%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG119+4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 1.43s 1.78s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 150 ( 45 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 172 ( 56 ~; 47 |; 56 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 39 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',m__2273) ).
fof(m__,conjecture,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
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/sandbox2/benchmark/theBenchmark.p',m__2174) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(m__2666,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
fof(m__2612,hypothesis,
~ ( ? [X1] :
( aElement0(X1)
& sdtasdt0(xu,X1) = xb )
| doDivides0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(c_0_9,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]) ).
fof(c_0_10,negated_conjecture,
xr = sz00,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_11,plain,
! [X154,X155] :
( ~ aSet0(X154)
| ~ aElementOf0(X155,X154)
| aElement0(X155) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_12,hypothesis,
! [X271,X272,X273] :
( aElementOf0(esk37_0,slsdtgt0(xa))
& aElementOf0(esk38_0,slsdtgt0(xb))
& sdtpldt0(esk37_0,esk38_0) = xu
& aElementOf0(xu,xI)
& xu != sz00
& ( ~ aElementOf0(X272,slsdtgt0(xa))
| ~ aElementOf0(X273,slsdtgt0(xb))
| sdtpldt0(X272,X273) != X271
| X271 = sz00
| ~ iLess0(sbrdtbr0(X271),sbrdtbr0(xu)) )
& ( ~ aElementOf0(X271,xI)
| X271 = sz00
| ~ iLess0(sbrdtbr0(X271),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_9])])])])]) ).
fof(c_0_13,hypothesis,
! [X239,X240,X241,X242,X244,X245,X246,X248,X249,X250,X253,X254,X255] :
( aSet0(xI)
& ( ~ aElementOf0(X240,xI)
| aElementOf0(sdtpldt0(X239,X240),xI)
| ~ aElementOf0(X239,xI) )
& ( ~ aElement0(X241)
| aElementOf0(sdtasdt0(X241,X239),xI)
| ~ aElementOf0(X239,xI) )
& aIdeal0(xI)
& ( aElement0(esk24_1(X242))
| ~ aElementOf0(X242,slsdtgt0(xa)) )
& ( sdtasdt0(xa,esk24_1(X242)) = X242
| ~ aElementOf0(X242,slsdtgt0(xa)) )
& ( ~ aElement0(X245)
| sdtasdt0(xa,X245) != X244
| aElementOf0(X244,slsdtgt0(xa)) )
& ( aElement0(esk25_1(X246))
| ~ aElementOf0(X246,slsdtgt0(xb)) )
& ( sdtasdt0(xb,esk25_1(X246)) = X246
| ~ aElementOf0(X246,slsdtgt0(xb)) )
& ( ~ aElement0(X249)
| sdtasdt0(xb,X249) != X248
| aElementOf0(X248,slsdtgt0(xb)) )
& ( aElementOf0(esk26_1(X250),slsdtgt0(xa))
| ~ aElementOf0(X250,xI) )
& ( aElementOf0(esk27_1(X250),slsdtgt0(xb))
| ~ aElementOf0(X250,xI) )
& ( sdtpldt0(esk26_1(X250),esk27_1(X250)) = X250
| ~ aElementOf0(X250,xI) )
& ( ~ aElementOf0(X254,slsdtgt0(xa))
| ~ aElementOf0(X255,slsdtgt0(xb))
| sdtpldt0(X254,X255) != X253
| aElementOf0(X253,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_14,plain,
! [X139] :
( ( sdtpldt0(X139,sz00) = X139
| ~ aElement0(X139) )
& ( X139 = sdtpldt0(sz00,X139)
| ~ aElement0(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_15,hypothesis,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_16,negated_conjecture,
xr = sz00,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,hypothesis,
! [X279] :
( ( ~ aElement0(X279)
| sdtasdt0(xu,X279) != xb )
& ~ doDivides0(xu,xb) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2612])])]) ).
fof(c_0_18,plain,
! [X141,X142] :
( ~ aElement0(X141)
| ~ aElement0(X142)
| sdtasdt0(X141,X142) = sdtasdt0(X142,X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_19,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,hypothesis,
aElementOf0(xu,xI),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
aSet0(xI),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,hypothesis,
sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_24,plain,
! [X132,X133] :
( ~ aElement0(X132)
| ~ aElement0(X133)
| aElement0(sdtasdt0(X132,X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_25,hypothesis,
( ~ aElement0(X1)
| sdtasdt0(xu,X1) != xb ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
aElement0(xu),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_28,hypothesis,
( sdtasdt0(xq,xu) = xb
| ~ aElement0(sdtasdt0(xq,xu)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
aElement0(xq),
inference(split_conjunct,[status(thm)],[m__2666]) ).
cnf(c_0_31,hypothesis,
( sdtasdt0(X1,xu) != xb
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(xq,xu) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27]),c_0_30])]) ).
cnf(c_0_33,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG119+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n001.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 01:52:03 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.43/1.78 % Version : CSE_E---1.7
% 1.43/1.78 % Problem : theBenchmark.p
% 1.43/1.78 % SZS status Theorem for theBenchmark.p
% 1.43/1.78 % SZS output start CNFRefutation
% See solution above
% 1.43/1.78 % Total time : 1.373s
%------------------------------------------------------------------------------