%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG126+1 : 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 : n017.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 05:05:26 PM UTC 2026
% Result : Theorem 15.22s 9.76s
% Output : CNFRefutation 15.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 244 ( 36 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 315 ( 126 ~; 127 |; 45 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefGCD,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ! [X3] :
( aGcdOfAnd0(X3,X1,X2)
<=> ( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2)
& ! [X4] :
( ( aDivisorOf0(X4,X1)
& aDivisorOf0(X4,X2) )
=> doDivides0(X4,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefGCD) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aElement0(X2)
& doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(m__2129,hypothesis,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2129) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(m__2273,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(m__2373,hypothesis,
( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2373) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__2744,hypothesis,
doDivides0(xu,xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2744) ).
fof(m__2174,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__,conjecture,
aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_13,plain,
! [X178,X179,X180,X181,X182] :
( ( aDivisorOf0(X180,X178)
| ~ aGcdOfAnd0(X180,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( aDivisorOf0(X180,X179)
| ~ aGcdOfAnd0(X180,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( ~ aDivisorOf0(X181,X178)
| ~ aDivisorOf0(X181,X179)
| doDivides0(X181,X180)
| ~ aGcdOfAnd0(X180,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( aDivisorOf0(esk17_3(X178,X179,X182),X178)
| ~ aDivisorOf0(X182,X178)
| ~ aDivisorOf0(X182,X179)
| aGcdOfAnd0(X182,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( aDivisorOf0(esk17_3(X178,X179,X182),X179)
| ~ aDivisorOf0(X182,X178)
| ~ aDivisorOf0(X182,X179)
| aGcdOfAnd0(X182,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) )
& ( ~ doDivides0(esk17_3(X178,X179,X182),X182)
| ~ aDivisorOf0(X182,X178)
| ~ aDivisorOf0(X182,X179)
| aGcdOfAnd0(X182,X178,X179)
| ~ aElement0(X178)
| ~ aElement0(X179) ) ),
inference(distribute,[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)],[mDefGCD])])])])])]) ).
fof(c_0_14,plain,
! [X176,X177] :
( ( aElement0(X177)
| ~ aDivisorOf0(X177,X176)
| ~ aElement0(X176) )
& ( doDivides0(X177,X176)
| ~ aDivisorOf0(X177,X176)
| ~ aElement0(X176) )
& ( ~ aElement0(X177)
| ~ doDivides0(X177,X176)
| aDivisorOf0(X177,X176)
| ~ aElement0(X176) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])]) ).
cnf(c_0_15,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X3,X2)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
aGcdOfAnd0(xc,xa,xb),
inference(split_conjunct,[status(thm)],[m__2129]) ).
cnf(c_0_17,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_18,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_19,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( aElementOf0(X1,xI)
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
fof(c_0_20,plain,
! [X186,X187,X188,X190,X191,X192,X194] :
( ( aSet0(X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( aElement0(esk18_3(X186,X187,X188))
| ~ aElementOf0(X188,X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( sdtasdt0(X186,esk18_3(X186,X187,X188)) = X188
| ~ aElementOf0(X188,X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( ~ aElement0(X191)
| sdtasdt0(X186,X191) != X190
| aElementOf0(X190,X187)
| X187 != slsdtgt0(X186)
| ~ aElement0(X186) )
& ( ~ aElementOf0(esk19_2(X186,X192),X192)
| ~ aElement0(X194)
| sdtasdt0(X186,X194) != esk19_2(X186,X192)
| ~ aSet0(X192)
| X192 = slsdtgt0(X186)
| ~ aElement0(X186) )
& ( aElement0(esk20_2(X186,X192))
| aElementOf0(esk19_2(X186,X192),X192)
| ~ aSet0(X192)
| X192 = slsdtgt0(X186)
| ~ aElement0(X186) )
& ( sdtasdt0(X186,esk20_2(X186,X192)) = esk19_2(X186,X192)
| aElementOf0(esk19_2(X186,X192),X192)
| ~ aSet0(X192)
| X192 = slsdtgt0(X186)
| ~ aElement0(X186) ) ),
inference(distribute,[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)],[mDefPrIdeal])])])])])]) ).
fof(c_0_21,plain,
! [X172,X173,X175] :
( ( aElement0(esk16_2(X172,X173))
| ~ doDivides0(X172,X173)
| ~ aElement0(X172)
| ~ aElement0(X173) )
& ( sdtasdt0(X172,esk16_2(X172,X173)) = X173
| ~ doDivides0(X172,X173)
| ~ aElement0(X172)
| ~ aElement0(X173) )
& ( ~ aElement0(X175)
| sdtasdt0(X172,X175) != X173
| doDivides0(X172,X173)
| ~ aElement0(X172)
| ~ aElement0(X173) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
cnf(c_0_22,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
aDivisorOf0(xc,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,hypothesis,
aDivisorOf0(xu,xa),
inference(split_conjunct,[status(thm)],[m__2373]) ).
fof(c_0_25,plain,
! [X146,X147,X148,X149,X150] :
( ( aSet0(X146)
| ~ aIdeal0(X146) )
& ( ~ aElementOf0(X148,X146)
| aElementOf0(sdtpldt0(X147,X148),X146)
| ~ aElementOf0(X147,X146)
| ~ aIdeal0(X146) )
& ( ~ aElement0(X149)
| aElementOf0(sdtasdt0(X149,X147),X146)
| ~ aElementOf0(X147,X146)
| ~ aIdeal0(X146) )
& ( aElementOf0(esk9_1(X150),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( aElement0(esk11_1(X150))
| aElementOf0(esk10_1(X150),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X150),esk9_1(X150)),X150)
| aElementOf0(esk10_1(X150),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( aElement0(esk11_1(X150))
| ~ aElementOf0(sdtpldt0(esk9_1(X150),esk10_1(X150)),X150)
| ~ aSet0(X150)
| aIdeal0(X150) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X150),esk9_1(X150)),X150)
| ~ aElementOf0(sdtpldt0(esk9_1(X150),esk10_1(X150)),X150)
| ~ aSet0(X150)
| aIdeal0(X150) ) ),
inference(distribute,[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)],[mDefIdeal])])])])])]) ).
fof(c_0_26,hypothesis,
! [X198] :
( aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X198,xI)
| X198 = sz00
| ~ iLess0(sbrdtbr0(X198),sbrdtbr0(xu)) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_27,plain,
( aElementOf0(X3,X4)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| X4 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( sdtasdt0(X1,esk16_2(X1,X2)) = X2
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
doDivides0(xu,xc),
inference(split_conjunct,[status(thm)],[m__2744]) ).
cnf(c_0_30,hypothesis,
aElement0(xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18])]) ).
cnf(c_0_31,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_17])]) ).
cnf(c_0_32,plain,
( aElement0(esk16_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_36,plain,
! [X105,X106] :
( ~ aElement0(X105)
| ~ aElement0(X106)
| sdtasdt0(X105,X106) = sdtasdt0(X106,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_37,plain,
( sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,plain,
( aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_27])]) ).
cnf(c_0_39,hypothesis,
sdtasdt0(xu,esk16_2(xu,xc)) = xc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_40,hypothesis,
aElement0(esk16_2(xu,xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_41,plain,
( aElement0(esk18_3(X1,X2,X3))
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_42,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_43,hypothesis,
( aElementOf0(sdtasdt0(X1,xu),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_44,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),X2)) = X2
| ~ aElementOf0(X2,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_46,hypothesis,
aElementOf0(xc,slsdtgt0(xu)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_31]),c_0_40])]) ).
cnf(c_0_47,plain,
( aElement0(esk18_3(X1,slsdtgt0(X1),X2))
| ~ aElementOf0(X2,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
~ aElementOf0(xc,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
cnf(c_0_50,hypothesis,
( aElementOf0(sdtasdt0(xu,X1),xI)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_31])]) ).
cnf(c_0_51,hypothesis,
sdtasdt0(xu,esk18_3(xu,slsdtgt0(xu),xc)) = xc,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_31])]) ).
cnf(c_0_52,hypothesis,
aElement0(esk18_3(xu,slsdtgt0(xu),xc)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_31])]) ).
cnf(c_0_53,negated_conjecture,
~ aElementOf0(xc,xI),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG126+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:50:58 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 15.22/9.76 % Version : CSE_E---1.7
% 15.22/9.76 % Problem : theBenchmark.p
% 15.22/9.76 % SZS status Theorem for theBenchmark.p
% 15.22/9.76 % SZS output start CNFRefutation
% See solution above
% 15.32/9.81 % Total time : 7.385s
%------------------------------------------------------------------------------