%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP123-2.003 : 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 : 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 12:37:56 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.63s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 49 ( 27 unt; 8 nHn; 47 RR)
% Number of literals : 101 ( 0 equ; 55 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 : 61 ( 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/sandbox/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/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
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(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
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(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_0_13,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_14,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_15,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_13 ).
cnf(c_0_16,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_17,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_18,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_14 ).
cnf(c_0_19,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_20,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_15,c_0_16]) ).
cnf(c_0_21,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_22,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_23,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_17 ).
cnf(c_0_24,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
~ equalish(e_1,e_3),
c_0_22 ).
cnf(c_0_27,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_28,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_29,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
~ equalish(e_3,e_1),
c_0_27 ).
cnf(c_0_31,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_32,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_33,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_34,plain,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,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_36,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_20,c_0_31]) ).
cnf(c_0_37,plain,
~ equalish(e_2,e_3),
c_0_32 ).
cnf(c_0_38,plain,
~ equalish(e_2,e_1),
c_0_33 ).
cnf(c_0_39,plain,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( ~ product(X6,X5,X4)
| ~ product(X6,X2,X1)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_35 ).
cnf(c_0_41,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_24,c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_44,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X1,X3)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_45,plain,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
~ equalish(e_3,e_2),
c_0_43 ).
cnf(c_0_47,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_2,e_2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_34]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.49 % Computer : n010.cluster.edu
% 0.21/0.49 % Model : x86_64 x86_64
% 0.21/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.49 % Memory : 8046.5625MB
% 0.21/0.49 % OS : Linux 6.8.0-71-generic
% 0.21/0.49 % CPULimit : 300
% 0.21/0.49 % WCLimit : 300
% 0.21/0.49 % DateTime : Sun Sep 20 19:58:40 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.58 Running first-order theorem proving
% 0.25/0.58 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
% 0.25/0.63 % Version: 3.5.1
% 0.25/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.63 % Starting sh5l with 300s (1) cores
% 0.25/0.63 % sh5l with pid 3383944 completed with status 0
% 0.25/0.63 % Result found by sh5l
% 0.25/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.63 % Starting sh5l with 300s (1) cores
% 0.25/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.25/0.63 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.25/0.63 % Search class: FGHNF-FFSM00-SFFFFFNN
% 0.25/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.63 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.63 % SubtermCWHack with pid 3383952 completed with status 0
% 0.25/0.63 % Result found by SubtermCWHack
% 0.25/0.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.63 % Starting sh5l with 300s (1) cores
% 0.25/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.25/0.63 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.25/0.63 % Search class: FGHNF-FFSM00-SFFFFFNN
% 0.25/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.63 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.63 % Preprocessing time : 0.002 s
% 0.25/0.63
% 0.25/0.63 % Proof found!
% 0.25/0.63 % SZS status Unsatisfiable
% 0.25/0.63 % SZS output start CNFRefutation
% See solution above
% 0.25/0.63 % Parsed axioms : 22
% 0.25/0.63 % Removed by relevancy pruning/SinE : 0
% 0.25/0.63 % Initial clauses : 22
% 0.25/0.63 % Removed in clause preprocessing : 0
% 0.25/0.63 % Initial clauses in saturation : 22
% 0.25/0.63 % Processed clauses : 80
% 0.25/0.63 % ...of these trivial : 0
% 0.25/0.63 % ...subsumed : 6
% 0.25/0.63 % ...remaining for further processing : 74
% 0.25/0.63 % Other redundant clauses eliminated : 0
% 0.25/0.63 % Clauses deleted for lack of memory : 0
% 0.25/0.63 % Backward-subsumed : 11
% 0.25/0.63 % Backward-rewritten : 1
% 0.25/0.63 % Generated clauses : 112
% 0.25/0.63 % ...of the previous two non-redundant : 103
% 0.25/0.63 % ...aggressively subsumed : 0
% 0.25/0.63 % Contextual simplify-reflections : 0
% 0.25/0.63 % Paramodulations : 111
% 0.25/0.63 % Factorizations : 0
% 0.25/0.63 % NegExts : 0
% 0.25/0.63 % Equation resolutions : 0
% 0.25/0.63 % Disequality decompositions : 0
% 0.25/0.63 % Total rewrite steps : 8
% 0.25/0.63 % ...of those cached : 3
% 0.25/0.63 % Propositional unsat checks : 0
% 0.25/0.63 % Propositional check models : 0
% 0.25/0.63 % Propositional check unsatisfiable : 0
% 0.25/0.63 % Propositional clauses : 0
% 0.25/0.63 % Propositional clauses after purity: 0
% 0.25/0.63 % Propositional unsat core size : 0
% 0.25/0.63 % Propositional preprocessing time : 0.000
% 0.25/0.63 % Propositional encoding time : 0.000
% 0.25/0.63 % Propositional solver time : 0.000
% 0.25/0.63 % Success case prop preproc time : 0.000
% 0.25/0.63 % Success case prop encoding time : 0.000
% 0.25/0.63 % Success case prop solver time : 0.000
% 0.25/0.63 % Current number of processed clauses : 61
% 0.25/0.63 % Positive orientable unit clauses : 12
% 0.25/0.63 % Positive unorientable unit clauses: 0
% 0.25/0.63 % Negative unit clauses : 18
% 0.25/0.63 % Non-unit-clauses : 31
% 0.25/0.63 % Current number of unprocessed clauses: 31
% 0.25/0.63 % ...number of literals in the above : 123
% 0.25/0.63 % Current number of archived formulas : 0
% 0.25/0.63 % Current number of archived clauses : 13
% 0.25/0.63 % Clause-clause subsumption calls (NU) : 231
% 0.25/0.63 % Rec. Clause-clause subsumption calls : 190
% 0.25/0.63 % Non-unit clause-clause subsumptions : 5
% 0.25/0.63 % Unit Clause-clause subsumption calls : 27
% 0.25/0.63 % Rewrite failures with RHS unbound : 0
% 0.25/0.63 % BW rewrite match attempts : 12
% 0.25/0.63 % BW rewrite match successes : 1
% 0.25/0.63 % Condensation attempts : 0
% 0.25/0.63 % Condensation successes : 0
% 0.25/0.63 % Termbank termtop insertions : 1790
% 0.25/0.63 % Search garbage collected termcells : 53
% 0.25/0.63
% 0.25/0.63 % -------------------------------------------------
% 0.25/0.63 % User time : 0.010 s
% 0.25/0.63 % System time : 0.003 s
% 0.25/0.63 % Total time : 0.014 s
% 0.25/0.63 % Maximum resident set size: 3644 pages
% 0.25/0.63
% 0.25/0.63 % -------------------------------------------------
% 0.25/0.63 % User time : 0.011 s
% 0.25/0.63 % System time : 0.012 s
% 0.25/0.63 % Total time : 0.023 s
% 0.25/0.63 % Maximum resident set size: 4352 pages
% 0.25/0.63 % E exiting
%------------------------------------------------------------------------------