%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG104+2 : 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 : n027.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 05:05:21 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 105 ( 31 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 118 ( 43 ~; 44 |; 24 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__1933,hypothesis,
( ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xx )
& aElementOf0(xx,slsdtgt0(xc))
& ? [X1] :
( aElement0(X1)
& sdtasdt0(xc,X1) = xy )
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
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(m__,conjecture,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1956,hypothesis,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).
fof(m__1905,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_8,plain,
! [X106,X107,X108] :
( ~ aElement0(X106)
| ~ aElement0(X107)
| ~ aElement0(X108)
| sdtasdt0(sdtasdt0(X106,X107),X108) = sdtasdt0(X106,sdtasdt0(X107,X108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_9,plain,
! [X117,X118] :
( ~ aSet0(X117)
| ~ aElementOf0(X118,X117)
| aElement0(X118) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_10,hypothesis,
( aElement0(esk21_0)
& sdtasdt0(xc,esk21_0) = xx
& aElementOf0(xx,slsdtgt0(xc))
& aElement0(esk22_0)
& sdtasdt0(xc,esk22_0) = xy
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1933])]) ).
fof(c_0_11,plain,
! [X185,X186,X187,X189,X190,X191,X193] :
( ( aSet0(X186)
| X186 != slsdtgt0(X185)
| ~ aElement0(X185) )
& ( aElement0(esk18_3(X185,X186,X187))
| ~ aElementOf0(X187,X186)
| X186 != slsdtgt0(X185)
| ~ aElement0(X185) )
& ( sdtasdt0(X185,esk18_3(X185,X186,X187)) = X187
| ~ aElementOf0(X187,X186)
| X186 != slsdtgt0(X185)
| ~ aElement0(X185) )
& ( ~ aElement0(X190)
| sdtasdt0(X185,X190) != X189
| aElementOf0(X189,X186)
| X186 != slsdtgt0(X185)
| ~ aElement0(X185) )
& ( ~ aElementOf0(esk19_2(X185,X191),X191)
| ~ aElement0(X193)
| sdtasdt0(X185,X193) != esk19_2(X185,X191)
| ~ aSet0(X191)
| X191 = slsdtgt0(X185)
| ~ aElement0(X185) )
& ( aElement0(esk20_2(X185,X191))
| aElementOf0(esk19_2(X185,X191),X191)
| ~ aSet0(X191)
| X191 = slsdtgt0(X185)
| ~ aElement0(X185) )
& ( sdtasdt0(X185,esk20_2(X185,X191)) = esk19_2(X185,X191)
| aElementOf0(esk19_2(X185,X191),X191)
| ~ aSet0(X191)
| X191 = slsdtgt0(X185)
| ~ aElement0(X185) ) ),
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_12,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_13,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,hypothesis,
sdtasdt0(xc,xu) = xx,
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_15,hypothesis,
aElement0(xu),
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_16,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]) ).
cnf(c_0_17,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,hypothesis,
aElementOf0(xx,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
( sdtasdt0(xc,sdtasdt0(xu,X1)) = sdtasdt0(xx,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_22,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,plain,
! [X104,X105] :
( ~ aElement0(X104)
| ~ aElement0(X105)
| sdtasdt0(X104,X105) = sdtasdt0(X105,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_24,hypothesis,
( aElement0(xx)
| ~ aSet0(slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( aSet0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xx,xz),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_27,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG104+2 : 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 : n027.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 01:51:20 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------