%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP123-3.003 : 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 : n016.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 12:37:56 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.59s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 28 unt; 11 nHn; 53 RR)
% Number of literals : 114 ( 0 equ; 57 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
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_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
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_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_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(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
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/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
cnf(c_0_12,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
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,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_12 ).
cnf(c_0_15,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_16,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_17,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_13 ).
cnf(c_0_18,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_19,plain,
( ~ group_element(X1)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_21,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_22,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_16 ).
cnf(c_0_23,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
~ equalish(e_2,e_3),
c_0_21 ).
cnf(c_0_26,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_27,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_28,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
~ equalish(e_3,e_2),
c_0_26 ).
cnf(c_0_30,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_31,plain,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
~ equalish(e_1,e_2),
c_0_30 ).
cnf(c_0_33,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_34,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_35,plain,
~ product(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_37,plain,
( ~ group_element(X1)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_38,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
~ equalish(e_1,e_3),
c_0_36 ).
cnf(c_0_40,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_41,plain,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_38]),c_0_39]) ).
cnf(c_0_42,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_25]) ).
cnf(c_0_43,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_44,plain,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_45,plain,
product(e_3,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_29]) ).
cnf(c_0_46,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_43 ).
cnf(c_0_47,plain,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_48,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_17,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X1,X3)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_18]) ).
cnf(c_0_50,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_34]),c_0_47]) ).
cnf(c_0_51,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_39,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( ~ product(e_1,e_2,X1)
| ~ product(e_3,e_3,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_45]),c_0_25]) ).
cnf(c_0_53,plain,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_18]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % 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 20:03:07 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.52 Running first-order theorem proving
% 0.27/0.52 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
% 0.27/0.59 % Version: 3.5.1
% 0.27/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.59 % Starting sh5l with 300s (1) cores
% 0.27/0.59 % new_bool_3 with pid 670653 completed with status 0
% 0.27/0.59 % Result found by new_bool_3
% 0.27/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.59 % Search class: FGHNF-FFMM00-SFFFFFNN
% 0.27/0.59 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.59 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.59 % SubtermCWHack with pid 670658 completed with status 0
% 0.27/0.59 % Result found by SubtermCWHack
% 0.27/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.59 % Search class: FGHNF-FFMM00-SFFFFFNN
% 0.27/0.59 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.59 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.59 % Preprocessing time : 0.002 s
% 0.27/0.59
% 0.27/0.59 % Proof found!
% 0.27/0.59 % SZS status Unsatisfiable
% 0.27/0.59 % SZS output start CNFRefutation
% See solution above
% 0.27/0.59 % Parsed axioms : 32
% 0.27/0.59 % Removed by relevancy pruning/SinE : 0
% 0.27/0.59 % Initial clauses : 32
% 0.27/0.59 % Removed in clause preprocessing : 0
% 0.27/0.59 % Initial clauses in saturation : 32
% 0.27/0.59 % Processed clauses : 182
% 0.27/0.59 % ...of these trivial : 0
% 0.27/0.59 % ...subsumed : 35
% 0.27/0.59 % ...remaining for further processing : 147
% 0.27/0.59 % Other redundant clauses eliminated : 0
% 0.27/0.59 % Clauses deleted for lack of memory : 0
% 0.27/0.59 % Backward-subsumed : 24
% 0.27/0.59 % Backward-rewritten : 12
% 0.27/0.59 % Generated clauses : 267
% 0.27/0.59 % ...of the previous two non-redundant : 249
% 0.27/0.59 % ...aggressively subsumed : 0
% 0.27/0.59 % Contextual simplify-reflections : 0
% 0.27/0.59 % Paramodulations : 263
% 0.27/0.59 % Factorizations : 0
% 0.27/0.59 % NegExts : 0
% 0.27/0.59 % Equation resolutions : 0
% 0.27/0.59 % Disequality decompositions : 0
% 0.27/0.59 % Total rewrite steps : 34
% 0.27/0.59 % ...of those cached : 18
% 0.27/0.59 % Propositional unsat checks : 0
% 0.27/0.59 % Propositional check models : 0
% 0.27/0.59 % Propositional check unsatisfiable : 0
% 0.27/0.59 % Propositional clauses : 0
% 0.27/0.59 % Propositional clauses after purity: 0
% 0.27/0.59 % Propositional unsat core size : 0
% 0.27/0.59 % Propositional preprocessing time : 0.000
% 0.27/0.59 % Propositional encoding time : 0.000
% 0.27/0.59 % Propositional solver time : 0.000
% 0.27/0.59 % Success case prop preproc time : 0.000
% 0.27/0.59 % Success case prop encoding time : 0.000
% 0.27/0.59 % Success case prop solver time : 0.000
% 0.27/0.59 % Current number of processed clauses : 107
% 0.27/0.59 % Positive orientable unit clauses : 23
% 0.27/0.59 % Positive unorientable unit clauses: 0
% 0.27/0.59 % Negative unit clauses : 31
% 0.27/0.59 % Non-unit-clauses : 53
% 0.27/0.59 % Current number of unprocessed clauses: 67
% 0.27/0.59 % ...number of literals in the above : 293
% 0.27/0.59 % Current number of archived formulas : 0
% 0.27/0.59 % Current number of archived clauses : 40
% 0.27/0.59 % Clause-clause subsumption calls (NU) : 816
% 0.27/0.59 % Rec. Clause-clause subsumption calls : 529
% 0.27/0.59 % Non-unit clause-clause subsumptions : 27
% 0.27/0.59 % Unit Clause-clause subsumption calls : 747
% 0.27/0.59 % Rewrite failures with RHS unbound : 0
% 0.27/0.59 % BW rewrite match attempts : 28
% 0.27/0.59 % BW rewrite match successes : 8
% 0.27/0.59 % Condensation attempts : 0
% 0.27/0.59 % Condensation successes : 0
% 0.27/0.59 % Termbank termtop insertions : 4277
% 0.27/0.59 % Search garbage collected termcells : 95
% 0.27/0.59
% 0.27/0.59 % -------------------------------------------------
% 0.27/0.59 % User time : 0.020 s
% 0.27/0.59 % System time : 0.004 s
% 0.27/0.59 % Total time : 0.023 s
% 0.27/0.59 % Maximum resident set size: 3652 pages
% 0.27/0.59
% 0.27/0.59 % -------------------------------------------------
% 0.27/0.59 % User time : 0.024 s
% 0.27/0.59 % System time : 0.008 s
% 0.27/0.59 % Total time : 0.032 s
% 0.27/0.59 % Maximum resident set size: 4864 pages
% 0.27/0.59 % E exiting
%------------------------------------------------------------------------------