%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM426+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 : n007.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 01:49:02 PM UTC 2026
% Result : Theorem 154.53s 23.43s
% Output : CNFRefutation 154.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 22
% Syntax : Number of formulae : 172 ( 73 unt; 0 def)
% Number of atoms : 405 ( 159 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 401 ( 168 ~; 160 |; 50 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__704,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(m__747,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
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(m__724,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__724) ).
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(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
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(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
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(m__,conjecture,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_22,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__704]) ).
fof(c_0_23,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
inference(fof_simplification,[status(thm)],[mEquMod]) ).
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,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[mDivisor]) ).
fof(c_0_27,plain,
! [X35,X36,X37] :
( ( X37 = sz00
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| ~ aInteger0(X35)
| sdteqdtlpzmzozddtrp0(X35,X36,X37)
| ~ aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36))) )
& ( X37 = sz00
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| ~ aInteger0(X35)
| aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
| ~ sdteqdtlpzmzozddtrp0(X35,X36,X37) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,hypothesis,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__747]) ).
cnf(c_0_30,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,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_32,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])])]) ).
fof(c_0_33,plain,
! [X30,X31,X33,X34] :
( ( ~ aInteger0(X30)
| aDivisorOf0(X33,X30)
| sdtasdt0(X33,X34) != X30
| ~ aInteger0(X34)
| X33 = sz00
| ~ aInteger0(X33) )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| sdtasdt0(X31,esk1_2(X30,X31)) = X30 )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| aInteger0(esk1_2(X30,X31)) )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| X31 != sz00 )
& ( ~ aInteger0(X30)
| ~ aDivisorOf0(X31,X30)
| aInteger0(X31) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])])])]) ).
cnf(c_0_34,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(split_conjunct,[status(thm)],[m__724]) ).
cnf(c_0_36,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,hypothesis,
( ~ aInteger0(smndt0(xb))
| aInteger0(sdtasdt0(xq,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_40,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_42,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])])]) ).
cnf(c_0_43,plain,
( ~ aInteger0(X2)
| ~ aDivisorOf0(X1,X2)
| sdtasdt0(X1,esk1_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,hypothesis,
aDivisorOf0(xq,sdtasdt0(xq,xn)),
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_34,c_0_35]),c_0_29]),c_0_36]),c_0_37]),c_0_30])]),c_0_38]) ).
cnf(c_0_45,hypothesis,
aInteger0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_37])]) ).
cnf(c_0_46,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X2,X1)
| aInteger0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_47,hypothesis,
( ~ aInteger0(X1)
| ~ aInteger0(smndt0(xb))
| sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_30])]) ).
fof(c_0_48,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_49,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,hypothesis,
sdtasdt0(xq,esk1_2(sdtasdt0(xq,xn),xq)) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_51,hypothesis,
aInteger0(esk1_2(sdtasdt0(xq,xn),xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_44]),c_0_45])]) ).
fof(c_0_52,plain,
! [X26] :
( ( ~ aInteger0(X26)
| sz00 = sdtasdt0(sz00,X26) )
& ( ~ aInteger0(X26)
| sdtasdt0(X26,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])])]) ).
fof(c_0_53,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_54,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_55,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(xa,sdtpldt0(smndt0(xb),X1)) = sdtpldt0(sdtasdt0(xq,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_40]),c_0_37])]) ).
cnf(c_0_56,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(xq,sdtasdt0(esk1_2(sdtasdt0(xq,xn),xq),X1)) = sdtasdt0(sdtasdt0(xq,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_36])]) ).
cnf(c_0_58,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_60,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = sdtpldt0(xa,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_37])]) ).
fof(c_0_63,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_64,hypothesis,
sdtasdt0(sdtasdt0(xq,xn),sz00) = sdtasdt0(xq,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_51])]) ).
cnf(c_0_65,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_41,c_0_60]),c_0_59])]) ).
cnf(c_0_66,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_61,c_0_62]),c_0_37]),c_0_45])]) ).
cnf(c_0_67,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,hypothesis,
sdtasdt0(xq,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_64]),c_0_45])]) ).
cnf(c_0_70,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_65,c_0_66]),c_0_45]),c_0_37])]) ).
cnf(c_0_71,plain,
( ~ aInteger0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_56]),c_0_59])]) ).
cnf(c_0_72,hypothesis,
sdtasdt0(sz00,xq) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_59]),c_0_36])]) ).
fof(c_0_73,plain,
! [X27] :
( ( ~ aInteger0(X27)
| smndt0(X27) = sdtasdt0(X27,smndt0(sz10)) )
& ( ~ aInteger0(X27)
| sdtasdt0(smndt0(sz10),X27) = smndt0(X27) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).
cnf(c_0_74,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_67,c_0_41]),c_0_59])]),c_0_28]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(sz00,xa) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_67]),c_0_30])]) ).
cnf(c_0_76,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_40]),c_0_59])]) ).
cnf(c_0_77,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(sz00,sdtasdt0(xq,X1)) = sdtasdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_72]),c_0_36]),c_0_59])]) ).
cnf(c_0_78,plain,
( ~ aInteger0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_40]) ).
cnf(c_0_80,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_74,c_0_70]),c_0_30]),c_0_59])]),c_0_75]) ).
cnf(c_0_81,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_76]),c_0_59])]) ).
cnf(c_0_82,hypothesis,
( ~ aInteger0(smndt0(sz10))
| sdtasdt0(sz00,smndt0(xq)) = sdtasdt0(sz00,smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_36])]) ).
cnf(c_0_83,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(smndt0(xa),xa) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_59]),c_0_30])]) ).
cnf(c_0_85,plain,
( ~ aInteger0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(sz00,smndt0(xq)) = sdtasdt0(sz00,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_40]),c_0_83])]) ).
cnf(c_0_87,hypothesis,
( ~ aInteger0(smndt0(xa))
| sdtpldt0(smndt0(smndt0(xa)),sz00) = xa ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_84]),c_0_75]),c_0_30])]) ).
cnf(c_0_88,hypothesis,
( ~ aInteger0(smndt0(xq))
| sdtasdt0(sz00,smndt0(sz10)) = sz00 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,hypothesis,
sdtpldt0(smndt0(smndt0(xa)),sz00) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_40]),c_0_30])]) ).
cnf(c_0_90,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_85]),c_0_59])]) ).
cnf(c_0_91,hypothesis,
sdtasdt0(sz00,smndt0(sz10)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_40]),c_0_36])]) ).
cnf(c_0_92,hypothesis,
( ~ aInteger0(smndt0(smndt0(xa)))
| smndt0(smndt0(xa)) = xa ),
inference(spm,[status(thm)],[c_0_67,c_0_89]) ).
cnf(c_0_93,plain,
( ~ aInteger0(X1)
| ~ aInteger0(smndt0(sz10))
| sdtasdt0(sz00,smndt0(X1)) = sz00 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_78]),c_0_91]) ).
cnf(c_0_94,hypothesis,
( ~ aInteger0(smndt0(xa))
| smndt0(smndt0(xa)) = xa ),
inference(spm,[status(thm)],[c_0_92,c_0_40]) ).
fof(c_0_95,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_96,plain,
( ~ aInteger0(X1)
| sdtasdt0(sz00,smndt0(X1)) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_40]),c_0_83])]) ).
cnf(c_0_97,hypothesis,
smndt0(smndt0(xa)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_40]),c_0_30])]) ).
cnf(c_0_98,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_95]) ).
cnf(c_0_99,hypothesis,
( ~ aInteger0(smndt0(xa))
| sdtasdt0(sz00,xa) = sz00 ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_85]),c_0_59])]) ).
cnf(c_0_101,hypothesis,
sdtpldt0(xb,sdtasdt0(xq,xn)) = xa,
inference(rw,[status(thm)],[c_0_66,c_0_80]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(sz00,xa) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_40]),c_0_30])]) ).
fof(c_0_103,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])])])]) ).
cnf(c_0_104,hypothesis,
sdtpldt0(sdtasdt0(sz00,xb),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_45]),c_0_37])]) ).
fof(c_0_105,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])])]) ).
cnf(c_0_106,hypothesis,
( ~ aInteger0(X1)
| ~ aInteger0(smndt0(xb))
| sdtpldt0(xa,sdtpldt0(X1,smndt0(xb))) = sdtpldt0(sdtasdt0(xq,xn),X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_61]) ).
cnf(c_0_107,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_108,plain,
( ~ aInteger0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_109,hypothesis,
( ~ aInteger0(sdtasdt0(sz00,xb))
| sdtasdt0(sz00,xb) = sz00 ),
inference(spm,[status(thm)],[c_0_67,c_0_104]) ).
cnf(c_0_110,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_111,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(xa,sdtpldt0(X1,smndt0(xb))) = sdtpldt0(sdtasdt0(xq,xn),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_40]),c_0_37])]) ).
cnf(c_0_112,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xb) = xa,
inference(rw,[status(thm)],[c_0_62,c_0_80]) ).
cnf(c_0_113,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_83])]) ).
cnf(c_0_114,hypothesis,
sdtasdt0(sz00,xb) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_37]),c_0_59])]) ).
cnf(c_0_115,hypothesis,
sdtpldt0(sdtasdt0(xq,xn),xa) = sdtpldt0(xa,sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_29]),c_0_30])]) ).
cnf(c_0_116,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| aInteger0(sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_49]),c_0_110]) ).
cnf(c_0_117,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
fof(c_0_118,plain,
! [X28,X29] :
( X29 = sz00
| X28 = sz00
| sdtasdt0(X28,X29) != sz00
| ~ aInteger0(X29)
| ~ aInteger0(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_119,hypothesis,
sdtasdt0(sdtasdt0(xq,xn),sz00) = sz00,
inference(rw,[status(thm)],[c_0_64,c_0_69]) ).
cnf(c_0_120,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__747]) ).
cnf(c_0_121,hypothesis,
sdtpldt0(smndt0(sdtasdt0(xq,xn)),xa) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_112]),c_0_37]),c_0_45])]) ).
cnf(c_0_122,hypothesis,
sdtasdt0(sdtpldt0(sz00,sz10),xb) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_37]),c_0_59])]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(smndt0(sdtasdt0(xq,xn)),sdtpldt0(xa,sdtasdt0(xq,xn))) = xa,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_115]),c_0_30]),c_0_45])]),c_0_75]) ).
cnf(c_0_124,hypothesis,
aInteger0(sdtpldt0(xa,sdtasdt0(xq,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_115]),c_0_30]),c_0_45])]) ).
cnf(c_0_125,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,sdtasdt0(xq,xn))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_50]),c_0_51]),c_0_36])]) ).
cnf(c_0_126,plain,
( ~ aInteger0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_127,hypothesis,
sdtasdt0(sdtasdt0(xq,xn),sz10) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_117]),c_0_50]),c_0_83]),c_0_51])]) ).
cnf(c_0_128,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_129,hypothesis,
sdtasdt0(xq,sdtasdt0(xn,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_119]),c_0_59]),c_0_120]),c_0_36])]) ).
cnf(c_0_130,hypothesis,
( ~ aInteger0(smndt0(sdtasdt0(xq,xn)))
| sdtpldt0(xa,smndt0(sdtasdt0(xq,xn))) = sdtpldt0(sz00,xb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_121]),c_0_30])]) ).
cnf(c_0_131,hypothesis,
sdtpldt0(sz00,xb) = sdtasdt0(sz10,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_60]),c_0_83])]) ).
cnf(c_0_132,hypothesis,
( ~ aInteger0(smndt0(sdtasdt0(xq,xn)))
| sdtpldt0(sdtpldt0(xa,sdtasdt0(xq,xn)),smndt0(sdtasdt0(xq,xn))) = xa ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_123]),c_0_124])]) ).
cnf(c_0_133,hypothesis,
( ~ aInteger0(smndt0(sz10))
| aInteger0(smndt0(sdtasdt0(xq,xn))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_45])]) ).
cnf(c_0_134,hypothesis,
sdtasdt0(xq,sdtasdt0(xn,sz10)) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_127]),c_0_83]),c_0_120]),c_0_36])]) ).
cnf(c_0_135,hypothesis,
( ~ aInteger0(sdtasdt0(xn,sz00))
| sdtasdt0(xn,sz00) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_36])]),c_0_38]) ).
cnf(c_0_136,hypothesis,
sdtpldt0(xa,smndt0(sdtasdt0(xq,xn))) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_40]),c_0_45])]) ).
cnf(c_0_137,hypothesis,
sdtasdt0(sz10,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_131]),c_0_37])]) ).
cnf(c_0_138,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_28,c_0_98]),c_0_110]),c_0_110]) ).
cnf(c_0_139,hypothesis,
sdtpldt0(sdtpldt0(xa,sdtasdt0(xq,xn)),smndt0(sdtasdt0(xq,xn))) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_40]),c_0_45])]) ).
cnf(c_0_140,hypothesis,
aInteger0(smndt0(sdtasdt0(xq,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_40]),c_0_83])]) ).
cnf(c_0_141,hypothesis,
sdtasdt0(xq,sdtasdt0(sz10,xn)) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_68]),c_0_83]),c_0_120])]) ).
cnf(c_0_142,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_68,c_0_49]),c_0_110]) ).
cnf(c_0_143,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_98,c_0_117]),c_0_83])]) ).
cnf(c_0_144,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_110]),c_0_59]),c_0_120])]) ).
fof(c_0_145,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_146,hypothesis,
sdtpldt0(xa,smndt0(sdtasdt0(xq,xn))) = xb,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_131]),c_0_137]) ).
cnf(c_0_147,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]),c_0_124])]) ).
cnf(c_0_148,hypothesis,
sdtasdt0(sz10,sdtasdt0(xn,xq)) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_36]),c_0_120]),c_0_83])]) ).
cnf(c_0_149,hypothesis,
sdtasdt0(xn,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_59]),c_0_120])]) ).
fof(c_0_150,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(fof_simplification,[status(thm)],[c_0_145]) ).
cnf(c_0_151,hypothesis,
sdtpldt0(sz00,smndt0(sdtasdt0(xq,xn))) = sdtpldt0(smndt0(xa),xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_146]),c_0_140]),c_0_30])]) ).
cnf(c_0_152,hypothesis,
( ~ aInteger0(smndt0(sz10))
| aInteger0(smndt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_126]),c_0_30])]) ).
cnf(c_0_153,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(smndt0(sz10))
| sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_126]) ).
cnf(c_0_154,hypothesis,
( ~ aInteger0(sdtasdt0(xn,xq))
| sdtasdt0(xn,xq) = sdtasdt0(xq,xn) ),
inference(spm,[status(thm)],[c_0_108,c_0_148]) ).
cnf(c_0_155,hypothesis,
sdtpldt0(sz00,xn) = sdtasdt0(xn,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_60]),c_0_83])]) ).
fof(c_0_156,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(fof_nnf,[status(thm)],[c_0_150]) ).
cnf(c_0_157,hypothesis,
sdtpldt0(smndt0(xa),xb) = smndt0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_151]),c_0_140])]) ).
cnf(c_0_158,hypothesis,
aInteger0(smndt0(xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_40]),c_0_83])]) ).
cnf(c_0_159,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_40]),c_0_83])]) ).
cnf(c_0_160,hypothesis,
sdtasdt0(xn,xq) = sdtasdt0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_110]),c_0_36]),c_0_120])]) ).
cnf(c_0_161,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_155]),c_0_120])]) ).
cnf(c_0_162,negated_conjecture,
sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_163,hypothesis,
sdtpldt0(xb,smndt0(xa)) = smndt0(sdtasdt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_157]),c_0_37]),c_0_158])]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(smndt0(sz10),sdtasdt0(xq,xn)) = sdtasdt0(smndt0(xn),xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_36]),c_0_120])]) ).
cnf(c_0_165,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_161]),c_0_83]),c_0_120])]) ).
cnf(c_0_166,negated_conjecture,
smndt0(sdtasdt0(xq,xn)) != sdtasdt0(xq,smndt0(xn)),
inference(rw,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_167,hypothesis,
smndt0(sdtasdt0(xq,xn)) = sdtasdt0(smndt0(xn),xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_164]),c_0_45])]) ).
cnf(c_0_168,hypothesis,
( ~ aInteger0(smndt0(sz10))
| aInteger0(smndt0(xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_126]),c_0_120])]) ).
cnf(c_0_169,negated_conjecture,
sdtasdt0(smndt0(xn),xq) != sdtasdt0(xq,smndt0(xn)),
inference(rw,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_170,hypothesis,
aInteger0(smndt0(xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_40]),c_0_83])]) ).
cnf(c_0_171,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_68]),c_0_36]),c_0_170])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM426+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 02:26:20 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.55 Running first-order theorem proving
% 0.23/0.56 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
% 154.53/23.43 % Version: 3.5.1
% 154.53/23.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 154.53/23.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 154.53/23.43 % Starting new_bool_3 with 300s (1) cores
% 154.53/23.43 % Starting new_bool_1 with 300s (1) cores
% 154.53/23.43 % Starting sh5l with 300s (1) cores
% 154.53/23.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4166718 completed with status 0
% 154.53/23.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 154.53/23.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 154.53/23.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 154.53/23.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 154.53/23.43 % No SInE strategy applied
% 154.53/23.43 % Search class: FGHSF-FFMM21-SFFFFFNN
% 154.53/23.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 154.53/23.43 % Starting SubtermCWHack with 136s (1) cores
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 154.53/23.43 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 154.53/23.43 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 154.53/23.43 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 4166725 completed with status 0
% 154.53/23.43 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 154.53/23.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 154.53/23.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 154.53/23.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 154.53/23.43 % No SInE strategy applied
% 154.53/23.43 % Search class: FGHSF-FFMM21-SFFFFFNN
% 154.53/23.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 154.53/23.43 % Starting SubtermCWHack with 136s (1) cores
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 154.53/23.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 154.53/23.43 % Preprocessing time : 0.001 s
% 154.53/23.43 % Presaturation interreduction done
% 154.53/23.43
% 154.53/23.43 % Proof found!
% 154.53/23.43 % SZS status Theorem
% 154.53/23.43 % SZS output start CNFRefutation
% See solution above
% 154.53/23.43 % Parsed axioms : 24
% 154.53/23.43 % Removed by relevancy pruning/SinE : 0
% 154.53/23.43 % Initial clauses : 39
% 154.53/23.43 % Removed in clause preprocessing : 1
% 154.53/23.43 % Initial clauses in saturation : 38
% 154.53/23.43 % Processed clauses : 16524
% 154.53/23.43 % ...of these trivial : 4886
% 154.53/23.43 % ...subsumed : 6399
% 154.53/23.43 % ...remaining for further processing : 5239
% 154.53/23.43 % Other redundant clauses eliminated : 9
% 154.53/23.43 % Clauses deleted for lack of memory : 0
% 154.53/23.43 % Backward-subsumed : 30
% 154.53/23.43 % Backward-rewritten : 1405
% 154.53/23.43 % Generated clauses : 980674
% 154.53/23.43 % ...of the previous two non-redundant : 909303
% 154.53/23.43 % ...aggressively subsumed : 0
% 154.53/23.43 % Contextual simplify-reflections : 541
% 154.53/23.43 % Paramodulations : 980665
% 154.53/23.43 % Factorizations : 0
% 154.53/23.43 % NegExts : 0
% 154.53/23.43 % Equation resolutions : 9
% 154.53/23.43 % Disequality decompositions : 0
% 154.53/23.43 % Total rewrite steps : 1595077
% 154.53/23.43 % ...of those cached : 1591756
% 154.53/23.43 % Propositional unsat checks : 1
% 154.53/23.43 % Propositional check models : 0
% 154.53/23.43 % Propositional check unsatisfiable : 0
% 154.53/23.43 % Propositional clauses : 0
% 154.53/23.43 % Propositional clauses after purity: 0
% 154.53/23.43 % Propositional unsat core size : 0
% 154.53/23.43 % Propositional preprocessing time : 0.000
% 154.53/23.43 % Propositional encoding time : 2.656
% 154.53/23.43 % Propositional solver time : 1.808
% 154.53/23.43 % Success case prop preproc time : 0.000
% 154.53/23.43 % Success case prop encoding time : 0.000
% 154.53/23.43 % Success case prop solver time : 0.000
% 154.53/23.43 % Current number of processed clauses : 3764
% 154.53/23.43 % Positive orientable unit clauses : 2554
% 154.53/23.43 % Positive unorientable unit clauses: 0
% 154.53/23.43 % Negative unit clauses : 2
% 154.53/23.43 % Non-unit-clauses : 1208
% 154.53/23.43 % Current number of unprocessed clauses: 891240
% 154.53/23.43 % ...number of literals in the above : 3597241
% 154.53/23.43 % Current number of archived formulas : 0
% 154.53/23.43 % Current number of archived clauses : 1473
% 154.53/23.43 % Clause-clause subsumption calls (NU) : 199093
% 154.53/23.43 % Rec. Clause-clause subsumption calls : 106720
% 154.53/23.43 % Non-unit clause-clause subsumptions : 6944
% 154.53/23.43 % Unit Clause-clause subsumption calls : 10228
% 154.53/23.43 % Rewrite failures with RHS unbound : 0
% 154.53/23.43 % BW rewrite match attempts : 15012
% 154.53/23.43 % BW rewrite match successes : 549
% 154.53/23.43 % Condensation attempts : 0
% 154.53/23.43 % Condensation successes : 0
% 154.53/23.43 % Termbank termtop insertions : 35927174
% 154.53/23.43 % Search garbage collected termcells : 430
% 154.53/23.43
% 154.53/23.43 % -------------------------------------------------
% 154.53/23.43 % User time : 20.898 s
% 154.53/23.43 % System time : 1.003 s
% 154.53/23.43 % Total time : 21.901 s
% 154.53/23.43 % Maximum resident set size: 3656 pages
% 154.53/23.43
% 154.53/23.43 % -------------------------------------------------
% 154.53/23.43 % User time : 104.038 s
% 154.53/23.43 % System time : 5.021 s
% 154.53/23.43 % Total time : 109.059 s
% 154.53/23.43 % Maximum resident set size: 4864 pages
% 154.53/23.43 % E exiting
%------------------------------------------------------------------------------