%------------------------------------------------------------------------------
% File : E---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 : n013.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 12:38:41 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.57s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 53 ( 15 unt; 17 nHn; 53 RR)
% Number of literals : 130 ( 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 : 67 ( 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(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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
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(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(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(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_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_14,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_11 ).
cnf(c_0_15,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,axiom,
group_element(e_1),
element_1 ).
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_13 ).
cnf(c_0_19,plain,
( ~ product(e_2,X1,e_2)
| product(e_2,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_21,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_17 ).
cnf(c_0_22,plain,
( ~ product(e_2,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,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_24,plain,
( ~ group_element(X1)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_25,plain,
( ~ product(e_1,X1,e_2)
| product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_26,plain,
( ~ product(X1,e_2,e_1)
| ~ product(e_2,e_1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_23 ).
cnf(c_0_28,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_10]) ).
cnf(c_0_29,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_30,plain,
( ~ product(e_1,e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_31,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_32,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_27,c_0_15]) ).
cnf(c_0_33,plain,
( ~ product(X1,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_34,plain,
~ equalish(e_2,e_1),
c_0_29 ).
cnf(c_0_35,plain,
( ~ product(X1,e_2,e_1)
| ~ product(e_1,e_1,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_36,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_37,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_32,c_0_15]) ).
cnf(c_0_38,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_39,plain,
( ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( ~ product(X1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_41,plain,
( ~ product(X1,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_42,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_43,negated_conjecture,
~ product(e_1,e_1,e_2),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_18]),c_0_39]) ).
cnf(c_0_44,plain,
( ~ product(e_2,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_45,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_41]) ).
cnf(c_0_46,plain,
product(e_1,e_1,e_1),
inference(sr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( product(e_1,e_2,e_1)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_15]) ).
cnf(c_0_48,plain,
~ product(e_1,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_49,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_27,c_0_20]) ).
cnf(c_0_50,plain,
product(e_2,e_2,e_1),
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( ~ product(X2,X1,e_1)
| ~ product(e_1,X1,X2)
| equalish(X1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_48]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_46])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n013.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 20 20:00:20 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 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
% 0.27/0.57 % Version: 3.5.1
% 0.27/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.57 % Starting sh5l with 300s (1) cores
% 0.27/0.57 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3285653 completed with status 0
% 0.27/0.57 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.27/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.57 % No SInE strategy applied
% 0.27/0.57 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.27/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.27/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.57 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.57 % SubtermCWHack with pid 3285654 completed with status 0
% 0.27/0.57 % Result found by SubtermCWHack
% 0.27/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.57 % No SInE strategy applied
% 0.27/0.57 % Search class: FGHNF-FFSS00-SFFFFFNN
% 0.27/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.57 % Preprocessing time : 0.002 s
% 0.27/0.57
% 0.27/0.57 % Proof found!
% 0.27/0.57 % SZS status Unsatisfiable
% 0.27/0.57 % SZS output start CNFRefutation
% See solution above
% 0.27/0.57 % Parsed axioms : 13
% 0.27/0.57 % Removed by relevancy pruning/SinE : 0
% 0.27/0.57 % Initial clauses : 13
% 0.27/0.57 % Removed in clause preprocessing : 0
% 0.27/0.57 % Initial clauses in saturation : 13
% 0.27/0.57 % Processed clauses : 177
% 0.27/0.57 % ...of these trivial : 1
% 0.27/0.57 % ...subsumed : 48
% 0.27/0.57 % ...remaining for further processing : 128
% 0.27/0.57 % Other redundant clauses eliminated : 0
% 0.27/0.57 % Clauses deleted for lack of memory : 0
% 0.27/0.57 % Backward-subsumed : 43
% 0.27/0.57 % Backward-rewritten : 37
% 0.27/0.57 % Generated clauses : 235
% 0.27/0.57 % ...of the previous two non-redundant : 233
% 0.27/0.57 % ...aggressively subsumed : 0
% 0.27/0.57 % Contextual simplify-reflections : 1
% 0.27/0.57 % Paramodulations : 231
% 0.27/0.57 % Factorizations : 0
% 0.27/0.57 % NegExts : 0
% 0.27/0.57 % Equation resolutions : 0
% 0.27/0.57 % Disequality decompositions : 0
% 0.27/0.57 % Total rewrite steps : 40
% 0.27/0.57 % ...of those cached : 36
% 0.27/0.57 % Propositional unsat checks : 0
% 0.27/0.57 % Propositional check models : 0
% 0.27/0.57 % Propositional check unsatisfiable : 0
% 0.27/0.57 % Propositional clauses : 0
% 0.27/0.57 % Propositional clauses after purity: 0
% 0.27/0.57 % Propositional unsat core size : 0
% 0.27/0.57 % Propositional preprocessing time : 0.000
% 0.27/0.57 % Propositional encoding time : 0.000
% 0.27/0.57 % Propositional solver time : 0.000
% 0.27/0.57 % Success case prop preproc time : 0.000
% 0.27/0.57 % Success case prop encoding time : 0.000
% 0.27/0.57 % Success case prop solver time : 0.000
% 0.27/0.57 % Current number of processed clauses : 44
% 0.27/0.57 % Positive orientable unit clauses : 8
% 0.27/0.57 % Positive unorientable unit clauses: 0
% 0.27/0.57 % Negative unit clauses : 7
% 0.27/0.57 % Non-unit-clauses : 29
% 0.27/0.57 % Current number of unprocessed clauses: 14
% 0.27/0.57 % ...number of literals in the above : 52
% 0.27/0.57 % Current number of archived formulas : 0
% 0.27/0.57 % Current number of archived clauses : 84
% 0.27/0.57 % Clause-clause subsumption calls (NU) : 1121
% 0.27/0.57 % Rec. Clause-clause subsumption calls : 853
% 0.27/0.57 % Non-unit clause-clause subsumptions : 50
% 0.27/0.57 % Unit Clause-clause subsumption calls : 123
% 0.27/0.57 % Rewrite failures with RHS unbound : 0
% 0.27/0.57 % BW rewrite match attempts : 15
% 0.27/0.57 % BW rewrite match successes : 4
% 0.27/0.57 % Condensation attempts : 0
% 0.27/0.57 % Condensation successes : 0
% 0.27/0.57 % Termbank termtop insertions : 3626
% 0.27/0.57 % Search garbage collected termcells : 45
% 0.27/0.57
% 0.27/0.57 % -------------------------------------------------
% 0.27/0.57 % User time : 0.016 s
% 0.27/0.57 % System time : 0.006 s
% 0.27/0.57 % Total time : 0.022 s
% 0.27/0.57 % Maximum resident set size: 3380 pages
% 0.27/0.57
% 0.27/0.57 % -------------------------------------------------
% 0.27/0.57 % User time : 0.045 s
% 0.27/0.57 % System time : 0.020 s
% 0.27/0.57 % Total time : 0.065 s
% 0.27/0.57 % Maximum resident set size: 4608 pages
% 0.27/0.57 % E exiting
%------------------------------------------------------------------------------