%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG120+4 : 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 : n026.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 05:05:24 PM UTC 2026
% Result : Theorem 1.30s 1.91s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 198 ( 34 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 240 ( 80 ~; 76 |; 67 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 47 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = smndt0(sdtasdt0(xq,xu)) )
| aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2174,hypothesis,
( aSet0(xI)
& ! [X1] :
( aElementOf0(X1,xI)
=> ( ! [X2] :
( aElementOf0(X2,xI)
=> aElementOf0(sdtpldt0(X1,X2),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),xI) ) ) )
& aIdeal0(xI)
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
& ! [X1] :
( aElementOf0(X1,xI)
<=> ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 ) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(mMulMnOne,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMnOne) ).
fof(m__2273,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).
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(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__2666,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_10,negated_conjecture,
~ ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = smndt0(sdtasdt0(xq,xu)) )
| aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_11,hypothesis,
! [X241,X242,X243,X244,X246,X247,X248,X250,X251,X252,X255,X256,X257] :
( aSet0(xI)
& ( ~ aElementOf0(X242,xI)
| aElementOf0(sdtpldt0(X241,X242),xI)
| ~ aElementOf0(X241,xI) )
& ( ~ aElement0(X243)
| aElementOf0(sdtasdt0(X243,X241),xI)
| ~ aElementOf0(X241,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X244))
| ~ aElementOf0(X244,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X244)) = X244
| ~ aElementOf0(X244,slsdtgt0(xa)) )
& ( ~ aElement0(X247)
| sdtasdt0(xa,X247) != X246
| aElementOf0(X246,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X248))
| ~ aElementOf0(X248,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X248)) = X248
| ~ aElementOf0(X248,slsdtgt0(xb)) )
& ( ~ aElement0(X251)
| sdtasdt0(xb,X251) != X250
| aElementOf0(X250,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X252),slsdtgt0(xa))
| ~ aElementOf0(X252,xI) )
& ( aElementOf0(esk27_1(X252),slsdtgt0(xb))
| ~ aElementOf0(X252,xI) )
& ( sdtpldt0(esk26_1(X252),esk27_1(X252)) = X252
| ~ aElementOf0(X252,xI) )
& ( ~ aElementOf0(X256,slsdtgt0(xa))
| ~ aElementOf0(X257,slsdtgt0(xb))
| sdtpldt0(X256,X257) != X255
| aElementOf0(X255,xI) )
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
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)],[m__2174])])])])])]) ).
fof(c_0_12,plain,
! [X152] :
( ( sdtasdt0(smndt0(sz10),X152) = smndt0(X152)
| ~ aElement0(X152) )
& ( smndt0(X152) = sdtasdt0(X152,smndt0(sz10))
| ~ aElement0(X152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMnOne])])]) ).
fof(c_0_13,negated_conjecture,
! [X282,X283] :
( ( ~ aElementOf0(X282,slsdtgt0(xa))
| ~ aElementOf0(X283,slsdtgt0(xb))
| sdtpldt0(X282,X283) != smndt0(sdtasdt0(xq,xu)) )
& ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_14,hypothesis,
( aElementOf0(sdtasdt0(X1,X2),xI)
| ~ aElement0(X1)
| ~ aElementOf0(X2,xI) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,hypothesis,
( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = xu )
& aElementOf0(xu,xI)
& xu != sz00
& ! [X1] :
( ( ( ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& sdtpldt0(X2,X3) = X1 )
| aElementOf0(X1,xI) )
& X1 != sz00 )
=> ~ iLess0(sbrdtbr0(X1),sbrdtbr0(xu)) ) ),
inference(fof_simplification,[status(thm)],[m__2273]) ).
cnf(c_0_17,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(smndt0(X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElement0(smndt0(sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X184,X185,X186,X187,X188] :
( ( aSet0(X184)
| ~ aIdeal0(X184) )
& ( ~ aElementOf0(X186,X184)
| aElementOf0(sdtpldt0(X185,X186),X184)
| ~ aElementOf0(X185,X184)
| ~ aIdeal0(X184) )
& ( ~ aElement0(X187)
| aElementOf0(sdtasdt0(X187,X185),X184)
| ~ aElementOf0(X185,X184)
| ~ aIdeal0(X184) )
& ( aElementOf0(esk9_1(X188),X188)
| ~ aSet0(X188)
| aIdeal0(X188) )
& ( aElement0(esk11_1(X188))
| aElementOf0(esk10_1(X188),X188)
| ~ aSet0(X188)
| aIdeal0(X188) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X188),esk9_1(X188)),X188)
| aElementOf0(esk10_1(X188),X188)
| ~ aSet0(X188)
| aIdeal0(X188) )
& ( aElement0(esk11_1(X188))
| ~ aElementOf0(sdtpldt0(esk9_1(X188),esk10_1(X188)),X188)
| ~ aSet0(X188)
| aIdeal0(X188) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X188),esk9_1(X188)),X188)
| ~ aElementOf0(sdtpldt0(esk9_1(X188),esk10_1(X188)),X188)
| ~ aSet0(X188)
| aIdeal0(X188) ) ),
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_20,hypothesis,
! [X273,X274,X275] :
( aElementOf0(esk37_0,slsdtgt0(xa))
& aElementOf0(esk38_0,slsdtgt0(xb))
& sdtpldt0(esk37_0,esk38_0) = xu
& aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X274,slsdtgt0(xa))
| ~ aElementOf0(X275,slsdtgt0(xb))
| sdtpldt0(X274,X275) != X273
| X273 = sz00
| ~ iLess0(sbrdtbr0(X273),sbrdtbr0(xu)) )
& ( ~ aElementOf0(X273,xI)
| X273 = sz00
| ~ iLess0(sbrdtbr0(X273),sbrdtbr0(xu)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).
fof(c_0_21,plain,
! [X156,X157] :
( ~ aSet0(X156)
| ~ aElementOf0(X157,X156)
| aElement0(X157) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xq,xu),xI)
| ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( aElementOf0(sdtasdt0(X1,X2),X3)
| ~ aElement0(X1)
| ~ aElementOf0(X2,X3)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
fof(c_0_27,plain,
! [X134,X135] :
( ~ aElement0(X134)
| ~ aElement0(X135)
| aElement0(sdtasdt0(X134,X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_28,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( ~ aElement0(sdtasdt0(xq,xu))
| ~ aElement0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_29])]) ).
fof(c_0_33,plain,
! [X131] :
( ~ aElement0(X131)
| aElement0(smndt0(X131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_34,negated_conjecture,
~ aElement0(smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_26])]) ).
cnf(c_0_35,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.18 % Problem : RNG120+4 : TPTP v9.2.1. Released v4.0.0.
% 0.03/0.18 % 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
% 0.12/0.42 % Computer : n026.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8042.1875MB
% 0.12/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Tue May 5 01:51:38 EDT 2026
% 0.12/0.43 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 1.30/1.91 % Version : CSE_E---1.7
% 1.30/1.91 % Problem : theBenchmark.p
% 1.30/1.91 % SZS status Theorem for theBenchmark.p
% 1.30/1.91 % SZS output start CNFRefutation
% See solution above
% 1.30/1.91 % Total time : 1.380s
%------------------------------------------------------------------------------