%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG104+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 : n010.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 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 94 ( 27 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 108 ( 43 ~; 44 |; 14 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 24 !; 1 ?)
% 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(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(m__1933,hypothesis,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
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,
! [X104,X105,X106] :
( ~ aElement0(X104)
| ~ aElement0(X105)
| ~ aElement0(X106)
| sdtasdt0(sdtasdt0(X104,X105),X106) = sdtasdt0(X104,sdtasdt0(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_9,plain,
! [X115,X116] :
( ~ aSet0(X115)
| ~ aElementOf0(X116,X115)
| aElement0(X116) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_10,plain,
! [X183,X184,X185,X187,X188,X189,X191] :
( ( aSet0(X184)
| X184 != slsdtgt0(X183)
| ~ aElement0(X183) )
& ( aElement0(esk18_3(X183,X184,X185))
| ~ aElementOf0(X185,X184)
| X184 != slsdtgt0(X183)
| ~ aElement0(X183) )
& ( sdtasdt0(X183,esk18_3(X183,X184,X185)) = X185
| ~ aElementOf0(X185,X184)
| X184 != slsdtgt0(X183)
| ~ aElement0(X183) )
& ( ~ aElement0(X188)
| sdtasdt0(X183,X188) != X187
| aElementOf0(X187,X184)
| X184 != slsdtgt0(X183)
| ~ aElement0(X183) )
& ( ~ aElementOf0(esk19_2(X183,X189),X189)
| ~ aElement0(X191)
| sdtasdt0(X183,X191) != esk19_2(X183,X189)
| ~ aSet0(X189)
| X189 = slsdtgt0(X183)
| ~ aElement0(X183) )
& ( aElement0(esk20_2(X183,X189))
| aElementOf0(esk19_2(X183,X189),X189)
| ~ aSet0(X189)
| X189 = slsdtgt0(X183)
| ~ aElement0(X183) )
& ( sdtasdt0(X183,esk20_2(X183,X189)) = esk19_2(X183,X189)
| aElementOf0(esk19_2(X183,X189),X189)
| ~ aSet0(X189)
| X189 = slsdtgt0(X183)
| ~ aElement0(X183) ) ),
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_11,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_12,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_13,hypothesis,
sdtasdt0(xc,xu) = xx,
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_14,hypothesis,
aElement0(xu),
inference(split_conjunct,[status(thm)],[m__1956]) ).
cnf(c_0_15,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__1905]) ).
cnf(c_0_16,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xx,slsdtgt0(xc)),
inference(split_conjunct,[status(thm)],[m__1933]) ).
cnf(c_0_18,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,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_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_21,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[m__1933]) ).
fof(c_0_22,plain,
! [X102,X103] :
( ~ aElement0(X102)
| ~ aElement0(X103)
| sdtasdt0(X102,X103) = sdtasdt0(X103,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_23,hypothesis,
( aElement0(xx)
| ~ aSet0(slsdtgt0(xc)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( aSet0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
sdtasdt0(xz,xx) != sdtasdt0(xx,xz),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG104+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n010.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:50:36 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------