%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG108+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 : n009.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 05:05:22 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 99 ( 25 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 122 ( 50 ~; 48 |; 19 &)
% ( 2 <=>; 3 =>; 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(c_0_7,plain,
! [X184,X185,X186,X188,X189,X190,X192] :
( ( aSet0(X185)
| X185 != slsdtgt0(X184)
| ~ aElement0(X184) )
& ( aElement0(esk18_3(X184,X185,X186))
| ~ aElementOf0(X186,X185)
| X185 != slsdtgt0(X184)
| ~ aElement0(X184) )
& ( sdtasdt0(X184,esk18_3(X184,X185,X186)) = X186
| ~ aElementOf0(X186,X185)
| X185 != slsdtgt0(X184)
| ~ aElement0(X184) )
& ( ~ aElement0(X189)
| sdtasdt0(X184,X189) != X188
| aElementOf0(X188,X185)
| X185 != slsdtgt0(X184)
| ~ aElement0(X184) )
& ( ~ aElementOf0(esk19_2(X184,X190),X190)
| ~ aElement0(X192)
| sdtasdt0(X184,X192) != esk19_2(X184,X190)
| ~ aSet0(X190)
| X190 = slsdtgt0(X184)
| ~ aElement0(X184) )
& ( aElement0(esk20_2(X184,X190))
| aElementOf0(esk19_2(X184,X190),X190)
| ~ aSet0(X190)
| X190 = slsdtgt0(X184)
| ~ aElement0(X184) )
& ( sdtasdt0(X184,esk20_2(X184,X190)) = esk19_2(X184,X190)
| aElementOf0(esk19_2(X184,X190),X190)
| ~ aSet0(X190)
| X190 = slsdtgt0(X184)
| ~ aElement0(X184) ) ),
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_8,negated_conjecture,
~ ( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_9,plain,
( aElementOf0(X3,X4)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| X4 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X113] :
( ( sdtasdt0(X113,sz00) = sz00
| ~ aElement0(X113) )
& ( sz00 = sdtasdt0(sz00,X113)
| ~ aElement0(X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_11,negated_conjecture,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_15,negated_conjecture,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( aElementOf0(sz00,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_17,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_18,plain,
! [X108] :
( ( sdtasdt0(X108,sz10) = X108
| ~ aElement0(X108) )
& ( X108 = sdtasdt0(sz10,X108)
| ~ aElement0(X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
cnf(c_0_19,negated_conjecture,
( ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_20,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_21,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_23,negated_conjecture,
( ~ aElementOf0(xa,slsdtgt0(xa))
| ~ aElementOf0(xb,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_20])]) ).
cnf(c_0_24,plain,
( aElementOf0(X1,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_22])]) ).
cnf(c_0_25,negated_conjecture,
~ aElementOf0(xb,slsdtgt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : RNG108+1 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % 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
% 0.17/0.34 % Computer : n009.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 01:50:41 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------