%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:41:27 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 60 ( 26 unt; 4 nHn; 52 RR)
% Number of literals : 121 ( 0 equ; 61 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_product,axiom,
( ~ product(X1,X2,X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(product_substitution3,axiom,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(property_of_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(subgroup_member_substitution,axiom,
( ~ subgroup_member(X1)
| ~ equalish(X1,X2)
| subgroup_member(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_substitution) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_14,plain,
( ~ product(X1,X2,X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
inference(fof_simplification,[status(thm)],[closure_of_product]) ).
cnf(c_0_15,negated_conjecture,
~ subgroup_member(d),
inference(fof_simplification,[status(thm)],[prove_d_is_in_subgroup]) ).
cnf(c_0_16,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X4,X2) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_14 ).
cnf(c_0_18,negated_conjecture,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_19,negated_conjecture,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_20,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
inference(fof_simplification,[status(thm)],[closure_of_inverse]) ).
cnf(c_0_21,negated_conjecture,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_22,negated_conjecture,
~ subgroup_member(d),
c_0_15 ).
cnf(c_0_23,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X4,X2) ),
c_0_16 ).
cnf(c_0_24,negated_conjecture,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_25,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
c_0_20 ).
cnf(c_0_26,negated_conjecture,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]) ).
cnf(c_0_27,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[product_substitution3]) ).
cnf(c_0_28,negated_conjecture,
( ~ product(a,X1,d)
| equalish(c,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
property_of_O2 ).
cnf(c_0_30,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,plain,
( ~ product(X3,X4,X1)
| ~ equalish(X1,X2)
| product(X3,X4,X2) ),
c_0_27 ).
cnf(c_0_32,negated_conjecture,
equalish(c,element_in_O2(a,d)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_22]),c_0_30]) ).
cnf(c_0_33,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_34,negated_conjecture,
( ~ product(X1,X2,c)
| product(X1,X2,element_in_O2(a,d)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( ~ product(identity,X2,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
product(identity,c,element_in_O2(a,d)),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
equalish(element_in_O2(a,d),c),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity1]) ).
cnf(c_0_39,negated_conjecture,
( ~ product(X1,X2,element_in_O2(a,d))
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_40,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_38 ).
cnf(c_0_41,negated_conjecture,
product(identity,element_in_O2(a,d),c),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
( ~ product(X1,X3,identity)
| ~ product(X3,element_in_O2(a,d),X2)
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_44,negated_conjecture,
( ~ product(X1,element_in_O2(a,d),X2)
| product(inverse(X1),X2,c) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_45,plain,
( ~ subgroup_member(X1)
| ~ equalish(X1,X2)
| subgroup_member(X2) ),
inference(fof_simplification,[status(thm)],[subgroup_member_substitution]) ).
cnf(c_0_46,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
cnf(c_0_47,negated_conjecture,
product(inverse(a),d,c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_22]),c_0_30]) ).
cnf(c_0_48,plain,
( ~ subgroup_member(X1)
| ~ equalish(X1,X2)
| subgroup_member(X2) ),
c_0_45 ).
cnf(c_0_49,negated_conjecture,
( ~ product(X1,inverse(a),identity)
| product(X1,c,d) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( ~ subgroup_member(element_in_O2(a,d))
| subgroup_member(c) ),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_51,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
an_element_in_O2 ).
cnf(c_0_52,negated_conjecture,
product(inverse(inverse(a)),c,d),
inference(spm,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_53,negated_conjecture,
subgroup_member(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_22]),c_0_30]) ).
cnf(c_0_54,negated_conjecture,
( ~ product(X1,b,identity)
| product(X1,c,inverse(a)) ),
inference(spm,[status(thm)],[c_0_46,c_0_18]) ).
cnf(c_0_55,negated_conjecture,
~ subgroup_member(inverse(inverse(a))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_52]),c_0_53])]),c_0_22]) ).
cnf(c_0_56,negated_conjecture,
product(inverse(b),c,inverse(a)),
inference(spm,[status(thm)],[c_0_54,c_0_43]) ).
cnf(c_0_57,negated_conjecture,
~ subgroup_member(inverse(a)),
inference(spm,[status(thm)],[c_0_55,c_0_25]) ).
cnf(c_0_58,negated_conjecture,
~ subgroup_member(inverse(b)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_56]),c_0_53])]),c_0_57]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_25]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 19:55:33 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.47 % Version: 3.5.1
% 0.13/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.47 % Starting sh5l with 300s (1) cores
% 0.13/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1624594 completed with status 0
% 0.13/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.47 % No SInE strategy applied
% 0.13/0.47 % Search class: FGUNM-FFSS21-SFFFFFNN
% 0.13/0.47 % partial match(1): FGUSM-FFSS21-SFFFFFNN
% 0.13/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.47 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.13/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.47 % new_bool_3 with pid 1624603 completed with status 0
% 0.13/0.47 % Result found by new_bool_3
% 0.13/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.47 % No SInE strategy applied
% 0.13/0.47 % Search class: FGUNM-FFSS21-SFFFFFNN
% 0.13/0.47 % partial match(1): FGUSM-FFSS21-SFFFFFNN
% 0.13/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.47 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.13/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.47 % Preprocessing time : 0.001 s
% 0.13/0.47 % Presaturation interreduction done
% 0.13/0.47
% 0.13/0.47 % Proof found!
% 0.13/0.47 % SZS status Unsatisfiable
% 0.13/0.47 % SZS output start CNFRefutation
% See solution above
% 0.13/0.47 % Parsed axioms : 22
% 0.13/0.47 % Removed by relevancy pruning/SinE : 0
% 0.13/0.47 % Initial clauses : 22
% 0.13/0.47 % Removed in clause preprocessing : 0
% 0.13/0.47 % Initial clauses in saturation : 22
% 0.13/0.47 % Processed clauses : 426
% 0.13/0.47 % ...of these trivial : 6
% 0.13/0.47 % ...subsumed : 23
% 0.13/0.47 % ...remaining for further processing : 397
% 0.13/0.47 % Other redundant clauses eliminated : 0
% 0.13/0.47 % Clauses deleted for lack of memory : 0
% 0.13/0.47 % Backward-subsumed : 21
% 0.13/0.47 % Backward-rewritten : 15
% 0.13/0.47 % Generated clauses : 1816
% 0.13/0.47 % ...of the previous two non-redundant : 1096
% 0.13/0.47 % ...aggressively subsumed : 0
% 0.13/0.47 % Contextual simplify-reflections : 1
% 0.13/0.47 % Paramodulations : 1816
% 0.13/0.47 % Factorizations : 0
% 0.13/0.47 % NegExts : 0
% 0.13/0.47 % Equation resolutions : 0
% 0.13/0.47 % Disequality decompositions : 0
% 0.13/0.47 % Total rewrite steps : 839
% 0.13/0.47 % ...of those cached : 721
% 0.13/0.47 % Propositional unsat checks : 0
% 0.13/0.47 % Propositional check models : 0
% 0.13/0.47 % Propositional check unsatisfiable : 0
% 0.13/0.47 % Propositional clauses : 0
% 0.13/0.47 % Propositional clauses after purity: 0
% 0.13/0.47 % Propositional unsat core size : 0
% 0.13/0.47 % Propositional preprocessing time : 0.000
% 0.13/0.47 % Propositional encoding time : 0.000
% 0.13/0.47 % Propositional solver time : 0.000
% 0.13/0.47 % Success case prop preproc time : 0.000
% 0.13/0.47 % Success case prop encoding time : 0.000
% 0.13/0.47 % Success case prop solver time : 0.000
% 0.13/0.47 % Current number of processed clauses : 339
% 0.13/0.47 % Positive orientable unit clauses : 84
% 0.13/0.47 % Positive unorientable unit clauses: 0
% 0.13/0.47 % Negative unit clauses : 5
% 0.13/0.47 % Non-unit-clauses : 250
% 0.13/0.47 % Current number of unprocessed clauses: 705
% 0.13/0.47 % ...number of literals in the above : 1472
% 0.13/0.47 % Current number of archived formulas : 0
% 0.13/0.47 % Current number of archived clauses : 58
% 0.13/0.47 % Clause-clause subsumption calls (NU) : 5942
% 0.13/0.47 % Rec. Clause-clause subsumption calls : 4685
% 0.13/0.47 % Non-unit clause-clause subsumptions : 37
% 0.13/0.47 % Unit Clause-clause subsumption calls : 55
% 0.13/0.47 % Rewrite failures with RHS unbound : 0
% 0.13/0.47 % BW rewrite match attempts : 147
% 0.13/0.47 % BW rewrite match successes : 13
% 0.13/0.47 % Condensation attempts : 0
% 0.13/0.47 % Condensation successes : 0
% 0.13/0.47 % Termbank termtop insertions : 23859
% 0.13/0.47 % Search garbage collected termcells : 42
% 0.13/0.47
% 0.13/0.47 % -------------------------------------------------
% 0.13/0.47 % User time : 0.036 s
% 0.13/0.47 % System time : 0.008 s
% 0.13/0.47 % Total time : 0.044 s
% 0.13/0.47 % Maximum resident set size: 3644 pages
% 0.13/0.47
% 0.13/0.47 % -------------------------------------------------
% 0.13/0.47 % User time : 0.195 s
% 0.13/0.47 % System time : 0.021 s
% 0.13/0.47 % Total time : 0.216 s
% 0.13/0.47 % Maximum resident set size: 4608 pages
% 0.13/0.47 % E exiting
%------------------------------------------------------------------------------