%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM426+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 04:57:17 PM UTC 2026
% Result : Theorem 1.58s 1.82s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 54 unt; 0 def)
% Number of atoms : 215 ( 96 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 182 ( 73 ~; 71 |; 27 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__724,hypothesis,
( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__724) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
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/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(m__747,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
fof(m__704,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
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/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(m__,conjecture,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_16,hypothesis,
( aInteger0(esk2_0)
& sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__724])]) ).
fof(c_0_17,plain,
! [X40,X41] :
( ~ aInteger0(X40)
| ~ aInteger0(X41)
| aInteger0(sdtpldt0(X40,X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
fof(c_0_18,plain,
! [X51,X52,X53] :
( ~ aInteger0(X51)
| ~ aInteger0(X52)
| ~ aInteger0(X53)
| sdtasdt0(X51,sdtasdt0(X52,X53)) = sdtasdt0(sdtasdt0(X51,X52),X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_19,hypothesis,
sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,hypothesis,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__747]) ).
cnf(c_0_21,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__704]) ).
fof(c_0_23,plain,
! [X39] :
( ~ aInteger0(X39)
| aInteger0(smndt0(X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_24,plain,
! [X61] :
( ( sdtasdt0(smndt0(sz10),X61) = smndt0(X61)
| ~ aInteger0(X61) )
& ( smndt0(X61) = sdtasdt0(X61,smndt0(sz10))
| ~ aInteger0(X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_25,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,hypothesis,
sdtasdt0(xq,esk2_0) = sdtasdt0(xq,xn),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,hypothesis,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_29,hypothesis,
( aInteger0(sdtasdt0(xq,xn))
| ~ aInteger0(smndt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22])]) ).
cnf(c_0_30,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_32,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,hypothesis,
( sdtasdt0(sdtasdt0(xq,xn),X1) = sdtasdt0(xq,sdtasdt0(esk2_0,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_34,hypothesis,
aInteger0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,hypothesis,
( sdtasdt0(xq,sdtasdt0(esk2_0,smndt0(sz10))) = smndt0(sdtasdt0(xq,xn))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_36,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_37,plain,
! [X50] :
( ( sdtpldt0(X50,smndt0(X50)) = sz00
| ~ aInteger0(X50) )
& ( sz00 = sdtpldt0(smndt0(X50),X50)
| ~ aInteger0(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_38,hypothesis,
sdtasdt0(xq,sdtasdt0(esk2_0,smndt0(sz10))) = smndt0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_36])]) ).
fof(c_0_39,plain,
! [X57,X58,X59] :
( ( sdtasdt0(X57,sdtpldt0(X58,X59)) = sdtpldt0(sdtasdt0(X57,X58),sdtasdt0(X57,X59))
| ~ aInteger0(X57)
| ~ aInteger0(X58)
| ~ aInteger0(X59) )
& ( sdtasdt0(sdtpldt0(X57,X58),X59) = sdtpldt0(sdtasdt0(X57,X59),sdtasdt0(X58,X59))
| ~ aInteger0(X57)
| ~ aInteger0(X58)
| ~ aInteger0(X59) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_40,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,hypothesis,
smndt0(sdtasdt0(xq,xn)) = sdtasdt0(xq,smndt0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_27])]) ).
cnf(c_0_42,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,hypothesis,
sdtpldt0(sdtasdt0(xq,smndt0(esk2_0)),sdtasdt0(xq,xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34])]) ).
cnf(c_0_44,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__747]) ).
fof(c_0_45,plain,
! [X62,X63] :
( ~ aInteger0(X62)
| ~ aInteger0(X63)
| sdtasdt0(X62,X63) != sz00
| X62 = sz00
| X63 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_46,hypothesis,
( sdtasdt0(xq,sdtpldt0(smndt0(esk2_0),xn)) = sz00
| ~ aInteger0(smndt0(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_28])]) ).
cnf(c_0_47,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(xq,sdtpldt0(smndt0(esk2_0),xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_30]),c_0_27])]) ).
cnf(c_0_49,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__704]) ).
cnf(c_0_50,hypothesis,
( sdtpldt0(smndt0(esk2_0),xn) = sz00
| ~ aInteger0(sdtpldt0(smndt0(esk2_0),xn)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_28])]),c_0_49]) ).
fof(c_0_51,plain,
! [X47,X48] :
( ~ aInteger0(X47)
| ~ aInteger0(X48)
| sdtpldt0(X47,X48) = sdtpldt0(X48,X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_52,hypothesis,
( sdtpldt0(smndt0(esk2_0),xn) = sz00
| ~ aInteger0(smndt0(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_21]),c_0_44])]) ).
fof(c_0_53,plain,
! [X44,X45,X46] :
( ~ aInteger0(X44)
| ~ aInteger0(X45)
| ~ aInteger0(X46)
| sdtpldt0(X44,sdtpldt0(X45,X46)) = sdtpldt0(sdtpldt0(X44,X45),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_54,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,hypothesis,
sdtpldt0(smndt0(esk2_0),xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_30]),c_0_27])]) ).
cnf(c_0_56,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,hypothesis,
( sdtpldt0(xn,smndt0(esk2_0)) = sz00
| ~ aInteger0(smndt0(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_44])]) ).
cnf(c_0_58,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_30]) ).
cnf(c_0_59,hypothesis,
sdtpldt0(xn,smndt0(esk2_0)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_30]),c_0_27])]) ).
fof(c_0_60,plain,
! [X49] :
( ( sdtpldt0(X49,sz00) = X49
| ~ aInteger0(X49) )
& ( X49 = sdtpldt0(sz00,X49)
| ~ aInteger0(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_61,hypothesis,
( sdtpldt0(smndt0(xn),sz00) = sdtpldt0(sz00,smndt0(esk2_0))
| ~ aInteger0(smndt0(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44])]) ).
cnf(c_0_62,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_63,hypothesis,
sdtpldt0(smndt0(xn),sz00) = sdtpldt0(sz00,smndt0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_30]),c_0_27])]) ).
cnf(c_0_64,hypothesis,
( sdtpldt0(sz00,smndt0(esk2_0)) = smndt0(xn)
| ~ aInteger0(smndt0(xn)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_65,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,hypothesis,
sdtpldt0(sz00,smndt0(esk2_0)) = smndt0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_30]),c_0_44])]) ).
cnf(c_0_67,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_68,hypothesis,
( smndt0(esk2_0) = smndt0(xn)
| ~ aInteger0(smndt0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,hypothesis,
( aInteger0(sdtpldt0(sz00,smndt0(esk2_0)))
| ~ aInteger0(smndt0(xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_63]),c_0_67])]) ).
cnf(c_0_70,hypothesis,
smndt0(esk2_0) = smndt0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_30]),c_0_27])]) ).
cnf(c_0_71,hypothesis,
aInteger0(sdtpldt0(sz00,smndt0(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_30]),c_0_44])]) ).
cnf(c_0_72,hypothesis,
sdtpldt0(smndt0(xn),xn) = sz00,
inference(rw,[status(thm)],[c_0_55,c_0_70]) ).
cnf(c_0_73,hypothesis,
aInteger0(smndt0(xn)),
inference(rw,[status(thm)],[c_0_71,c_0_66]) ).
cnf(c_0_74,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_20]),c_0_22])]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(smndt0(smndt0(xn)),sz00) = sdtpldt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_72]),c_0_44]),c_0_73])]) ).
cnf(c_0_76,hypothesis,
( sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_30]),c_0_31])]) ).
cnf(c_0_77,hypothesis,
( smndt0(smndt0(xn)) = sdtpldt0(sz00,xn)
| ~ aInteger0(smndt0(smndt0(xn))) ),
inference(spm,[status(thm)],[c_0_62,c_0_75]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_40]),c_0_31])]) ).
cnf(c_0_79,hypothesis,
smndt0(smndt0(xn)) = sdtpldt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_30]),c_0_73])]) ).
cnf(c_0_80,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_65]),c_0_67])]) ).
cnf(c_0_81,hypothesis,
sdtpldt0(xb,sdtasdt0(xq,xn)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_78]),c_0_31]),c_0_34])]) ).
cnf(c_0_82,hypothesis,
sdtpldt0(sdtpldt0(sz00,xn),sz00) = sdtpldt0(sz00,xn),
inference(rw,[status(thm)],[c_0_75,c_0_79]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(sz00,sdtpldt0(xa,sz00)) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_34]),c_0_31])]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(xn,sz00) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_65]),c_0_44])]) ).
cnf(c_0_85,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_56]),c_0_67])]),c_0_21]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_62]),c_0_22])]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(smndt0(xn),esk2_0) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_70]),c_0_27])]) ).
cnf(c_0_88,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_84]),c_0_67]),c_0_44])]) ).
cnf(c_0_89,hypothesis,
sdtpldt0(xa,sz00) = xa,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_83]),c_0_22]),c_0_67])]),c_0_86]) ).
cnf(c_0_90,hypothesis,
sdtpldt0(sz00,esk2_0) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_87]),c_0_27]),c_0_73])]),c_0_79]),c_0_88]),c_0_84]) ).
cnf(c_0_91,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = xa,
inference(rw,[status(thm)],[c_0_78,c_0_89]) ).
cnf(c_0_92,hypothesis,
esk2_0 = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_90]),c_0_27])]) ).
cnf(c_0_93,hypothesis,
aInteger0(sdtasdt0(xq,smndt0(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_41]),c_0_34])]) ).
cnf(c_0_94,hypothesis,
sdtpldt0(sdtasdt0(xq,smndt0(xn)),xa) = sdtpldt0(sz00,xb),
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_58,c_0_91]),c_0_41]),c_0_92]),c_0_31]),c_0_34])]) ).
cnf(c_0_95,hypothesis,
aInteger0(sdtasdt0(xq,smndt0(xn))),
inference(rw,[status(thm)],[c_0_93,c_0_70]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz00,xb)) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_94]),c_0_22]),c_0_95])]) ).
cnf(c_0_97,hypothesis,
sdtpldt0(xa,sdtasdt0(xq,smndt0(xn))) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_94]),c_0_22]),c_0_95])]) ).
cnf(c_0_98,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_65]),c_0_31])]) ).
cnf(c_0_99,hypothesis,
sdtpldt0(xa,sdtasdt0(xq,smndt0(xn))) = xb,
inference(rw,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_100,hypothesis,
sdtpldt0(sz00,sdtasdt0(xq,smndt0(xn))) = sdtpldt0(smndt0(xa),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_99]),c_0_95]),c_0_22])]) ).
fof(c_0_101,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_102,hypothesis,
sdtpldt0(smndt0(xa),xb) = sdtasdt0(xq,smndt0(xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_100]),c_0_95])]) ).
cnf(c_0_103,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_104,hypothesis,
~ aInteger0(smndt0(xa)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_102]),c_0_31])]),c_0_103]) ).
cnf(c_0_105,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_30]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM426+3 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 00:32:36 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.58/1.82 % Version : CSE_E---1.7
% 1.58/1.82 % Problem : theBenchmark.p
% 1.58/1.82 % SZS status Theorem for theBenchmark.p
% 1.58/1.82 % SZS output start CNFRefutation
% See solution above
% 1.58/1.82 % Total time : 1.374s
%------------------------------------------------------------------------------