%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:37:32 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 69 ( 34 unt; 6 nHn; 51 RR)
% Number of literals : 136 ( 10 equ; 62 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 118 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(closure_of_product,axiom,
( ~ product(X1,X2,X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-1.ax',closure_of_product) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
cnf(property_of_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(b_is_in_subgroup,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-1.ax',closure_of_inverse) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_16,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity2]) ).
cnf(c_0_17,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_16 ).
cnf(c_0_18,negated_conjecture,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_19,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_20,negated_conjecture,
( ~ product(X3,a,X1)
| ~ product(X3,d,X2)
| product(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_22,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_19 ).
cnf(c_0_23,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_24,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_25,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_26,negated_conjecture,
( ~ product(X2,a,X1)
| product(X1,c,multiply(X2,d)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_28,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_24 ).
cnf(c_0_30,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
product(identity,c,multiply(inverse(a),d)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
multiply(identity,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_34,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_35,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_36,negated_conjecture,
~ subgroup_member(d),
inference(fof_simplification,[status(thm)],[prove_d_is_in_subgroup]) ).
cnf(c_0_37,plain,
( ~ product(X4,identity,X3)
| ~ product(X4,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_38,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_39,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
property_of_O2 ).
cnf(c_0_40,negated_conjecture,
multiply(inverse(a),d) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_41,plain,
( ~ product(X1,inverse(X2),identity)
| product(X1,identity,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_42,plain,
( ~ product(X1,X2,X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_35 ).
cnf(c_0_43,negated_conjecture,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_44,negated_conjecture,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_45,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
inference(fof_simplification,[status(thm)],[closure_of_inverse]) ).
cnf(c_0_46,negated_conjecture,
~ subgroup_member(d),
c_0_36 ).
cnf(c_0_47,plain,
( ~ product(X3,inverse(X2),X1)
| product(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_21]),c_0_38]) ).
cnf(c_0_48,plain,
( ~ product(X5,X1,X3)
| ~ product(X5,X2,X4)
| product(X3,element_in_O2(X1,X2),X4)
| subgroup_member(X2)
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
product(inverse(a),d,c),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_50,plain,
product(inverse(inverse(X1)),identity,X1),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_51,negated_conjecture,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
c_0_45 ).
cnf(c_0_53,negated_conjecture,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_18]),c_0_46]) ).
cnf(c_0_54,negated_conjecture,
product(c,a,b),
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( ~ product(inverse(a),X1,X2)
| product(X2,element_in_O2(X1,d),c)
| subgroup_member(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_46]) ).
cnf(c_0_56,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_57,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_50]),c_0_38]) ).
cnf(c_0_58,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_59,plain,
( ~ subgroup_member(X1)
| subgroup_member(identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_27]),c_0_52]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(X1,c,identity)
| product(X1,b,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
product(identity,element_in_O2(a,d),c),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_57]),c_0_58]) ).
cnf(c_0_62,negated_conjecture,
subgroup_member(identity),
inference(spm,[status(thm)],[c_0_59,c_0_44]) ).
cnf(c_0_63,negated_conjecture,
product(inverse(c),b,a),
inference(spm,[status(thm)],[c_0_60,c_0_27]) ).
cnf(c_0_64,negated_conjecture,
( ~ subgroup_member(element_in_O2(a,d))
| subgroup_member(c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_61]),c_0_62])]) ).
cnf(c_0_65,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
an_element_in_O2 ).
cnf(c_0_66,negated_conjecture,
~ subgroup_member(inverse(c)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_63]),c_0_44])]),c_0_58]) ).
cnf(c_0_67,negated_conjecture,
subgroup_member(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_46]),c_0_58]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_52]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 19:55:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.15/0.45 % Version: 3.5.1
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4098868 completed with status 0
% 0.15/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.45 % No SInE strategy applied
% 0.15/0.45 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.45 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.15/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.45 % new_bool_3 with pid 4098878 completed with status 0
% 0.15/0.45 % Result found by new_bool_3
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.45 % No SInE strategy applied
% 0.15/0.45 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.45 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.15/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.45 % Preprocessing time : 0.001 s
% 0.15/0.45 % Presaturation interreduction done
% 0.15/0.45
% 0.15/0.45 % Proof found!
% 0.15/0.45 % SZS status Unsatisfiable
% 0.15/0.45 % SZS output start CNFRefutation
% See solution above
% 0.15/0.45 % Parsed axioms : 16
% 0.15/0.45 % Removed by relevancy pruning/SinE : 0
% 0.15/0.45 % Initial clauses : 16
% 0.15/0.45 % Removed in clause preprocessing : 0
% 0.15/0.45 % Initial clauses in saturation : 16
% 0.15/0.45 % Processed clauses : 195
% 0.15/0.45 % ...of these trivial : 5
% 0.15/0.45 % ...subsumed : 33
% 0.15/0.45 % ...remaining for further processing : 157
% 0.15/0.45 % Other redundant clauses eliminated : 0
% 0.15/0.45 % Clauses deleted for lack of memory : 0
% 0.15/0.45 % Backward-subsumed : 4
% 0.15/0.45 % Backward-rewritten : 29
% 0.15/0.45 % Generated clauses : 547
% 0.15/0.45 % ...of the previous two non-redundant : 400
% 0.15/0.45 % ...aggressively subsumed : 0
% 0.15/0.45 % Contextual simplify-reflections : 2
% 0.15/0.45 % Paramodulations : 545
% 0.15/0.45 % Factorizations : 0
% 0.15/0.45 % NegExts : 0
% 0.15/0.45 % Equation resolutions : 0
% 0.15/0.45 % Disequality decompositions : 0
% 0.15/0.45 % Total rewrite steps : 259
% 0.15/0.45 % ...of those cached : 186
% 0.15/0.45 % Propositional unsat checks : 0
% 0.15/0.45 % Propositional check models : 0
% 0.15/0.45 % Propositional check unsatisfiable : 0
% 0.15/0.45 % Propositional clauses : 0
% 0.15/0.45 % Propositional clauses after purity: 0
% 0.15/0.45 % Propositional unsat core size : 0
% 0.15/0.45 % Propositional preprocessing time : 0.000
% 0.15/0.45 % Propositional encoding time : 0.000
% 0.15/0.45 % Propositional solver time : 0.000
% 0.15/0.45 % Success case prop preproc time : 0.000
% 0.15/0.45 % Success case prop encoding time : 0.000
% 0.15/0.45 % Success case prop solver time : 0.000
% 0.15/0.45 % Current number of processed clauses : 106
% 0.15/0.45 % Positive orientable unit clauses : 36
% 0.15/0.45 % Positive unorientable unit clauses: 0
% 0.15/0.45 % Negative unit clauses : 3
% 0.15/0.45 % Non-unit-clauses : 67
% 0.15/0.45 % Current number of unprocessed clauses: 207
% 0.15/0.45 % ...number of literals in the above : 524
% 0.15/0.45 % Current number of archived formulas : 0
% 0.15/0.45 % Current number of archived clauses : 51
% 0.15/0.45 % Clause-clause subsumption calls (NU) : 1058
% 0.15/0.45 % Rec. Clause-clause subsumption calls : 896
% 0.15/0.45 % Non-unit clause-clause subsumptions : 29
% 0.15/0.45 % Unit Clause-clause subsumption calls : 33
% 0.15/0.45 % Rewrite failures with RHS unbound : 0
% 0.15/0.45 % BW rewrite match attempts : 31
% 0.15/0.45 % BW rewrite match successes : 13
% 0.15/0.45 % Condensation attempts : 0
% 0.15/0.45 % Condensation successes : 0
% 0.15/0.45 % Termbank termtop insertions : 7022
% 0.15/0.45 % Search garbage collected termcells : 24
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.018 s
% 0.15/0.45 % System time : 0.002 s
% 0.15/0.45 % Total time : 0.020 s
% 0.15/0.45 % Maximum resident set size: 3644 pages
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.084 s
% 0.15/0.45 % System time : 0.013 s
% 0.15/0.45 % Total time : 0.097 s
% 0.15/0.45 % Maximum resident set size: 4608 pages
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------