%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM421+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:49:01 PM UTC 2026
% Result : Theorem 143.24s 21.79s
% Output : CNFRefutation 143.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 117 ( 34 unt; 0 def)
% Number of atoms : 279 ( 103 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 298 ( 136 ~; 131 |; 20 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 140 ( 2 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
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/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__419,hypothesis,
aInteger0(xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__419) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(m__,conjecture,
( sz00 = sdtasdt0(sz00,xa)
& sdtasdt0(xa,sz00) = sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_15,plain,
! [X15] :
( ( ~ aInteger0(X15)
| X15 = sdtpldt0(sz00,X15) )
& ( ~ aInteger0(X15)
| sdtpldt0(X15,sz00) = X15 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
fof(c_0_16,plain,
! [X16] :
( ( ~ aInteger0(X16)
| sz00 = sdtpldt0(smndt0(X16),X16) )
& ( ~ aInteger0(X16)
| sdtpldt0(X16,smndt0(X16)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
cnf(c_0_17,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_20,plain,
! [X5] :
( aInteger0(smndt0(X5))
| ~ aInteger0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_21,plain,
! [X17,X18,X19] :
( sdtasdt0(X17,sdtasdt0(X18,X19)) = sdtasdt0(sdtasdt0(X17,X18),X19)
| ~ aInteger0(X19)
| ~ aInteger0(X18)
| ~ aInteger0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
fof(c_0_22,plain,
! [X22] :
( ( ~ aInteger0(X22)
| X22 = sdtasdt0(sz10,X22) )
& ( ~ aInteger0(X22)
| sdtasdt0(X22,sz10) = X22 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])])]) ).
fof(c_0_23,plain,
! [X8,X9] :
( aInteger0(sdtasdt0(X8,X9))
| ~ aInteger0(X9)
| ~ aInteger0(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).
fof(c_0_24,plain,
! [X6,X7] :
( aInteger0(sdtpldt0(X6,X7))
| ~ aInteger0(X7)
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
fof(c_0_25,plain,
! [X23,X24,X25] :
( ( ~ aInteger0(X25)
| ~ aInteger0(X24)
| ~ aInteger0(X23)
| sdtasdt0(sdtpldt0(X23,X24),X25) = sdtpldt0(sdtasdt0(X23,X25),sdtasdt0(X24,X25)) )
& ( ~ aInteger0(X25)
| ~ aInteger0(X24)
| ~ aInteger0(X23)
| sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
cnf(c_0_26,plain,
( ~ aInteger0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( ~ aInteger0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,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_25]) ).
cnf(c_0_35,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19])]) ).
fof(c_0_36,plain,
! [X10,X11,X12] :
( sdtpldt0(X10,sdtpldt0(X11,X12)) = sdtpldt0(sdtpldt0(X10,X11),X12)
| ~ aInteger0(X12)
| ~ aInteger0(X11)
| ~ aInteger0(X10) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_37,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_28,c_0_29]),c_0_30])]) ).
cnf(c_0_38,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_30])]),c_0_32]) ).
cnf(c_0_39,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| aInteger0(sdtasdt0(X1,sdtpldt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32]),c_0_32]) ).
cnf(c_0_40,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_35]),c_0_19])]) ).
fof(c_0_41,plain,
! [X20,X21] :
( sdtasdt0(X20,X21) = sdtasdt0(X21,X20)
| ~ aInteger0(X21)
| ~ aInteger0(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_42,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz10,X1) = sdtasdt0(X1,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_30])]) ).
cnf(c_0_44,plain,
( ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_19])]) ).
cnf(c_0_45,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_18]),c_0_27]) ).
cnf(c_0_47,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_30])]) ).
cnf(c_0_48,plain,
( ~ aInteger0(X1)
| aInteger0(sdtasdt0(sz10,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_43]),c_0_30])]) ).
cnf(c_0_49,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_30])]) ).
cnf(c_0_50,plain,
( ~ aInteger0(X1)
| aInteger0(sdtasdt0(sz00,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_19])]) ).
cnf(c_0_51,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| sdtpldt0(smndt0(sdtasdt0(X1,X2)),sdtasdt0(X1,sdtpldt0(X2,X3))) = sdtpldt0(sz00,sdtasdt0(X1,X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_32]),c_0_32]) ).
cnf(c_0_52,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(sdtasdt0(sz10,X1)),sdtasdt0(sz10,sdtpldt0(X1,X2))) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_53,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz00,sdtpldt0(X1,sz10)) = sdtasdt0(sz00,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_49]),c_0_19])]),c_0_50]) ).
cnf(c_0_54,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_55,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_30])]) ).
cnf(c_0_56,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__419]) ).
cnf(c_0_57,plain,
sdtasdt0(sz00,sz10) = sdtasdt0(sz00,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_19]),c_0_30])]) ).
cnf(c_0_58,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtasdt0(sz10,xa)) = sdtpldt0(sz00,xa) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_57]),c_0_19])]) ).
cnf(c_0_60,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_30])]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(sz00,sdtasdt0(sz10,xa)) = sdtpldt0(sz00,xa),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_62,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_59]),c_0_19])]) ).
cnf(c_0_63,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_45,c_0_28]),c_0_32]) ).
cnf(c_0_64,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz00,sdtasdt0(sz00,X1)) = sdtasdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_59]),c_0_19])]) ).
fof(c_0_65,plain,
! [X13,X14] :
( sdtpldt0(X13,X14) = sdtpldt0(X14,X13)
| ~ aInteger0(X14)
| ~ aInteger0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_66,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(rw,[status(thm)],[c_0_57,c_0_59]) ).
cnf(c_0_67,hypothesis,
sdtasdt0(sz10,sdtpldt0(sz00,xa)) = sdtpldt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_56]),c_0_19])]) ).
cnf(c_0_68,plain,
sdtasdt0(sz10,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_62]),c_0_19]),c_0_30])]) ).
cnf(c_0_69,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_43]),c_0_30])]) ).
cnf(c_0_70,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_30])]) ).
cnf(c_0_71,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| aInteger0(sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_32]) ).
cnf(c_0_72,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz00,X1) = sdtasdt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_59]),c_0_19])]) ).
cnf(c_0_73,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_66]),c_0_30]),c_0_19])]) ).
cnf(c_0_75,hypothesis,
sdtasdt0(sz10,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_54]),c_0_56])]) ).
cnf(c_0_76,plain,
sdtpldt0(sz00,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,sz10),
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_51,c_0_68]),c_0_62]),c_0_35]),c_0_69]),c_0_30]),c_0_19])]) ).
cnf(c_0_77,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_63]),c_0_30])]) ).
cnf(c_0_78,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| aInteger0(sdtasdt0(X1,sdtasdt0(sz00,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_19])]) ).
cnf(c_0_79,plain,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_19])]) ).
cnf(c_0_80,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_42]),c_0_33]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(xa,sz00) = sdtasdt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_56])]) ).
cnf(c_0_82,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_54]),c_0_30])]) ).
cnf(c_0_83,hypothesis,
sdtasdt0(xa,sz10) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_75]),c_0_75]),c_0_30]),c_0_56])]) ).
cnf(c_0_84,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(sz00,sdtasdt0(X1,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_63]),c_0_19])]) ).
cnf(c_0_85,plain,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_73]),c_0_19])]) ).
cnf(c_0_86,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_42]),c_0_19])]),c_0_33]) ).
cnf(c_0_87,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_54]),c_0_19])]) ).
cnf(c_0_88,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(X2,sz00) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_18]),c_0_27]) ).
cnf(c_0_89,hypothesis,
sdtpldt0(sdtasdt0(sz00,xa),xa) = xa,
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_49,c_0_81]),c_0_82]),c_0_83]),c_0_19]),c_0_56])]) ).
cnf(c_0_90,hypothesis,
aInteger0(sdtasdt0(sz00,xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_75]),c_0_30]),c_0_56])]) ).
cnf(c_0_91,plain,
( ~ aInteger0(X1)
| sdtpldt0(sz00,X1) = sdtpldt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_19])]) ).
cnf(c_0_92,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| sdtpldt0(sz00,sdtasdt0(X1,sdtpldt0(X2,X3))) = sdtasdt0(X1,sdtpldt0(X2,X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_34]),c_0_32]),c_0_32]) ).
fof(c_0_93,negated_conjecture,
~ ( sz00 = sdtasdt0(sz00,xa)
& sdtasdt0(xa,sz00) = sz00 ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_94,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_95,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_30])]) ).
cnf(c_0_96,plain,
sdtpldt0(sz10,sz00) = sz10,
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_88,c_0_82]),c_0_35]),c_0_82]),c_0_30]),c_0_19])]) ).
cnf(c_0_97,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_89]),c_0_56]),c_0_90])]) ).
cnf(c_0_98,plain,
( ~ aInteger0(X1)
| sdtpldt0(smndt0(X1),sdtpldt0(sz00,X1)) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_91]),c_0_40]),c_0_19])]) ).
cnf(c_0_99,plain,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(sz00,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_91]),c_0_19])]) ).
cnf(c_0_100,plain,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtasdt0(X1,sz00)) = sdtasdt0(X1,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_40]),c_0_19])]) ).
fof(c_0_101,negated_conjecture,
( sz00 != sdtasdt0(sz00,xa)
| sdtasdt0(xa,sz00) != sz00 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_93])]) ).
cnf(c_0_102,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(smndt0(sdtpldt0(X1,X2)))
| sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_42]),c_0_33]) ).
cnf(c_0_103,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_94]),c_0_27]) ).
cnf(c_0_104,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(smndt0(X1),sdtpldt0(X2,X1)) = sdtpldt0(X2,sz00) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_94]),c_0_27]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(xa,sdtasdt0(sz00,xa)) = xa,
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_95,c_0_81]),c_0_96]),c_0_83]),c_0_19]),c_0_56])]) ).
cnf(c_0_106,hypothesis,
sdtpldt0(xa,sz00) = xa,
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_88,c_0_97]),c_0_35]),c_0_97]),c_0_56]),c_0_19])]) ).
cnf(c_0_107,plain,
( ~ aInteger0(X1)
| sdtpldt0(sdtpldt0(sz00,X1),smndt0(X1)) = sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_98]),c_0_27]),c_0_99]) ).
cnf(c_0_108,hypothesis,
sdtpldt0(sz00,sdtasdt0(sz00,xa)) = sdtasdt0(sz00,xa),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_81]),c_0_56])]) ).
cnf(c_0_109,negated_conjecture,
( sz00 != sdtasdt0(sz00,xa)
| sdtasdt0(xa,sz00) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_110,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(sdtpldt0(smndt0(X1),X2))
| ~ aInteger0(smndt0(sdtpldt0(sz00,X2)))
| sdtpldt0(X1,sdtpldt0(sdtpldt0(smndt0(X1),X2),smndt0(sdtpldt0(sz00,X2)))) = sz00 ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,hypothesis,
sdtpldt0(smndt0(sdtasdt0(sz00,xa)),xa) = 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_90]),c_0_56])]) ).
cnf(c_0_112,hypothesis,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_97]),c_0_56])]) ).
cnf(c_0_113,hypothesis,
sdtpldt0(sdtasdt0(sz00,xa),sz00) = sdtasdt0(sz00,xa),
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_88,c_0_108]),c_0_35]),c_0_108]),c_0_90]),c_0_19])]) ).
cnf(c_0_114,negated_conjecture,
sdtasdt0(sz00,xa) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_45]),c_0_56]),c_0_19])]) ).
cnf(c_0_115,hypothesis,
~ aInteger0(smndt0(xa)),
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(spm,[status(thm)],[c_0_110,c_0_111]),c_0_97]),c_0_112]),c_0_113]),c_0_97]),c_0_56]),c_0_90])]),c_0_114]) ).
cnf(c_0_116,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_27]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM421+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 02:33:43 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 143.24/21.79 % Version: 3.5.1
% 143.24/21.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 143.24/21.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 143.24/21.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 143.24/21.79 % Starting new_bool_3 with 300s (1) cores
% 143.24/21.79 % Starting new_bool_1 with 300s (1) cores
% 143.24/21.79 % Starting sh5l with 300s (1) cores
% 143.24/21.79 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1999859 completed with status 0
% 143.24/21.79 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 143.24/21.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 143.24/21.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 143.24/21.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 143.24/21.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 143.24/21.79 % No SInE strategy applied
% 143.24/21.79 % Search class: FHHSF-FFSS21-SFFFFFNN
% 143.24/21.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 143.24/21.79 % Starting SubtermCWHack with 136s (1) cores
% 143.24/21.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 143.24/21.79 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 143.24/21.79 % Starting new_bool_3 with 136s (1) cores
% 143.24/21.79 % Starting new_bool_1 with 136s (1) cores
% 143.24/21.79 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1999864 completed with status 0
% 143.24/21.79 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 143.24/21.79 % Preprocessing class: FSMSSMSSSSSNFFN.
% 143.24/21.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 143.24/21.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 143.24/21.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 143.24/21.79 % No SInE strategy applied
% 143.24/21.79 % Search class: FHHSF-FFSS21-SFFFFFNN
% 143.24/21.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 143.24/21.79 % Starting SubtermCWHack with 136s (1) cores
% 143.24/21.79 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 143.24/21.79 % Preprocessing time : 0.002 s
% 143.24/21.79 % Presaturation interreduction done
% 143.24/21.79
% 143.24/21.79 % Proof found!
% 143.24/21.79 % SZS status Theorem
% 143.24/21.79 % SZS output start CNFRefutation
% See solution above
% 143.24/21.79 % Parsed axioms : 16
% 143.24/21.79 % Removed by relevancy pruning/SinE : 0
% 143.24/21.79 % Initial clauses : 20
% 143.24/21.79 % Removed in clause preprocessing : 1
% 143.24/21.79 % Initial clauses in saturation : 19
% 143.24/21.79 % Processed clauses : 12097
% 143.24/21.79 % ...of these trivial : 384
% 143.24/21.79 % ...subsumed : 10441
% 143.24/21.79 % ...remaining for further processing : 1272
% 143.24/21.79 % Other redundant clauses eliminated : 0
% 143.24/21.79 % Clauses deleted for lack of memory : 0
% 143.24/21.79 % Backward-subsumed : 24
% 143.24/21.79 % Backward-rewritten : 43
% 143.24/21.79 % Generated clauses : 715585
% 143.24/21.79 % ...of the previous two non-redundant : 698754
% 143.24/21.79 % ...aggressively subsumed : 0
% 143.24/21.79 % Contextual simplify-reflections : 716
% 143.24/21.79 % Paramodulations : 715585
% 143.24/21.79 % Factorizations : 0
% 143.24/21.79 % NegExts : 0
% 143.24/21.79 % Equation resolutions : 0
% 143.24/21.79 % Disequality decompositions : 0
% 143.24/21.79 % Total rewrite steps : 511738
% 143.24/21.79 % ...of those cached : 511623
% 143.24/21.79 % Propositional unsat checks : 0
% 143.24/21.79 % Propositional check models : 0
% 143.24/21.79 % Propositional check unsatisfiable : 0
% 143.24/21.79 % Propositional clauses : 0
% 143.24/21.79 % Propositional clauses after purity: 0
% 143.24/21.79 % Propositional unsat core size : 0
% 143.24/21.79 % Propositional preprocessing time : 0.000
% 143.24/21.79 % Propositional encoding time : 0.000
% 143.24/21.79 % Propositional solver time : 0.000
% 143.24/21.79 % Success case prop preproc time : 0.000
% 143.24/21.79 % Success case prop encoding time : 0.000
% 143.24/21.79 % Success case prop solver time : 0.000
% 143.24/21.79 % Current number of processed clauses : 1186
% 143.24/21.79 % Positive orientable unit clauses : 77
% 143.24/21.79 % Positive unorientable unit clauses: 0
% 143.24/21.79 % Negative unit clauses : 2
% 143.24/21.79 % Non-unit-clauses : 1107
% 143.24/21.79 % Current number of unprocessed clauses: 686417
% 143.24/21.79 % ...number of literals in the above : 4225414
% 143.24/21.79 % Current number of archived formulas : 0
% 143.24/21.79 % Current number of archived clauses : 86
% 143.24/21.79 % Clause-clause subsumption calls (NU) : 359626
% 143.24/21.79 % Rec. Clause-clause subsumption calls : 177120
% 143.24/21.79 % Non-unit clause-clause subsumptions : 11178
% 143.24/21.79 % Unit Clause-clause subsumption calls : 14
% 143.24/21.79 % Rewrite failures with RHS unbound : 0
% 143.24/21.79 % BW rewrite match attempts : 106
% 143.24/21.79 % BW rewrite match successes : 21
% 143.24/21.79 % Condensation attempts : 0
% 143.24/21.79 % Condensation successes : 0
% 143.24/21.79 % Termbank termtop insertions : 18458935
% 143.24/21.79 % Search garbage collected termcells : 194
% 143.24/21.79
% 143.24/21.79 % -------------------------------------------------
% 143.24/21.79 % User time : 19.582 s
% 143.24/21.79 % System time : 0.811 s
% 143.24/21.79 % Total time : 20.392 s
% 143.24/21.79 % Maximum resident set size: 3640 pages
% 143.24/21.79
% 143.24/21.79 % -------------------------------------------------
% 143.24/21.79 % User time : 98.141 s
% 143.24/21.79 % System time : 4.032 s
% 143.24/21.79 % Total time : 102.173 s
% 143.24/21.79 % Maximum resident set size: 4864 pages
% 143.24/21.79 % E exiting
%------------------------------------------------------------------------------