%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM454+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:55:04 PM UTC 2026
% Result : Theorem 0.22s 5.77s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 104 ( 37 unt; 0 def)
% Number of atoms : 240 ( 106 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 236 ( 100 ~; 94 |; 28 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(c_0_17,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_18,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_19,plain,
! [X60] :
( ( ~ aInteger0(X60)
| sz00 = sdtpldt0(smndt0(X60),X60) )
& ( ~ aInteger0(X60)
| sdtpldt0(X60,smndt0(X60)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
fof(c_0_20,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
& sdtpldt0(sz10,xp) = smndt0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X64] :
( aInteger0(smndt0(X64))
| ~ aInteger0(X64) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_22,plain,
! [X54,X55,X56] :
( sdtpldt0(X54,sdtpldt0(X55,X56)) = sdtpldt0(sdtpldt0(X54,X55),X56)
| ~ aInteger0(X56)
| ~ aInteger0(X55)
| ~ aInteger0(X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_23,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_26,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(sz10,xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25])]) ).
fof(c_0_32,plain,
! [X59] :
( ( ~ aInteger0(X59)
| X59 = sdtpldt0(sz00,X59) )
& ( ~ aInteger0(X59)
| sdtpldt0(X59,sz00) = X59 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_33,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_30])]) ).
fof(c_0_34,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
cnf(c_0_35,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(sdtpldt0(sz10,xp),X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_30]),c_0_25])]) ).
cnf(c_0_36,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz00,sdtpldt0(sz10,xp)),
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_33,c_0_27]),c_0_24]),c_0_24]),c_0_30]),c_0_25])]) ).
fof(c_0_38,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
inference(fof_nnf,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_25])]) ).
cnf(c_0_40,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz10,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_30])]) ).
fof(c_0_41,plain,
! [X52,X53] :
( aInteger0(sdtpldt0(X52,X53))
| ~ aInteger0(X53)
| ~ aInteger0(X52) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
cnf(c_0_42,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_39]),c_0_25])]) ).
cnf(c_0_44,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sz00) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_45,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_46,plain,
! [X57,X58] :
( sdtpldt0(X57,X58) = sdtpldt0(X58,X57)
| ~ aInteger0(X58)
| ~ aInteger0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_47,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(sz10,sdtpldt0(xp,X1))) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_42]),c_0_25])]) ).
cnf(c_0_49,negated_conjecture,
sdtpldt0(sz10,sz00) = sz10,
inference(rw,[status(thm)],[c_0_39,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(xp,sz00)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_45]),c_0_42]),c_0_25])]) ).
cnf(c_0_51,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( ~ aInteger0(X1)
| ~ aInteger0(sdtpldt0(sz10,X1))
| aInteger0(sdtpldt0(sz00,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_30])]) ).
cnf(c_0_53,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_54,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz00,smndt0(xp)) = sdtpldt0(sz10,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_27]),c_0_49]),c_0_42])]) ).
cnf(c_0_55,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(sz00,xp)) = sdtpldt0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_45]),c_0_42])]) ).
cnf(c_0_56,negated_conjecture,
aInteger0(sdtpldt0(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_30]),c_0_42])]) ).
cnf(c_0_57,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_58,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| smndt0(xp) = sdtpldt0(sz10,sz10) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
sdtpldt0(sdtpldt0(sz10,xp),sdtpldt0(sz10,xp)) = sdtpldt0(sz00,sdtpldt0(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_55]),c_0_56])]) ).
cnf(c_0_60,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| aInteger0(sdtpldt0(sz10,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_54]),c_0_45])]) ).
fof(c_0_61,plain,
! [X81,X82,X83] :
( sdtasdt0(X81,sdtasdt0(X82,X83)) = sdtasdt0(sdtasdt0(X81,X82),X83)
| ~ aInteger0(X83)
| ~ aInteger0(X82)
| ~ aInteger0(X81) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_62,plain,
! [X47] :
( ( ~ aInteger0(X47)
| X47 = sdtasdt0(sz10,X47) )
& ( ~ aInteger0(X47)
| sdtasdt0(X47,sz10) = X47 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])])]) ).
fof(c_0_63,plain,
! [X48] :
( ( ~ aInteger0(X48)
| smndt0(X48) = sdtasdt0(X48,smndt0(sz10)) )
& ( ~ aInteger0(X48)
| sdtasdt0(smndt0(sz10),X48) = smndt0(X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).
cnf(c_0_64,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_57,c_0_24]) ).
cnf(c_0_65,negated_conjecture,
smndt0(xp) = sdtpldt0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_26]),c_0_42])]) ).
cnf(c_0_66,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz00,xp)) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_59]),c_0_42])]) ).
cnf(c_0_67,negated_conjecture,
aInteger0(sdtpldt0(sz10,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_26]),c_0_42])]) ).
cnf(c_0_68,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
( ~ aInteger0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( ~ aInteger0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,negated_conjecture,
sdtpldt0(sz10,sdtpldt0(sz10,sz10)) = sdtpldt0(sz10,xp),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_53]),c_0_42])]) ).
cnf(c_0_73,negated_conjecture,
sdtpldt0(sz00,sdtpldt0(sz10,sz10)) = sdtpldt0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_65]),c_0_65]),c_0_67])]) ).
cnf(c_0_74,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_25])]) ).
cnf(c_0_75,plain,
( ~ aInteger0(X1)
| sdtasdt0(sdtpldt0(sz10,xp),X1) = smndt0(X1) ),
inference(rw,[status(thm)],[c_0_70,c_0_24]) ).
cnf(c_0_76,negated_conjecture,
sdtpldt0(sz10,sz10) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_71]),c_0_59]),c_0_72]),c_0_72]),c_0_73]),c_0_67])]) ).
cnf(c_0_77,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz10,smndt0(X1)) = smndt0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_30])]) ).
cnf(c_0_78,negated_conjecture,
smndt0(xp) = xp,
inference(rw,[status(thm)],[c_0_65,c_0_76]) ).
fof(c_0_79,plain,
! [X84,X85] :
( sdtasdt0(X84,X85) = sdtasdt0(X85,X84)
| ~ aInteger0(X85)
| ~ aInteger0(X84) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
fof(c_0_80,plain,
! [X79,X80] :
( aInteger0(sdtasdt0(X79,X80))
| ~ aInteger0(X80)
| ~ aInteger0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).
cnf(c_0_81,negated_conjecture,
sdtasdt0(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_42])]) ).
cnf(c_0_82,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_83,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_84,plain,
( ~ aInteger0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_85,plain,
! [X87,X88] :
( X88 = sz00
| X87 = sz00
| sdtasdt0(X87,X88) != sz00
| ~ aInteger0(X88)
| ~ aInteger0(X87) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_86,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(sz10,sdtasdt0(xp,X1)) = sdtasdt0(xp,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_81]),c_0_42]),c_0_25])]) ).
cnf(c_0_87,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_68]),c_0_83]) ).
fof(c_0_88,plain,
! [X61,X62,X63] :
( ( ~ aInteger0(X63)
| ~ aInteger0(X62)
| ~ aInteger0(X61)
| sdtasdt0(sdtpldt0(X61,X62),X63) = sdtpldt0(sdtasdt0(X61,X63),sdtasdt0(X62,X63)) )
& ( ~ aInteger0(X63)
| ~ aInteger0(X62)
| ~ aInteger0(X61)
| sdtasdt0(X61,sdtpldt0(X62,X63)) = sdtpldt0(sdtasdt0(X61,X62),sdtasdt0(X61,X63)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
cnf(c_0_89,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sdtpldt0(sz10,xp)) = smndt0(X1) ),
inference(rw,[status(thm)],[c_0_84,c_0_24]) ).
cnf(c_0_90,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(sz10,sdtasdt0(X1,xp)) = sdtasdt0(X1,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_82]),c_0_42])]) ).
cnf(c_0_92,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(X1,xp) = sdtasdt0(xp,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_81]),c_0_42]),c_0_25])]) ).
cnf(c_0_93,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_94,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sdtpldt0(sz10,xp))) = smndt0(sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_68]),c_0_30])]),c_0_83]) ).
cnf(c_0_95,negated_conjecture,
sdtpldt0(xp,sdtpldt0(sz10,sz10)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_65]),c_0_42])]) ).
cnf(c_0_96,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| X3 = sz00
| sdtasdt0(X1,X2) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_68]),c_0_83]) ).
cnf(c_0_97,negated_conjecture,
sdtasdt0(sz10,sdtasdt0(xp,xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_42])]) ).
cnf(c_0_98,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_99,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,sdtpldt0(sz10,xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_89]),c_0_30])]) ).
cnf(c_0_100,negated_conjecture,
sdtasdt0(xp,sdtpldt0(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_94]),c_0_81]),c_0_65]),c_0_76]),c_0_30]),c_0_42]),c_0_25])]) ).
cnf(c_0_101,negated_conjecture,
sdtpldt0(xp,xp) = sz00,
inference(rw,[status(thm)],[c_0_95,c_0_76]) ).
cnf(c_0_102,negated_conjecture,
sdtasdt0(xp,xp) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_81]),c_0_42]),c_0_25])]),c_0_98]) ).
cnf(c_0_103,negated_conjecture,
$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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_65]),c_0_76]),c_0_101]),c_0_59]),c_0_72]),c_0_72]),c_0_30]),c_0_42])]),c_0_102]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM454+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.46 % Computer : n020.cluster.edu
% 0.17/5.46 % Model : x86_64 x86_64
% 0.17/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.46 % Memory : 8046.5625MB
% 0.17/5.46 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Mon Sep 21 02:32:23 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/5.53 Running first-order theorem proving
% 0.22/5.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/5.77 % Version: 3.5.1
% 0.22/5.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.77 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.77 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.77 % Starting sh5l with 300s (1) cores
% 0.22/5.77 % new_bool_3 with pid 1802048 completed with status 0
% 0.22/5.77 % Result found by new_bool_3
% 0.22/5.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.77 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.77 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.22/5.77 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.77 % Starting SubtermCWHack with 31s (1) cores
% 0.22/5.77 % SubtermCWHack with pid 1802051 completed with status 0
% 0.22/5.77 % Result found by SubtermCWHack
% 0.22/5.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/5.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/5.77 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/5.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/5.77 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.22/5.77 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/5.77 % Starting SubtermCWHack with 31s (1) cores
% 0.22/5.77 % Preprocessing time : 0.002 s
% 0.22/5.77
% 0.22/5.77 % Proof found!
% 0.22/5.77 % SZS status Theorem
% 0.22/5.77 % SZS output start CNFRefutation
% See solution above
% 0.22/5.77 % Parsed axioms : 49
% 0.22/5.77 % Removed by relevancy pruning/SinE : 8
% 0.22/5.77 % Initial clauses : 94
% 0.22/5.77 % Removed in clause preprocessing : 4
% 0.22/5.77 % Initial clauses in saturation : 90
% 0.22/5.77 % Processed clauses : 2222
% 0.22/5.77 % ...of these trivial : 47
% 0.22/5.77 % ...subsumed : 1688
% 0.22/5.77 % ...remaining for further processing : 487
% 0.22/5.77 % Other redundant clauses eliminated : 18
% 0.22/5.77 % Clauses deleted for lack of memory : 0
% 0.22/5.77 % Backward-subsumed : 3
% 0.22/5.77 % Backward-rewritten : 39
% 0.22/5.77 % Generated clauses : 15626
% 0.22/5.77 % ...of the previous two non-redundant : 12092
% 0.22/5.77 % ...aggressively subsumed : 0
% 0.22/5.77 % Contextual simplify-reflections : 90
% 0.22/5.77 % Paramodulations : 15608
% 0.22/5.77 % Factorizations : 0
% 0.22/5.77 % NegExts : 0
% 0.22/5.77 % Equation resolutions : 18
% 0.22/5.77 % Disequality decompositions : 0
% 0.22/5.77 % Total rewrite steps : 21917
% 0.22/5.77 % ...of those cached : 21840
% 0.22/5.77 % Propositional unsat checks : 0
% 0.22/5.77 % Propositional check models : 0
% 0.22/5.77 % Propositional check unsatisfiable : 0
% 0.22/5.77 % Propositional clauses : 0
% 0.22/5.77 % Propositional clauses after purity: 0
% 0.22/5.77 % Propositional unsat core size : 0
% 0.22/5.77 % Propositional preprocessing time : 0.000
% 0.22/5.77 % Propositional encoding time : 0.000
% 0.22/5.77 % Propositional solver time : 0.000
% 0.22/5.77 % Success case prop preproc time : 0.000
% 0.22/5.77 % Success case prop encoding time : 0.000
% 0.22/5.77 % Success case prop solver time : 0.000
% 0.22/5.77 % Current number of processed clauses : 427
% 0.22/5.77 % Positive orientable unit clauses : 60
% 0.22/5.77 % Positive unorientable unit clauses: 0
% 0.22/5.77 % Negative unit clauses : 4
% 0.22/5.77 % Non-unit-clauses : 363
% 0.22/5.77 % Current number of unprocessed clauses: 9853
% 0.22/5.77 % ...number of literals in the above : 39484
% 0.22/5.77 % Current number of archived formulas : 0
% 0.22/5.77 % Current number of archived clauses : 42
% 0.22/5.77 % Clause-clause subsumption calls (NU) : 24872
% 0.22/5.77 % Rec. Clause-clause subsumption calls : 19347
% 0.22/5.77 % Non-unit clause-clause subsumptions : 1763
% 0.22/5.77 % Unit Clause-clause subsumption calls : 408
% 0.22/5.77 % Rewrite failures with RHS unbound : 0
% 0.22/5.77 % BW rewrite match attempts : 22
% 0.22/5.77 % BW rewrite match successes : 19
% 0.22/5.77 % Condensation attempts : 0
% 0.22/5.77 % Condensation successes : 0
% 0.22/5.77 % Termbank termtop insertions : 257456
% 0.22/5.77 % Search garbage collected termcells : 1636
% 0.22/5.77
% 0.22/5.77 % -------------------------------------------------
% 0.22/5.77 % User time : 0.195 s
% 0.22/5.77 % System time : 0.008 s
% 0.22/5.77 % Total time : 0.203 s
% 0.22/5.77 % Maximum resident set size: 3948 pages
% 0.22/5.77
% 0.22/5.77 % -------------------------------------------------
% 0.22/5.77 % User time : 0.198 s
% 0.22/5.77 % System time : 0.015 s
% 0.22/5.77 % Total time : 0.213 s
% 0.22/5.77 % Maximum resident set size: 4864 pages
% 0.22/5.77 % E exiting
%------------------------------------------------------------------------------