%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:38:42 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.55s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 44 ( 15 unt; 17 nHn; 44 RR)
% Number of literals : 105 ( 0 equ; 51 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(qg2_2,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(c_0_8,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_9,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_8 ).
cnf(c_0_10,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_11,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_12,plain,
( ~ group_element(X1)
| product(e_2,X1,e_1)
| product(e_2,X1,e_2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_14,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_15,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
inference(fof_simplification,[status(thm)],[qg2_2]) ).
cnf(c_0_16,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_11 ).
cnf(c_0_17,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_18,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_19,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_13 ).
cnf(c_0_20,plain,
( ~ group_element(X1)
| product(e_1,X1,e_1)
| product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_15 ).
cnf(c_0_22,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_23,plain,
( ~ product(e_2,X1,e_2)
| product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
~ equalish(e_1,e_2),
c_0_18 ).
cnf(c_0_25,plain,
( ~ product(X1,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_26,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_2,X3,X1)
| ~ product(e_1,e_2,X2)
| product(e_2,e_1,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
cnf(c_0_29,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_24]),c_0_28]) ).
cnf(c_0_31,plain,
( ~ product(e_2,X1,e_1)
| product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_16,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
product(e_1,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]) ).
cnf(c_0_34,plain,
( ~ product(X1,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_35,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_36,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_1,X3,X1)
| ~ product(e_2,e_1,X2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
product(e_2,e_1,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_24]) ).
cnf(c_0_38,plain,
~ equalish(e_2,e_1),
c_0_35 ).
cnf(c_0_39,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_40,negated_conjecture,
~ product(e_1,e_1,e_2),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_37])]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_19,c_0_37]) ).
cnf(c_0_42,plain,
product(e_1,e_1,e_1),
inference(sr,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 20:03:42 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.55 % Version: 3.5.1
% 0.24/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.55 % Starting sh5l with 300s (1) cores
% 0.24/0.55 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 63392 completed with status 0
% 0.24/0.55 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.24/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.55 % No SInE strategy applied
% 0.24/0.55 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.24/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/0.55 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.55 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.55 % new_bool_3 with pid 63401 completed with status 0
% 0.24/0.55 % Result found by new_bool_3
% 0.24/0.55 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.55 % No SInE strategy applied
% 0.24/0.55 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.24/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.24/0.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/0.55 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.55 % Preprocessing time : 0.001 s
% 0.24/0.55 % Presaturation interreduction done
% 0.24/0.55
% 0.24/0.55 % Proof found!
% 0.24/0.55 % SZS status Unsatisfiable
% 0.24/0.55 % SZS output start CNFRefutation
% See solution above
% 0.24/0.55 % Parsed axioms : 13
% 0.24/0.55 % Removed by relevancy pruning/SinE : 0
% 0.24/0.55 % Initial clauses : 13
% 0.24/0.55 % Removed in clause preprocessing : 0
% 0.24/0.55 % Initial clauses in saturation : 13
% 0.24/0.55 % Processed clauses : 120
% 0.24/0.55 % ...of these trivial : 1
% 0.24/0.55 % ...subsumed : 33
% 0.24/0.55 % ...remaining for further processing : 86
% 0.24/0.55 % Other redundant clauses eliminated : 0
% 0.24/0.55 % Clauses deleted for lack of memory : 0
% 0.24/0.55 % Backward-subsumed : 9
% 0.24/0.55 % Backward-rewritten : 21
% 0.24/0.55 % Generated clauses : 220
% 0.24/0.55 % ...of the previous two non-redundant : 189
% 0.24/0.55 % ...aggressively subsumed : 0
% 0.24/0.55 % Contextual simplify-reflections : 1
% 0.24/0.55 % Paramodulations : 219
% 0.24/0.55 % Factorizations : 0
% 0.24/0.55 % NegExts : 0
% 0.24/0.55 % Equation resolutions : 0
% 0.24/0.55 % Disequality decompositions : 0
% 0.24/0.55 % Total rewrite steps : 85
% 0.24/0.55 % ...of those cached : 78
% 0.24/0.55 % Propositional unsat checks : 0
% 0.24/0.55 % Propositional check models : 0
% 0.24/0.55 % Propositional check unsatisfiable : 0
% 0.24/0.55 % Propositional clauses : 0
% 0.24/0.55 % Propositional clauses after purity: 0
% 0.24/0.55 % Propositional unsat core size : 0
% 0.24/0.55 % Propositional preprocessing time : 0.000
% 0.24/0.55 % Propositional encoding time : 0.000
% 0.24/0.55 % Propositional solver time : 0.000
% 0.24/0.55 % Success case prop preproc time : 0.000
% 0.24/0.55 % Success case prop encoding time : 0.000
% 0.24/0.55 % Success case prop solver time : 0.000
% 0.24/0.55 % Current number of processed clauses : 42
% 0.24/0.55 % Positive orientable unit clauses : 9
% 0.24/0.55 % Positive unorientable unit clauses: 0
% 0.24/0.55 % Negative unit clauses : 3
% 0.24/0.55 % Non-unit-clauses : 30
% 0.24/0.55 % Current number of unprocessed clauses: 68
% 0.24/0.55 % ...number of literals in the above : 321
% 0.24/0.55 % Current number of archived formulas : 0
% 0.24/0.55 % Current number of archived clauses : 44
% 0.24/0.55 % Clause-clause subsumption calls (NU) : 579
% 0.24/0.55 % Rec. Clause-clause subsumption calls : 423
% 0.24/0.55 % Non-unit clause-clause subsumptions : 38
% 0.24/0.55 % Unit Clause-clause subsumption calls : 43
% 0.24/0.55 % Rewrite failures with RHS unbound : 0
% 0.24/0.55 % BW rewrite match attempts : 12
% 0.24/0.55 % BW rewrite match successes : 5
% 0.24/0.55 % Condensation attempts : 0
% 0.24/0.55 % Condensation successes : 0
% 0.24/0.55 % Termbank termtop insertions : 4084
% 0.24/0.55 % Search garbage collected termcells : 45
% 0.24/0.55
% 0.24/0.55 % -------------------------------------------------
% 0.24/0.55 % User time : 0.007 s
% 0.24/0.55 % System time : 0.005 s
% 0.24/0.55 % Total time : 0.012 s
% 0.24/0.55 % Maximum resident set size: 3380 pages
% 0.24/0.55
% 0.24/0.55 % -------------------------------------------------
% 0.24/0.55 % User time : 0.040 s
% 0.24/0.55 % System time : 0.017 s
% 0.24/0.55 % Total time : 0.056 s
% 0.24/0.55 % Maximum resident set size: 4608 pages
% 0.24/0.55 % E exiting
%------------------------------------------------------------------------------