%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM421+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.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 : Tue May 5 04:57:16 PM UTC 2026
% Result : Theorem 122.96s 90.76s
% Output : CNFRefutation 124.06s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 55)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtasdt0(xa,sz00) = sz00
& sz00 = sdtasdt0(sz00,xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__419,hypothesis,
aInteger0(xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__419) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(i_0_15,negated_conjecture,
~ ( sdtasdt0(xa,sz00) = sz00
& sz00 = sdtasdt0(sz00,xa) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_16,plain,
! [X44,X45,X46] :
( ( sdtasdt0(X44,sdtpldt0(X45,X46)) = sdtpldt0(sdtasdt0(X44,X45),sdtasdt0(X44,X46))
| ~ aInteger0(X44)
| ~ aInteger0(X45)
| ~ aInteger0(X46) )
& ( sdtasdt0(sdtpldt0(X44,X45),X46) = sdtpldt0(sdtasdt0(X44,X46),sdtasdt0(X45,X46))
| ~ aInteger0(X44)
| ~ aInteger0(X45)
| ~ aInteger0(X46) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
fof(i_0_17,plain,
! [X38,X39,X40] :
( ~ aInteger0(X38)
| ~ aInteger0(X39)
| ~ aInteger0(X40)
| sdtasdt0(X38,sdtasdt0(X39,X40)) = sdtasdt0(sdtasdt0(X38,X39),X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_18,plain,
! [X31,X32,X33] :
( ~ aInteger0(X31)
| ~ aInteger0(X32)
| ~ aInteger0(X33)
| sdtpldt0(X31,sdtpldt0(X32,X33)) = sdtpldt0(sdtpldt0(X31,X32),X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_19,plain,
! [X29,X30] :
( ~ aInteger0(X29)
| ~ aInteger0(X30)
| aInteger0(sdtasdt0(X29,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
fof(i_0_20,plain,
! [X27,X28] :
( ~ aInteger0(X27)
| ~ aInteger0(X28)
| aInteger0(sdtpldt0(X27,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
fof(i_0_21,plain,
! [X41,X42] :
( ~ aInteger0(X41)
| ~ aInteger0(X42)
| sdtasdt0(X41,X42) = sdtasdt0(X42,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_22,plain,
! [X34,X35] :
( ~ aInteger0(X34)
| ~ aInteger0(X35)
| sdtpldt0(X34,X35) = sdtpldt0(X35,X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_23,negated_conjecture,
( sdtasdt0(xa,sz00) != sz00
| sz00 != sdtasdt0(sz00,xa) ),
inference(fof_nnf,[status(thm)],[i_0_15]) ).
fof(i_0_24,plain,
! [X37] :
( ( sdtpldt0(X37,smndt0(X37)) = sz00
| ~ aInteger0(X37) )
& ( sz00 = sdtpldt0(smndt0(X37),X37)
| ~ aInteger0(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(i_0_25,plain,
! [X43] :
( ( sdtasdt0(X43,sz10) = X43
| ~ aInteger0(X43) )
& ( X43 = sdtasdt0(sz10,X43)
| ~ aInteger0(X43) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
fof(i_0_26,plain,
! [X36] :
( ( sdtpldt0(X36,sz00) = X36
| ~ aInteger0(X36) )
& ( X36 = sdtpldt0(sz00,X36)
| ~ aInteger0(X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(i_0_27,plain,
! [X26] :
( ~ aInteger0(X26)
| aInteger0(smndt0(X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(i_0_28,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_29,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_34,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_35,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_36,negated_conjecture,
( sdtasdt0(xa,sz00) != sz00
| sz00 != sdtasdt0(sz00,xa) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_37,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_38,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_39,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_40,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_41,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_42,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_43,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_44,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__419]),
[final] ).
cnf(i_0_45,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]),
[final] ).
cnf(i_0_46,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]),
[final] ).
cnf(i_0_47,axiom,
X1 = X1 ).
cnf(i_0_48,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_49,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_50,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_52,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_53,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| ~ aInteger0(X1)
| aInteger0(X2) ) ).
cnf(i_0_61,plain,
aInteger0(smndt0(xa)),
inference(scs_inference,[],[i_0_44,i_0_43]) ).
cnf(i_0_63,plain,
sdtasdt0(xa,sz10) = xa,
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39]) ).
cnf(i_0_65,plain,
sdtpldt0(xa,sz00) = xa,
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40]) ).
cnf(i_0_67,plain,
xa = sdtasdt0(sz10,xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41]) ).
cnf(i_0_69,plain,
xa = sdtpldt0(sz00,xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42]) ).
cnf(i_0_71,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37]) ).
cnf(i_0_73,plain,
sz00 = sdtpldt0(smndt0(xa),xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38]) ).
cnf(i_0_75,plain,
aInteger0(sdtasdt0(xa,xa)),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32]) ).
cnf(i_0_77,plain,
aInteger0(sdtpldt0(xa,xa)),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33]) ).
cnf(i_0_79,plain,
sdtasdt0(xa,sdtasdt0(xa,xa)) = sdtasdt0(sdtasdt0(xa,xa),xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30]) ).
cnf(i_0_81,plain,
sdtpldt0(xa,sdtpldt0(xa,xa)) = sdtpldt0(sdtpldt0(xa,xa),xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31]) ).
cnf(i_0_83,plain,
sdtasdt0(sdtpldt0(xa,xa),xa) = sdtpldt0(sdtasdt0(xa,xa),sdtasdt0(xa,xa)),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28]) ).
cnf(i_0_85,plain,
sdtasdt0(xa,sdtpldt0(xa,xa)) = sdtpldt0(sdtasdt0(xa,xa),sdtasdt0(xa,xa)),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29]) ).
cnf(i_0_87,plain,
sdtasdt0(sdtasdt0(xa,sz10),X1) = sdtasdt0(xa,X1),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29,i_0_50]) ).
cnf(i_0_88,plain,
sdtasdt0(X1,sdtasdt0(xa,sz10)) = sdtasdt0(X1,xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29,i_0_50,i_0_51]) ).
cnf(i_0_89,plain,
sdtpldt0(sdtasdt0(xa,sz10),X1) = sdtpldt0(xa,X1),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_90,plain,
sdtpldt0(X1,sdtasdt0(xa,sz10)) = sdtpldt0(X1,xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29,i_0_50,i_0_51,i_0_52,i_0_53]) ).
cnf(i_0_91,plain,
sdtasdt0(xa,sz10) = sdtasdt0(sz10,xa),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29,i_0_50,i_0_51,i_0_52,i_0_53,i_0_49]) ).
cnf(i_0_92,plain,
aInteger0(sdtasdt0(sz10,xa)),
inference(scs_inference,[],[i_0_44,i_0_43,i_0_39,i_0_40,i_0_41,i_0_42,i_0_37,i_0_38,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29,i_0_50,i_0_51,i_0_52,i_0_53,i_0_49,i_0_54]) ).
cnf(i_0_573,plain,
aInteger0(smndt0(sz10)),
inference(scs_inference,[],[i_0_45,i_0_43]) ).
cnf(i_0_575,plain,
sz10 = sdtasdt0(sz10,sz10),
inference(scs_inference,[],[i_0_45,i_0_43,i_0_41]) ).
cnf(i_0_577,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(scs_inference,[],[i_0_45,i_0_43,i_0_41,i_0_39]) ).
cnf(i_0_579,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(scs_inference,[],[i_0_45,i_0_43,i_0_41,i_0_39,i_0_40]) ).
cnf(i_0_581,plain,
sz00 = sdtpldt0(sz00,sz00),
inference(scs_inference,[],[i_0_45,i_0_46,i_0_43,i_0_41,i_0_39,i_0_40,i_0_42]) ).
cnf(i_0_56,plain,
aInteger0(xa),
inference(equality_inference,[],[55]) ).
cnf(i_0_58,plain,
aInteger0(sz10),
inference(equality_inference,[],[57]) ).
cnf(i_0_60,plain,
aInteger0(sz00),
inference(equality_inference,[],[59]) ).
cnf(i_0_93,plain,
aInteger0(smndt0(sdtasdt0(sz10,xa))),
inference(scs_inference,[],[i_0_92,i_0_43]) ).
cnf(i_0_95,plain,
sdtasdt0(sz10,xa) = sdtasdt0(sz10,sdtasdt0(sz10,xa)),
inference(scs_inference,[],[i_0_92,i_0_43,i_0_41]) ).
cnf(i_0_97,plain,
sdtasdt0(sz10,xa) = sdtpldt0(sz00,sdtasdt0(sz10,xa)),
inference(scs_inference,[],[i_0_92,i_0_43,i_0_41,i_0_42]) ).
cnf(i_0_99,plain,
sdtpldt0(sdtasdt0(sz10,xa),smndt0(sdtasdt0(sz10,xa))) = sz00,
inference(scs_inference,[],[i_0_92,i_0_43,i_0_41,i_0_42,i_0_37]) ).
cnf(i_0_101,plain,
sz00 = sdtpldt0(smndt0(sdtasdt0(sz10,xa)),sdtasdt0(sz10,xa)),
inference(scs_inference,[],[i_0_92,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38]) ).
cnf(i_0_103,plain,
sdtasdt0(sdtasdt0(sz10,xa),sz10) = sdtasdt0(sz10,xa),
inference(scs_inference,[],[i_0_92,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39]) ).
cnf(i_0_105,plain,
sdtpldt0(sdtasdt0(sz10,xa),sz00) = sdtasdt0(sz10,xa),
inference(scs_inference,[],[i_0_92,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40]) ).
cnf(i_0_107,plain,
sdtasdt0(sdtasdt0(xa,sz10),X1) = sdtasdt0(sdtasdt0(sz10,xa),X1),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50]) ).
cnf(i_0_108,plain,
sdtasdt0(X1,sdtasdt0(xa,sz10)) = sdtasdt0(X1,sdtasdt0(sz10,xa)),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51]) ).
cnf(i_0_109,plain,
sdtpldt0(sdtasdt0(xa,sz10),X1) = sdtpldt0(sdtasdt0(sz10,xa),X1),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_110,plain,
sdtpldt0(X1,sdtasdt0(xa,sz10)) = sdtpldt0(X1,sdtasdt0(sz10,xa)),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53]) ).
cnf(i_0_111,plain,
aInteger0(sdtasdt0(sdtasdt0(sz10,xa),sdtasdt0(sz10,xa))),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32]) ).
cnf(i_0_113,plain,
aInteger0(sdtpldt0(sdtasdt0(sz10,xa),sdtasdt0(sz10,xa))),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32,i_0_33]) ).
cnf(i_0_119,plain,
sdtasdt0(sdtpldt0(sz10,sz10),sz10) = sdtpldt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_45,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28]) ).
cnf(i_0_121,plain,
sdtasdt0(sz10,sdtpldt0(sz10,sz10)) = sdtpldt0(sdtasdt0(sz10,sz10),sdtasdt0(sz10,sz10)),
inference(scs_inference,[],[i_0_92,i_0_91,i_0_45,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29]) ).
cnf(i_0_123,plain,
aInteger0(smndt0(smndt0(xa))),
inference(scs_inference,[],[i_0_61,i_0_43]) ).
cnf(i_0_125,plain,
smndt0(xa) = sdtasdt0(sz10,smndt0(xa)),
inference(scs_inference,[],[i_0_61,i_0_43,i_0_41]) ).
cnf(i_0_127,plain,
smndt0(xa) = sdtpldt0(sz00,smndt0(xa)),
inference(scs_inference,[],[i_0_61,i_0_43,i_0_41,i_0_42]) ).
cnf(i_0_129,plain,
sdtpldt0(smndt0(xa),smndt0(smndt0(xa))) = sz00,
inference(scs_inference,[],[i_0_61,i_0_43,i_0_41,i_0_42,i_0_37]) ).
cnf(i_0_131,plain,
sz00 = sdtpldt0(smndt0(smndt0(xa)),smndt0(xa)),
inference(scs_inference,[],[i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38]) ).
cnf(i_0_133,plain,
sdtasdt0(smndt0(xa),sz10) = smndt0(xa),
inference(scs_inference,[],[i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39]) ).
cnf(i_0_135,plain,
sdtpldt0(smndt0(xa),sz00) = smndt0(xa),
inference(scs_inference,[],[i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40]) ).
cnf(i_0_137,plain,
sdtasdt0(sdtpldt0(xa,sz00),X1) = sdtasdt0(xa,X1),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50]) ).
cnf(i_0_138,plain,
sdtasdt0(X1,sdtpldt0(xa,sz00)) = sdtasdt0(X1,xa),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51]) ).
cnf(i_0_139,plain,
sdtpldt0(sdtpldt0(xa,sz00),X1) = sdtpldt0(xa,X1),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_140,plain,
sdtpldt0(X1,sdtpldt0(xa,sz00)) = sdtpldt0(X1,xa),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53]) ).
cnf(i_0_141,plain,
aInteger0(sdtasdt0(smndt0(xa),smndt0(xa))),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32]) ).
cnf(i_0_143,plain,
aInteger0(sdtpldt0(smndt0(xa),smndt0(xa))),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32,i_0_33]) ).
cnf(i_0_149,plain,
sdtasdt0(sdtpldt0(sz00,sz00),sz00) = sdtpldt0(sdtasdt0(sz00,sz00),sdtasdt0(sz00,sz00)),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_46,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28]) ).
cnf(i_0_151,plain,
sdtasdt0(sz00,sdtpldt0(sz00,sz00)) = sdtpldt0(sdtasdt0(sz00,sz00),sdtasdt0(sz00,sz00)),
inference(scs_inference,[],[i_0_65,i_0_61,i_0_46,i_0_43,i_0_41,i_0_42,i_0_37,i_0_38,i_0_39,i_0_40,i_0_50,i_0_51,i_0_52,i_0_53,i_0_32,i_0_33,i_0_30,i_0_31,i_0_28,i_0_29]) ).
cnf(i_0_153,plain,
aInteger0(smndt0(sdtasdt0(xa,xa))),
inference(scs_inference,[],[i_0_75,i_0_43]) ).
cnf(i_0_155,plain,
sdtasdt0(xa,xa) = sdtasdt0(sz10,sdtasdt0(xa,xa)),
inference(scs_inference,[],[i_0_75,i_0_43,i_0_41]) ).
cnf(i_0_157,plain,
sdtasdt0(xa,xa) = sdtpldt0(sz00,sdtasdt0(xa,xa)),
inference(scs_inference,[],[i_0_75,i_0_43,i_0_41,i_0_42]) ).
cnf(i_0_159,plain,
sdtpldt0(sdtasdt0(xa,xa),smndt0(sdtasdt0(xa,xa))) = sz00,
inference(scs_inference,[],[i_0_75,i_0_43,i_0_41,i_0_42,i_0_37]) ).
cnf(c_0_88,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
i_0_34 ).
cnf(c_0_89,plain,
aInteger0(sz00),
i_0_46 ).
cnf(c_0_90,plain,
( sdtasdt0(X1,sz00) = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_91,hypothesis,
aInteger0(xa),
i_0_44 ).
cnf(c_0_92,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
i_0_35 ).
cnf(c_0_93,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
i_0_32 ).
cnf(c_0_94,hypothesis,
sdtasdt0(sz00,xa) = sdtasdt0(xa,sz00),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,hypothesis,
( sdtpldt0(X1,xa) = sdtpldt0(xa,X1)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_91]) ).
cnf(c_0_96,plain,
aInteger0(sdtasdt0(xa,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_91]),c_0_89])]) ).
cnf(c_0_97,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
i_0_29 ).
cnf(c_0_98,plain,
sdtasdt0(xa,sz10) = xa,
i_0_63 ).
cnf(c_0_99,plain,
aInteger0(sz10),
i_0_45 ).
cnf(c_0_100,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
i_0_42 ).
cnf(c_0_101,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
i_0_31 ).
cnf(c_0_102,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
i_0_38 ).
cnf(c_0_103,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
i_0_43 ).
cnf(c_0_104,hypothesis,
sdtpldt0(sdtasdt0(xa,sz00),xa) = sdtpldt0(xa,sdtasdt0(xa,sz00)),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_105,plain,
( sdtpldt0(sdtasdt0(xa,X1),xa) = sdtasdt0(xa,sdtpldt0(X1,sz10))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_91])]) ).
cnf(c_0_106,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(spm,[status(thm)],[c_0_100,c_0_99]) ).
cnf(c_0_107,negated_conjecture,
( sdtasdt0(xa,sz00) != sz00
| sz00 != sdtasdt0(sz00,xa) ),
i_0_36 ).
cnf(c_0_108,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).
cnf(c_0_109,hypothesis,
sdtpldt0(xa,sdtasdt0(xa,sz00)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_98]),c_0_89])]) ).
cnf(c_0_110,plain,
sz00 = sdtpldt0(smndt0(xa),xa),
i_0_73 ).
cnf(c_0_111,plain,
sdtpldt0(sz00,sdtasdt0(xa,sz00)) = sdtasdt0(xa,sz00),
inference(spm,[status(thm)],[c_0_100,c_0_96]) ).
cnf(c_0_112,negated_conjecture,
sdtasdt0(xa,sz00) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_94])]) ).
cnf(c_0_113,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_111]),c_0_96]),c_0_91])]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM421+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:32:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 122.96/90.76 % Version : CSE_E---1.7
% 122.96/90.76 % Problem : theBenchmark.p
% 122.96/90.76 % SZS status Theorem for theBenchmark.p
% 122.96/90.76 % SZS output start CNFRefutation
% See solution above
% 124.06/91.81 % Total time : 90.210s
%------------------------------------------------------------------------------