%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 11:55:36 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 23 unt; 0 def)
% Number of atoms : 56 ( 34 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 36 ( 13 ~; 10 |; 10 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conjecture_1,conjecture,
! [X1,X2,X3] :
( ( X3 = times(X1,X2)
& element(X2)
& element(X1) )
=> element(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(axiom_2,axiom,
! [X2] :
( element(X2)
<=> ? [X3] :
( times(X2,X2) = X3
& times(X2,X3) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(axiom_1,axiom,
! [X1,X2,X3] : times(times(X1,X2),X3) = times(X2,times(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( X3 = times(X1,X2)
& element(X2)
& element(X1) )
=> element(X3) ),
inference(assume_negation,[status(cth)],[conjecture_1]) ).
fof(c_0_4,plain,
! [X7,X9,X10] :
( ( element(X9)
| times(X9,X9) != X10
| times(X9,X10) != X9 )
& ( ~ element(X7)
| times(X7,X7) = esk1_1(X7) )
& ( ~ element(X7)
| times(X7,esk1_1(X7)) = X7 ) ),
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)],[axiom_2])])])])])])]) ).
fof(c_0_5,negated_conjecture,
( ~ element(esk4_0)
& esk4_0 = times(esk2_0,esk3_0)
& element(esk3_0)
& element(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).
fof(c_0_6,plain,
! [X4,X5,X6] : times(times(X4,X5),X6) = times(X5,times(X6,X4)),
inference(variable_rename,[status(thm)],[axiom_1]) ).
cnf(c_0_7,plain,
( ~ element(X1)
| times(X1,X1) = esk1_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
element(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ element(X1)
| times(X1,esk1_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
element(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
times(times(X1,X2),X3) = times(X2,times(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
times(esk2_0,esk2_0) = esk1_1(esk2_0),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
times(esk3_0,esk1_1(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
esk1_1(esk3_0) = times(esk3_0,esk3_0),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
esk4_0 = times(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
times(esk2_0,times(X1,esk2_0)) = times(esk1_1(esk2_0),X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
times(esk2_0,esk1_1(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
times(esk3_0,times(esk3_0,esk3_0)) = esk3_0,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
times(esk3_0,times(X1,esk2_0)) = times(esk4_0,X1),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
times(esk1_1(esk2_0),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_17]) ).
cnf(c_0_21,plain,
( times(X1,X1) != X2
| times(X1,X2) != X1
| element(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,negated_conjecture,
times(esk3_0,times(esk3_0,times(esk3_0,X1))) = times(esk3_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_11]),c_0_11]) ).
cnf(c_0_23,negated_conjecture,
times(esk3_0,esk1_1(esk2_0)) = times(esk4_0,esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,negated_conjecture,
times(esk2_0,times(X1,esk1_1(esk2_0))) = times(esk2_0,X1),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_25,plain,
( times(X1,times(X1,X1)) != X1
| element(X1) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
times(esk2_0,times(esk3_0,times(X1,X2))) = times(X1,times(X2,esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_11]),c_0_11]),c_0_11]) ).
cnf(c_0_27,negated_conjecture,
times(esk3_0,times(esk4_0,esk4_0)) = times(esk4_0,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
times(esk1_1(esk2_0),esk4_0) = esk4_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_16]),c_0_15]) ).
cnf(c_0_29,plain,
( times(X2,times(X1,times(X1,times(X2,times(X2,X1))))) != times(X1,X2)
| element(times(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_11]),c_0_11]),c_0_11]),c_0_11]),c_0_11]),c_0_11]),c_0_11]),c_0_11]),c_0_11]),c_0_11]) ).
cnf(c_0_30,negated_conjecture,
times(esk4_0,times(esk4_0,esk4_0)) = esk4_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
~ element(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_11]),c_0_30]),c_0_11]),c_0_11]),c_0_30]),c_0_11]),c_0_11]),c_0_30]),c_0_30]),c_0_11]),c_0_30])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:02:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 928002 completed with status 0
% 0.11/0.44 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.11/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FHUSF-FFSS21-SFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.11/0.44 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.44 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 928009 completed with status 0
% 0.11/0.44 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FHUSF-FFSS21-SFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.11/0.44 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44 % Presaturation interreduction done
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 3
% 0.11/0.44 % Removed by relevancy pruning/SinE : 0
% 0.11/0.44 % Initial clauses : 8
% 0.11/0.44 % Removed in clause preprocessing : 0
% 0.11/0.44 % Initial clauses in saturation : 8
% 0.11/0.44 % Processed clauses : 64
% 0.11/0.44 % ...of these trivial : 5
% 0.11/0.44 % ...subsumed : 3
% 0.11/0.44 % ...remaining for further processing : 56
% 0.11/0.44 % Other redundant clauses eliminated : 1
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 5
% 0.11/0.44 % Generated clauses : 238
% 0.11/0.44 % ...of the previous two non-redundant : 215
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 237
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 1
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 2333
% 0.11/0.44 % ...of those cached : 1313
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 42
% 0.11/0.44 % Positive orientable unit clauses : 28
% 0.11/0.44 % Positive unorientable unit clauses: 1
% 0.11/0.44 % Negative unit clauses : 3
% 0.11/0.44 % Non-unit-clauses : 10
% 0.11/0.44 % Current number of unprocessed clauses: 160
% 0.11/0.44 % ...number of literals in the above : 198
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 13
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 23
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 23
% 0.11/0.44 % Non-unit clause-clause subsumptions : 3
% 0.11/0.44 % Unit Clause-clause subsumption calls : 11
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 24
% 0.11/0.44 % BW rewrite match successes : 24
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 6722
% 0.11/0.44 % Search garbage collected termcells : 108
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.008 s
% 0.11/0.44 % System time : 0.002 s
% 0.11/0.44 % Total time : 0.010 s
% 0.11/0.44 % Maximum resident set size: 3628 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.023 s
% 0.11/0.44 % System time : 0.016 s
% 0.11/0.44 % Total time : 0.039 s
% 0.11/0.44 % Maximum resident set size: 4608 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------