%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:06:26 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 130 ( 56 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 143 ( 42 ~; 41 |; 47 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 17 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( X1 != sz00
& ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xa))
<=> ? [X3] :
( sdtasdt0(xa,X3) = X2
& aElement0(X3) ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
=> ( aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(m__2203,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& ? [X1] :
( sdtasdt0(xb,X1) = xb
& aElement0(X1) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X1] :
( sdtasdt0(xb,X1) = sz00
& aElement0(X1) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X1] :
( sdtasdt0(xa,X1) = xa
& aElement0(X1) )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X1] :
( sdtasdt0(xa,X1) = sz00
& aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(m__2091,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
fof(m__2110,hypothesis,
( xb != sz00
| xa != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
fof(c_0_5,negated_conjecture,
~ ? [X1] :
( X1 != sz00
& ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xa))
<=> ? [X3] :
( sdtasdt0(xa,X3) = X2
& aElement0(X3) ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
=> ( aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
~ ? [X1] :
( X1 != sz00
& ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xa))
<=> ? [X3] :
( sdtasdt0(xa,X3) = X2
& aElement0(X3) ) )
=> ( ! [X2] :
( aElementOf0(X2,slsdtgt0(xb))
<=> ? [X3] :
( sdtasdt0(xb,X3) = X2
& aElement0(X3) ) )
=> ( aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,negated_conjecture,
! [X143,X144,X146,X147,X148,X150,X151,X152,X153] :
( ( X143 = sz00
| ~ aElementOf0(X143,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ( X143 = sz00
| sdtpldt0(X152,X153) != X143
| ~ aElementOf0(X153,slsdtgt0(xb))
| ~ aElementOf0(X152,slsdtgt0(xa)) )
& ( X143 = sz00
| aElementOf0(X150,slsdtgt0(xb))
| sdtasdt0(xb,X151) != X150
| ~ aElement0(X151) )
& ( X143 = sz00
| ~ aElementOf0(X148,slsdtgt0(xb))
| sdtasdt0(xb,esk33_2(X143,X148)) = X148 )
& ( X143 = sz00
| ~ aElementOf0(X148,slsdtgt0(xb))
| aElement0(esk33_2(X143,X148)) )
& ( X143 = sz00
| aElementOf0(X146,slsdtgt0(xa))
| sdtasdt0(xa,X147) != X146
| ~ aElement0(X147) )
& ( X143 = sz00
| ~ aElementOf0(X144,slsdtgt0(xa))
| sdtasdt0(xa,esk32_2(X143,X144)) = X144 )
& ( X143 = sz00
| ~ aElementOf0(X144,slsdtgt0(xa))
| aElement0(esk32_2(X143,X144)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_6])])])])])])]) ).
fof(c_0_8,plain,
! [X18] :
( ( ~ aElement0(X18)
| X18 = sdtpldt0(sz00,X18) )
& ( ~ aElement0(X18)
| sdtpldt0(X18,sz00) = X18 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_9,negated_conjecture,
( sdtpldt0(X1,X2) != X3
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa))
| X3 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,hypothesis,
( aElementOf0(xb,slsdtgt0(xb))
& sdtasdt0(xb,esk31_0) = xb
& aElement0(esk31_0)
& aElementOf0(sz00,slsdtgt0(xb))
& sdtasdt0(xb,esk30_0) = sz00
& aElement0(esk30_0)
& aElementOf0(xa,slsdtgt0(xa))
& sdtasdt0(xa,esk29_0) = xa
& aElement0(esk29_0)
& aElementOf0(sz00,slsdtgt0(xa))
& sdtasdt0(xa,esk28_0) = sz00
& aElement0(esk28_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2203])]) ).
cnf(c_0_11,plain,
( ~ aElement0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
aElementOf0(sz00,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X1,slsdtgt0(xb))
| sz00 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_15,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_17,hypothesis,
( xb != sz00
| xa != sz00 ),
inference(fof_simplification,[status(thm)],[m__2110]) ).
cnf(c_0_18,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,hypothesis,
sz00 = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
fof(c_0_20,hypothesis,
( xb != sz00
| xa != sz00 ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( ~ aElement0(X1)
| sdtpldt0(X1,xb) = X1 ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) = xb ),
inference(rw,[status(thm)],[c_0_12,c_0_19]) ).
cnf(c_0_23,hypothesis,
( xb != sz00
| xa != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElement0(X1)
| ~ aElementOf0(X1,slsdtgt0(xa))
| xb = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15])]) ).
cnf(c_0_25,hypothesis,
aElementOf0(xa,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_26,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_27,hypothesis,
xb != xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_19]),c_0_19])]) ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:20:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 12247 completed with status 0
% 0.10/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.10/0.46 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.10/0.46 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.10/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0U with 136s (1) cores
% 0.10/0.46 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 12256 completed with status 0
% 0.10/0.46 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.46 % No SInE strategy applied
% 0.10/0.46 % Search class: FGHSF-FSLM32-MFFFFFNN
% 0.10/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.10/0.46 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.10/0.46 % Preprocessing time : 0.004 s
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 44
% 0.10/0.46 % Removed by relevancy pruning/SinE : 0
% 0.10/0.46 % Initial clauses : 169
% 0.10/0.46 % Removed in clause preprocessing : 4
% 0.10/0.46 % Initial clauses in saturation : 165
% 0.10/0.46 % Processed clauses : 104
% 0.10/0.46 % ...of these trivial : 3
% 0.10/0.46 % ...subsumed : 4
% 0.10/0.46 % ...remaining for further processing : 97
% 0.10/0.46 % Other redundant clauses eliminated : 1
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 0
% 0.10/0.46 % Backward-rewritten : 23
% 0.10/0.46 % Generated clauses : 87
% 0.10/0.46 % ...of the previous two non-redundant : 50
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 1
% 0.10/0.46 % Paramodulations : 86
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 1
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 159
% 0.10/0.46 % ...of those cached : 131
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 73
% 0.10/0.46 % Positive orientable unit clauses : 31
% 0.10/0.46 % Positive unorientable unit clauses: 0
% 0.10/0.46 % Negative unit clauses : 2
% 0.10/0.46 % Non-unit-clauses : 40
% 0.10/0.46 % Current number of unprocessed clauses: 106
% 0.10/0.46 % ...number of literals in the above : 476
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 23
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 192
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 159
% 0.10/0.46 % Non-unit clause-clause subsumptions : 4
% 0.10/0.46 % Unit Clause-clause subsumption calls : 12
% 0.10/0.46 % Rewrite failures with RHS unbound : 0
% 0.10/0.46 % BW rewrite match attempts : 4
% 0.10/0.46 % BW rewrite match successes : 4
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 11984
% 0.10/0.46 % Search garbage collected termcells : 2605
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.019 s
% 0.10/0.46 % System time : 0.003 s
% 0.10/0.46 % Total time : 0.022 s
% 0.10/0.46 % Maximum resident set size: 3964 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.061 s
% 0.10/0.46 % System time : 0.011 s
% 0.10/0.46 % Total time : 0.072 s
% 0.10/0.46 % Maximum resident set size: 4608 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------