%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:42:36 PM UTC 2026
% Result : Unsatisfiable 0.29s 0.64s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 52 ( 14 unt; 17 nHn; 52 RR)
% Number of literals : 129 ( 0 equ; 71 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 : 66 ( 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/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(qg1_2,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
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(X1,e_2,e_1)
| product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_14,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_15,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_11 ).
cnf(c_0_16,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_18,plain,
~ equalish(e_1,e_2),
c_0_14 ).
cnf(c_0_19,plain,
( ~ product(e_1,X1,e_2)
| product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,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_21,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_22,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_17 ).
cnf(c_0_23,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ product(e_2,X1,e_2)
| product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
inference(fof_simplification,[status(thm)],[qg1_2]) ).
cnf(c_0_26,plain,
~ equalish(e_2,e_1),
c_0_21 ).
cnf(c_0_27,plain,
( ~ product(X1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_25 ).
cnf(c_0_30,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_32,plain,
( ~ product(X1,e_2,e_1)
| ~ product(e_2,e_1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_33,plain,
( ~ product(X1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_34,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_2,X1,X3)
| ~ product(e_2,e_2,X2)
| product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_35,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_36,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_10]) ).
cnf(c_0_37,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_38,plain,
( ~ product(e_2,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( ~ product(X2,X1,e_2)
| ~ product(e_2,X1,X2)
| product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_40,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( ~ product(X3,X1,X2)
| ~ product(e_1,X1,X3)
| ~ product(e_2,e_2,X2)
| product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_43,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_44,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_45,negated_conjecture,
~ product(e_1,e_1,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_18]),c_0_30]) ).
cnf(c_0_46,plain,
( ~ product(X1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(e_1,X1,X2)
| product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
product(e_1,e_1,e_1),
inference(sr,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
product(e_1,e_2,e_1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_48])]),c_0_18]) ).
cnf(c_0_51,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_48])]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.49 % Computer : n019.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Sun Sep 20 20:01:04 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.19/0.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.57 Running first-order theorem proving
% 0.23/0.57 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
% 0.29/0.64 % Version: 3.5.1
% 0.29/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.29/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.29/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.29/0.64 % Starting sh5l with 300s (1) cores
% 0.29/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 798706 completed with status 0
% 0.29/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.29/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.29/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.64 % No SInE strategy applied
% 0.29/0.64 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.29/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.29/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.29/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.29/0.64 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 798712 completed with status 0
% 0.29/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.29/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.29/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.29/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.29/0.64 % No SInE strategy applied
% 0.29/0.64 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.29/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.29/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.29/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.29/0.64 % Preprocessing time : 0.001 s
% 0.29/0.64 % Presaturation interreduction done
% 0.29/0.64
% 0.29/0.64 % Proof found!
% 0.29/0.64 % SZS status Unsatisfiable
% 0.29/0.64 % SZS output start CNFRefutation
% See solution above
% 0.29/0.64 % Parsed axioms : 13
% 0.29/0.64 % Removed by relevancy pruning/SinE : 0
% 0.29/0.64 % Initial clauses : 13
% 0.29/0.64 % Removed in clause preprocessing : 0
% 0.29/0.64 % Initial clauses in saturation : 13
% 0.29/0.64 % Processed clauses : 151
% 0.29/0.64 % ...of these trivial : 0
% 0.29/0.64 % ...subsumed : 32
% 0.29/0.64 % ...remaining for further processing : 118
% 0.29/0.64 % Other redundant clauses eliminated : 0
% 0.29/0.64 % Clauses deleted for lack of memory : 0
% 0.29/0.64 % Backward-subsumed : 13
% 0.29/0.64 % Backward-rewritten : 39
% 0.29/0.64 % Generated clauses : 211
% 0.29/0.64 % ...of the previous two non-redundant : 204
% 0.29/0.64 % ...aggressively subsumed : 0
% 0.29/0.64 % Contextual simplify-reflections : 1
% 0.29/0.64 % Paramodulations : 210
% 0.29/0.64 % Factorizations : 0
% 0.29/0.64 % NegExts : 0
% 0.29/0.64 % Equation resolutions : 0
% 0.29/0.64 % Disequality decompositions : 0
% 0.29/0.64 % Total rewrite steps : 41
% 0.29/0.64 % ...of those cached : 39
% 0.29/0.64 % Propositional unsat checks : 0
% 0.29/0.64 % Propositional check models : 0
% 0.29/0.64 % Propositional check unsatisfiable : 0
% 0.29/0.64 % Propositional clauses : 0
% 0.29/0.64 % Propositional clauses after purity: 0
% 0.29/0.64 % Propositional unsat core size : 0
% 0.29/0.64 % Propositional preprocessing time : 0.000
% 0.29/0.64 % Propositional encoding time : 0.000
% 0.29/0.64 % Propositional solver time : 0.000
% 0.29/0.64 % Success case prop preproc time : 0.000
% 0.29/0.64 % Success case prop encoding time : 0.000
% 0.29/0.64 % Success case prop solver time : 0.000
% 0.29/0.64 % Current number of processed clauses : 52
% 0.29/0.64 % Positive orientable unit clauses : 6
% 0.29/0.64 % Positive unorientable unit clauses: 0
% 0.29/0.64 % Negative unit clauses : 3
% 0.29/0.64 % Non-unit-clauses : 43
% 0.29/0.64 % Current number of unprocessed clauses: 79
% 0.29/0.64 % ...number of literals in the above : 323
% 0.29/0.64 % Current number of archived formulas : 0
% 0.29/0.64 % Current number of archived clauses : 66
% 0.29/0.64 % Clause-clause subsumption calls (NU) : 985
% 0.29/0.64 % Rec. Clause-clause subsumption calls : 722
% 0.29/0.64 % Non-unit clause-clause subsumptions : 33
% 0.29/0.64 % Unit Clause-clause subsumption calls : 56
% 0.29/0.64 % Rewrite failures with RHS unbound : 0
% 0.29/0.64 % BW rewrite match attempts : 7
% 0.29/0.64 % BW rewrite match successes : 2
% 0.29/0.64 % Condensation attempts : 0
% 0.29/0.64 % Condensation successes : 0
% 0.29/0.64 % Termbank termtop insertions : 3453
% 0.29/0.64 % Search garbage collected termcells : 45
% 0.29/0.64
% 0.29/0.64 % -------------------------------------------------
% 0.29/0.64 % User time : 0.010 s
% 0.29/0.64 % System time : 0.004 s
% 0.29/0.64 % Total time : 0.014 s
% 0.29/0.64 % Maximum resident set size: 3380 pages
% 0.29/0.64
% 0.29/0.64 % -------------------------------------------------
% 0.29/0.64 % User time : 0.035 s
% 0.29/0.64 % System time : 0.018 s
% 0.29/0.64 % Total time : 0.053 s
% 0.29/0.64 % Maximum resident set size: 4608 pages
% 0.29/0.64 % E exiting
%------------------------------------------------------------------------------