%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 94 ( 43 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 110 ( 45 ~; 33 |; 25 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 6 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2228,hypothesis,
? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2228) ).
fof(m__,conjecture,
? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__2351,hypothesis,
! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& aElementOf0(X2,xI) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2351) ).
fof(m__2174,hypothesis,
( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
& aIdeal0(xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
fof(c_0_4,hypothesis,
? [X1] :
( X1 != sz00
& aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_simplification,[status(thm)],[m__2228]) ).
fof(c_0_5,negated_conjecture,
~ ? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,hypothesis,
! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& aElementOf0(X2,xI) ) ),
inference(fof_simplification,[status(thm)],[m__2351]) ).
fof(c_0_7,hypothesis,
( esk21_0 != sz00
& aElementOf0(esk21_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,negated_conjecture,
~ ? [X1] :
( ! [X2] :
( ( X2 != sz00
& aElementOf0(X2,xI) )
=> ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) )
& X1 != sz00
& aElementOf0(X1,xI) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_9,hypothesis,
! [X117,X119] :
( ( X117 = sz00
| ~ aElementOf0(X117,xI)
| ~ iLess0(sbrdtbr0(X119),sbrdtbr0(esk22_0))
| X119 = sz00
| ~ aElementOf0(X119,xI) )
& ( X117 = sz00
| ~ aElementOf0(X117,xI)
| esk22_0 != sz00 )
& ( X117 = sz00
| ~ aElementOf0(X117,xI)
| aElementOf0(esk22_0,xI) ) ),
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])])])])])])]) ).
cnf(c_0_10,hypothesis,
aElementOf0(esk21_0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2174]) ).
fof(c_0_12,negated_conjecture,
! [X120] :
( ( X120 = sz00
| ~ aElementOf0(X120,xI)
| iLess0(sbrdtbr0(esk23_1(X120)),sbrdtbr0(X120)) )
& ( X120 = sz00
| ~ aElementOf0(X120,xI)
| esk23_1(X120) != sz00 )
& ( X120 = sz00
| ~ aElementOf0(X120,xI)
| aElementOf0(esk23_1(X120),xI) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_13,hypothesis,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| aElementOf0(esk22_0,xI) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
aElementOf0(esk21_0,xI),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,hypothesis,
esk21_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| iLess0(sbrdtbr0(esk23_1(X1)),sbrdtbr0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,hypothesis,
aElementOf0(esk22_0,xI),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| aElementOf0(esk23_1(X1),xI) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,hypothesis,
( ~ aElementOf0(X2,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk22_0))
| ~ aElementOf0(X1,xI)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,hypothesis,
( iLess0(sbrdtbr0(esk23_1(esk22_0)),sbrdtbr0(esk22_0))
| esk22_0 = sz00 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( aElementOf0(esk23_1(esk22_0),xI)
| esk22_0 = sz00 ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,hypothesis,
( ~ aElementOf0(X1,xI)
| esk22_0 != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,hypothesis,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| esk23_1(esk22_0) = sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(X1,xI)
| esk23_1(X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,hypothesis,
esk23_1(esk22_0) = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_15]) ).
cnf(c_0_26,negated_conjecture,
esk22_0 = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17])]) ).
cnf(c_0_27,hypothesis,
( ~ aElementOf0(X1,xI)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_26])]) ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG112+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:21:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.13/0.45 % Version: 3.5.1
% 0.13/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.45 % Starting sh5l with 300s (1) cores
% 0.13/0.45 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1989821 completed with status 0
% 0.13/0.45 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.13/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FGHSF-FSMM32-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.13/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.45 % new_bool_3 with pid 1989831 completed with status 0
% 0.13/0.45 % Result found by new_bool_3
% 0.13/0.45 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.45 % No SInE strategy applied
% 0.13/0.45 % Search class: FGHSF-FSMM32-MFFFFFNN
% 0.13/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.45 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.13/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 0.13/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.45 % Preprocessing time : 0.003 s
% 0.13/0.45 % Presaturation interreduction done
% 0.13/0.45
% 0.13/0.45 % Proof found!
% 0.13/0.45 % SZS status Theorem
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
% 0.13/0.45 % Parsed axioms : 46
% 0.13/0.45 % Removed by relevancy pruning/SinE : 0
% 0.13/0.45 % Initial clauses : 111
% 0.13/0.45 % Removed in clause preprocessing : 4
% 0.13/0.45 % Initial clauses in saturation : 107
% 0.13/0.45 % Processed clauses : 195
% 0.13/0.45 % ...of these trivial : 0
% 0.13/0.45 % ...subsumed : 1
% 0.13/0.45 % ...remaining for further processing : 194
% 0.13/0.45 % Other redundant clauses eliminated : 16
% 0.13/0.45 % Clauses deleted for lack of memory : 0
% 0.13/0.45 % Backward-subsumed : 4
% 0.13/0.45 % Backward-rewritten : 11
% 0.13/0.45 % Generated clauses : 79
% 0.13/0.45 % ...of the previous two non-redundant : 66
% 0.13/0.45 % ...aggressively subsumed : 0
% 0.13/0.45 % Contextual simplify-reflections : 3
% 0.13/0.45 % Paramodulations : 65
% 0.13/0.45 % Factorizations : 0
% 0.13/0.45 % NegExts : 0
% 0.13/0.45 % Equation resolutions : 16
% 0.13/0.45 % Disequality decompositions : 0
% 0.13/0.45 % Total rewrite steps : 57
% 0.13/0.45 % ...of those cached : 44
% 0.13/0.45 % Propositional unsat checks : 0
% 0.13/0.45 % Propositional check models : 0
% 0.13/0.45 % Propositional check unsatisfiable : 0
% 0.13/0.45 % Propositional clauses : 0
% 0.13/0.45 % Propositional clauses after purity: 0
% 0.13/0.45 % Propositional unsat core size : 0
% 0.13/0.45 % Propositional preprocessing time : 0.000
% 0.13/0.45 % Propositional encoding time : 0.000
% 0.13/0.45 % Propositional solver time : 0.000
% 0.13/0.45 % Success case prop preproc time : 0.000
% 0.13/0.45 % Success case prop encoding time : 0.000
% 0.13/0.45 % Success case prop solver time : 0.000
% 0.13/0.45 % Current number of processed clauses : 58
% 0.13/0.45 % Positive orientable unit clauses : 24
% 0.13/0.45 % Positive unorientable unit clauses: 0
% 0.13/0.45 % Negative unit clauses : 2
% 0.13/0.45 % Non-unit-clauses : 32
% 0.13/0.45 % Current number of unprocessed clauses: 80
% 0.13/0.45 % ...number of literals in the above : 337
% 0.13/0.45 % Current number of archived formulas : 0
% 0.13/0.45 % Current number of archived clauses : 122
% 0.13/0.45 % Clause-clause subsumption calls (NU) : 1929
% 0.13/0.45 % Rec. Clause-clause subsumption calls : 578
% 0.13/0.45 % Non-unit clause-clause subsumptions : 8
% 0.13/0.45 % Unit Clause-clause subsumption calls : 47
% 0.13/0.45 % Rewrite failures with RHS unbound : 0
% 0.13/0.45 % BW rewrite match attempts : 3
% 0.13/0.45 % BW rewrite match successes : 3
% 0.13/0.45 % Condensation attempts : 0
% 0.13/0.45 % Condensation successes : 0
% 0.13/0.45 % Termbank termtop insertions : 10253
% 0.13/0.45 % Search garbage collected termcells : 1991
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.022 s
% 0.13/0.45 % System time : 0.005 s
% 0.13/0.45 % Total time : 0.027 s
% 0.13/0.45 % Maximum resident set size: 3952 pages
% 0.13/0.45
% 0.13/0.45 % -------------------------------------------------
% 0.13/0.45 % User time : 0.082 s
% 0.13/0.45 % System time : 0.017 s
% 0.13/0.45 % Total time : 0.100 s
% 0.13/0.45 % Maximum resident set size: 4864 pages
% 0.13/0.45 % E exiting
%------------------------------------------------------------------------------