15:26 EST 2024
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.33 % Computer : n006.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 : Sun Mar 3 15:58:35 EST 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46 % SZS output start Proof for theBenchmark
% 0.19/0.46
% 0.19/0.46 % Formula: mNatSort ( axiom ) converted to clauses:
% 0.19/0.46
% 0.19/0.46 % Formula: mSortsC ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mSortsC-1, axiom, ( aNaturalNumber0(sz00) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mSortsC_01 ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mSortsC_01-1, axiom, ( aNaturalNumber0(sz10) )).
% 0.19/0.46 cnf(mSortsC_01-2, axiom, ( ( sz10 != sz00) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mSortsB ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mSortsB-1, axiom, ( ~aNaturalNumber0(_u2) | ~aNaturalNumber0(_u1) | aNaturalNumber0(sdtpldt0(_u2, _u1)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mSortsB_02 ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mSortsB_02-1, axiom, ( ~aNaturalNumber0(_u4) | ~aNaturalNumber0(_u3) | aNaturalNumber0(sdtasdt0(_u4, _u3)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mAddComm ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mAddComm-1, axiom, ( ~aNaturalNumber0(_u6) | ~aNaturalNumber0(_u5) | ( sdtpldt0(_u6, _u5) = sdtpldt0(_u5, _u6)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mAddAsso ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mAddAsso-1, axiom, ( ~aNaturalNumber0(_u9) | ~aNaturalNumber0(_u8) | ~aNaturalNumber0(_u7) | ( sdtpldt0(sdtpldt0(_u9, _u8), _u7) = sdtpldt0(_u9, sdtpldt0(_u8, _u7))) )).
% 0.19/0.46
% 0.19/0.46 % Formula: m_AddZero ( axiom ) converted to clauses:
% 0.19/0.46 cnf(m_AddZero-1, axiom, ( ~aNaturalNumber0(_u10) | ( sdtpldt0(_u10, sz00) = _u10) )).
% 0.19/0.46 cnf(m_AddZero-2, axiom, ( ~aNaturalNumber0(_u10) | ( _u10 = sdtpldt0(sz00, _u10)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mMulComm ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mMulComm-1, axiom, ( ~aNaturalNumber0(_u12) | ~aNaturalNumber0(_u11) | ( sdtasdt0(_u12, _u11) = sdtasdt0(_u11, _u12)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mMulAsso ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mMulAsso-1, axiom, ( ~aNaturalNumber0(_u15) | ~aNaturalNumber0(_u14) | ~aNaturalNumber0(_u13) | ( sdtasdt0(sdtasdt0(_u15, _u14), _u13) = sdtasdt0(_u15, sdtasdt0(_u14, _u13))) )).
% 0.19/0.46
% 0.19/0.46 % Formula: m_MulUnit ( axiom ) converted to clauses:
% 0.19/0.46 cnf(m_MulUnit-1, axiom, ( ~aNaturalNumber0(_u16) | ( sdtasdt0(_u16, sz10) = _u16) )).
% 0.19/0.46 cnf(m_MulUnit-2, axiom, ( ~aNaturalNumber0(_u16) | ( _u16 = sdtasdt0(sz10, _u16)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: m_MulZero ( axiom ) converted to clauses:
% 0.19/0.46 cnf(m_MulZero-1, axiom, ( ~aNaturalNumber0(_u17) | ( sdtasdt0(_u17, sz00) = sz00) )).
% 0.19/0.46 cnf(m_MulZero-2, axiom, ( ~aNaturalNumber0(_u17) | ( sz00 = sdtasdt0(sz00, _u17)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mAMDistr ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mAMDistr-1, axiom, ( ~aNaturalNumber0(_u20) | ~aNaturalNumber0(_u19) | ~aNaturalNumber0(_u18) | ( sdtasdt0(_u20, sdtpldt0(_u19, _u18)) = sdtpldt0(sdtasdt0(_u20, _u19), sdtasdt0(_u20, _u18))) )).
% 0.19/0.46 cnf(mAMDistr-2, axiom, ( ~aNaturalNumber0(_u20) | ~aNaturalNumber0(_u19) | ~aNaturalNumber0(_u18) | ( sdtasdt0(sdtpldt0(_u19, _u18), _u20) = sdtpldt0(sdtasdt0(_u19, _u20), sdtasdt0(_u18, _u20))) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mAddCanc ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mAddCanc-1, axiom, ( ~aNaturalNumber0(_u23) | ~aNaturalNumber0(_u22) | ~aNaturalNumber0(_u21) | ( _u22 = _u21) | ( sdtpldt0(_u23, _u22) != sdtpldt0(_u23, _u21)) )).
% 0.19/0.46 cnf(mAddCanc-2, axiom, ( ~aNaturalNumber0(_u23) | ~aNaturalNumber0(_u22) | ~aNaturalNumber0(_u21) | ( _u22 = _u21) | ( sdtpldt0(_u22, _u23) != sdtpldt0(_u21, _u23)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mMulCanc ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mMulCanc-1, axiom, ( ~aNaturalNumber0(_u26) | ( _u26 = sz00) | ~aNaturalNumber0(_u25) | ~aNaturalNumber0(_u24) | ( _u25 = _u24) | ( sdtasdt0(_u26, _u25) != sdtasdt0(_u26, _u24)) )).
% 0.19/0.46 cnf(mMulCanc-2, axiom, ( ~aNaturalNumber0(_u26) | ( _u26 = sz00) | ~aNaturalNumber0(_u25) | ~aNaturalNumber0(_u24) | ( _u25 = _u24) | ( sdtasdt0(_u25, _u26) != sdtasdt0(_u24, _u26)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mZeroAdd ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mZeroAdd-1, axiom, ( ~aNaturalNumber0(_u28) | ~aNaturalNumber0(_u27) | ( sdtpldt0(_u28, _u27) != sz00) | ( _u28 = sz00) )).
% 0.19/0.46 cnf(mZeroAdd-2, axiom, ( ~aNaturalNumber0(_u28) | ~aNaturalNumber0(_u27) | ( sdtpldt0(_u28, _u27) != sz00) | ( _u27 = sz00) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mZeroMul ( axiom ) converted to clauses:
% 0.19/0.46 cnf(mZeroMul-1, axiom, ( ~aNaturalNumber0(_u30) | ~aNaturalNumber0(_u29) | ( sdtasdt0(_u30, _u29) != sz00) | ( _u30 = sz00) | ( _u29 = sz00) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mDefLE ( definition ) converted to clauses:
% 0.19/0.46 cnf(mDefLE-1, definition, ( ~aNaturalNumber0(_u34) | ~aNaturalNumber0(_u33) | ~sdtlseqdt0(_u34, _u33) | aNaturalNumber0(skolem1(_u34, _u33)) )).
% 0.19/0.46 cnf(mDefLE-2, definition, ( ~aNaturalNumber0(_u34) | ~aNaturalNumber0(_u33) | ~sdtlseqdt0(_u34, _u33) | ( sdtpldt0(_u34, skolem1(_u34, _u33)) = _u33) )).
% 0.19/0.46 cnf(mDefLE-3, definition, ( ~aNaturalNumber0(_u34) | ~aNaturalNumber0(_u33) | ~aNaturalNumber0(_u32) | ( sdtpldt0(_u34, _u32) != _u33) | sdtlseqdt0(_u34, _u33) )).
% 0.19/0.46
% 0.19/0.46 % Formula: mDefDiff ( definition ) converted to clauses:
% 0.19/0.46 cnf(mDefDiff-1, definition, ( ~aNaturalNumber0(_u37) | ~aNaturalNumber0(_u36) | ~sdtlseqdt0(_u37, _u36) | ( _u38 != sdtmndt0(_u36, _u37)) | aNaturalNumber0(_u38) )).
% 0.19/0.46 cnf(mDefDiff-2, definition, ( ~aNaturalNumber0(_u37) | ~aNaturalNumber0(_u36) | ~sdtlseqdt0(_u37, _u36) | ( _u38 != sdtmndt0(_u36, _u37)) | ( sdtpldt0(_u37, _u38) = _u36) )).
% 0.19/0.46 cnf(mDefDiff-3, definition, ( ~aNaturalNumber0(_u37) | ~aNaturalNumber0(_u36) | ~sdtlseqdt0(_u37, _u36) | ~aNaturalNumber0(_u39) | ( sdtpldt0(_u37, _u39) != _u36) | ( _u39 = sdtmndt0(_u36, _u37)) )).
% 0.19/0.46
% 0.19/0.46 % Formula: m__718 ( hypothesis ) converted to clauses:
% 0.19/0.46 cnf(m__718-1, hypothesis, ( aNaturalNumber0(xm) )).
% 0.19/0.46
% 0.19/0.46 % Formula: m__ ( conjecture ) converted to clauses:
% 0.19/0.46 cnf(m__-1, negated_conjecture, ( ~aNaturalNumber0(_u40) | ( sdtpldt0(xm, _u40) != xm) )).
% 0.19/0.46 cnf(m__-2, negated_conjecture, ( ~sdtlseqdt0(xm, xm) )).
% 0.19/0.46
% 0.19/0.46 % Problem matrix:
% 0.19/0.46 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.19/0.46 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.19/0.46 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.19/0.46 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtpldt0(__eqx_0, __eqx_1) = sdtpldt0(__eqy_0, __eqy_1)) )).
% 0.19/0.46 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtasdt0(__eqx_0, __eqx_1) = sdtasdt0(__eqy_0, __eqy_1)) )).
% 0.19/0.46 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sdtmndt0(__eqx_0, __eqx_1) = sdtmndt0(__eqy_0, __eqy_1)) )).
% 0.19/0.46 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.19/0.46 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ~aNaturalNumber0(__eqx_0) | aNaturalNumber0(__eqy_0) )).
% 0.19/0.46 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~sdtlseqdt0(__eqx_0, __eqx_1) | sdtlseqdt0(__eqy_0, __eqy_1) )).
% 0.19/0.46 cnf(matrix-9, plain, ( aNaturalNumber0(sz00) )).
% 0.19/0.46 cnf(matrix-10, plain, ( aNaturalNumber0(sz10) )).
% 0.19/0.46 cnf(matrix-11, plain, ( ( sz10 != sz00) )).
% 0.19/0.46 cnf(matrix-12, plain, ( ~aNaturalNumber0(_u2) | ~aNaturalNumber0(_u1) | aNaturalNumber0(sdtpldt0(_u2, _u1)) )).
% 0.19/0.46 cnf(matrix-13, plain, ( ~aNaturalNumber0(_u4) | ~aNaturalNumber0(_u3) | aNaturalNumber0(sdtasdt0(_u4, _u3)) )).
% 0.19/0.46 cnf(matrix-14, plain, ( ~aNaturalNumber0(_u6) | ~aNaturalNumber0(_u5) | ( sdtpldt0(_u6, _u5) = sdtpldt0(_u5, _u6)) )).
% 0.19/0.46 cnf(matrix-15, plain, ( ~aNaturalNumber0(_u9) | ~aNaturalNumber0(_u8) | ~aNaturalNumber0(_u7) | ( sdtpldt0(sdtpldt0(_u9, _u8), _u7) = sdtpldt0(_u9, sdtpldt0(_u8, _u7))) )).
% 0.19/0.46 cnf(matrix-16, plain, ( ~aNaturalNumber0(_u10) | ( sdtpldt0(_u10, sz00) = _u10) )).
% 0.19/0.46 cnf(matrix-17, plain, ( ~aNaturalNumber0(_u10) | ( _u10 = sdtpldt0(sz00, _u10)) )).
% 0.19/0.46 cnf(matrix-18, plain, ( ~aNaturalNumber0(_u12) | ~aNaturalNumber0(_u11) | ( sdtasdt0(_u12, _u11) = sdtasdt0(_u11, _u12)) )).
% 0.19/0.46 cnf(matrix-19, plain, ( ~aNaturalNumber0(_u15) | ~aNaturalNumber0(_u14) | ~aNaturalNumber0(_u13) | ( sdtasdt0(sdtasdt0(_u15, _u14), _u13) = sdtasdt0(_u15, sdtasdt0(_u14, _u13))) )).
% 0.19/0.46 cnf(matrix-20, plain, ( ~aNaturalNumber0(_u16) | ( sdtasdt0(_u16, sz10) = _u16) )).
% 0.19/0.46 cnf(matrix-21, plain, ( ~aNaturalNumber0(_u16) | ( _u16 = sdtasdt0(sz10, _u16)) )).
% 0.19/0.46 cnf(matrix-22, plain, ( ~aNaturalNumber0(_u17) | ( sdtasdt0(_u17, sz00) = sz00) )).
% 0.19/0.46 cnf(matrix-23, plain, ( ~aNaturalNumber0(_u17) | ( sz00 = sdtasdt0(sz00, _u17)) )).
% 0.19/0.46 cnf(matrix-24, plain, ( ~aNaturalNumber0(_u20) | ~aNaturalNumber0(_u19) | ~aNaturalNumber0(_u18) | ( sdtasdt0(_u20, sdtpldt0(_u19, _u18)) = sdtpldt0(sdtasdt0(_u20, _u19), sdtasdt0(_u20, _u18))) )).
% 0.19/0.46 cnf(matrix-25, plain, ( ~aNaturalNumber0(_u20) | ~aNaturalNumber0(_u19) | ~aNaturalNumber0(_u18) | ( sdtasdt0(sdtpldt0(_u19, _u18), _u20) = sdtpldt0(sdtasdt0(_u19, _u20), sdtasdt0(_u18, _u20))) )).
% 0.19/0.46 cnf(matrix-26, plain, ( ~aNaturalNumber0(_u23) | ~aNaturalNumber0(_u22) | ~aNaturalNumber0(_u21) | ( _u22 = _u21) | ( sdtpldt0(_u23, _u22) != sdtpldt0(_u23, _u21)) )).
% 0.19/0.46 cnf(matrix-27, plain, ( ~aNaturalNumber0(_u23) | ~aNaturalNumber0(_u22) | ~aNaturalNumber0(_u21) | ( _u22 = _u21) | ( sdtpldt0(_u22, _u23) != sdtpldt0(_u21, _u23)) )).
% 0.19/0.46 cnf(matrix-28, plain, ( ~aNaturalNumber0(_u26) | ( _u26 = sz00) | ~aNaturalNumber0(_u25) | ~aNaturalNumber0(_u24) | ( _u25 = _u24) | ( sdtasdt0(_u26, _u25) != sdtasdt0(_u26, _u24)) )).
% 0.19/0.46 cnf(matrix-29, plain, ( ~aNaturalNumber0(_u26) | ( _u26 = sz00) | ~aNaturalNumber0(_u25) | ~aNaturalNumber0(_u24) | ( _u25 = _u24) | ( sdtasdt0(_u25, _u26) != sdtasdt0(_u24, _u26)) )).
% 0.19/0.46 cnf(matrix-30, plain, ( ~aNaturalNumber0(_u28) | ~aNaturalNumber0(_u27) | ( sdtpldt0(_u28, _u27) != sz00) | ( _u28 = sz00) )).
% 0.19/0.46 cnf(matrix-31, plain, ( ~aNaturalNumber0(_u28) | ~aNaturalNumber0(_u27) | ( sdtpldt0(_u28, _u27) != sz00) | ( _u27 = sz00) )).
% 0.19/0.46 cnf(matrix-32, plain, ( ~aNaturalNumber0(_u30) | ~aNaturalNumber0(_u29) | ( sdtasdt0(_u30, _u29) != sz00) | ( _u30 = sz00) | ( _u29 = sz00) )).
% 0.19/0.46 cnf(matrix-33, plain, ( ~aNaturalNumber0(_u34) | ~aNaturalNumber0(_u33) | ~sdtlseqdt0(_u34, _u33) | aNaturalNumber0(skolem1(_u34, _u33)) )).
% 0.19/0.46 cnf(matrix-34, plain, ( ~aNaturalNumber0(_u34) | ~aNaturalNumber0(_u33) | ~sdtlseqdt0(_u34, _u33) | ( sdtpldt0(_u34, skolem1(_u34, _u33)) = _u33) )).
% 0.19/0.46 cnf(matrix-35, plain, ( ~aNaturalNumber0(_u34) | ~aNaturalNumber0(_u33) | ~aNaturalNumber0(_u32) | ( sdtpldt0(_u34, _u32) != _u33) | sdtlseqdt0(_u34, _u33) )).
% 0.19/0.46 cnf(matrix-36, plain, ( ~aNaturalNumber0(_u37) | ~aNaturalNumber0(_u36) | ~sdtlseqdt0(_u37, _u36) | ( _u38 != sdtmndt0(_u36, _u37)) | aNaturalNumber0(_u38) )).
% 0.19/0.46 cnf(matrix-37, plain, ( ~aNaturalNumber0(_u37) | ~aNaturalNumber0(_u36) | ~sdtlseqdt0(_u37, _u36) | ( _u38 != sdtmndt0(_u36, _u37)) | ( sdtpldt0(_u37, _u38) = _u36) )).
% 0.19/0.46 cnf(matrix-38, plain, ( ~aNaturalNumber0(_u37) | ~aNaturalNumber0(_u36) | ~sdtlseqdt0(_u37, _u36) | ~aNaturalNumber0(_u39) | ( sdtpldt0(_u37, _u39) != _u36) | ( _u39 = sdtmndt0(_u36, _u37)) )).
% 0.19/0.46 cnf(matrix-39, plain, ( aNaturalNumber0(xm) )).
% 0.19/0.46 cnf(matrix-40, plain, ( ~aNaturalNumber0(_u40) | ( sdtpldt0(xm, _u40) != xm) )).
% 0.19/0.46 cnf(matrix-41, plain, ( ~sdtlseqdt0(xm, xm) )).
% 0.19/0.46
% 0.19/0.46 % Proof stack:
% 0.19/0.46 cnf(proof-stack, plain,
% 0.19/0.46 proof_stack(
% 0.19/0.46 start(41),
% 0.19/0.46 left_branch(0, 35, 4, 2),
% 0.19/0.46 left_branch(0, 39, 0, 3),
% 0.19/0.46 right_branch(3),
% 0.19/0.46 left_branch(0, 16, 1, 4),
% 0.19/0.46 lemmata(0, 0),
% 0.19/0.46 right_branch(4),
% 0.19/0.46 left_branch(0, 9, 0, 5),
% 0.19/0.46 right_branch(5),
% 0.19/0.46 lemmata(0, 0),
% 0.19/0.46 right_branch(2)
% 0.19/0.46 )).
% 0.19/0.46 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------