%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP040-4 : 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 : n019.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 12:37:33 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.44s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of clauses : 65 ( 32 unt; 5 nHn; 50 RR)
% Number of literals : 132 ( 14 equ; 63 neg)
% Maximal clause size : 4 ( 2 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 : 116 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(a_times_c_is_d,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| X4 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(associativity1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(total_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| X4 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(closure_of_product_and_inverse,axiom,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
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(d_in_subgroup,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_in_subgroup) ).
cnf(a_in_subgroup,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_in_subgroup) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_self_cancelling) ).
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(closure_of_inverse,axiom,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(c_0_18,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_19,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_18 ).
cnf(c_0_20,hypothesis,
product(a,c,d),
a_times_c_is_d ).
cnf(c_0_21,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| X4 = X1 ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_22,hypothesis,
( ~ product(X3,a,X1)
| ~ product(X3,d,X2)
| product(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
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,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| X4 = X1 ),
c_0_21 ).
cnf(c_0_26,hypothesis,
( ~ product(inverse(d),a,X1)
| product(X1,c,identity) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_28,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_24 ).
cnf(c_0_29,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_30,plain,
( ~ product(X1,X2,identity)
| X1 = inverse(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_31,hypothesis,
product(multiply(inverse(d),a),c,identity),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| X4 = X2 ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_33,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_35,hypothesis,
multiply(inverse(d),a) = inverse(c),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
inference(fof_simplification,[status(thm)],[closure_of_product_and_inverse]) ).
cnf(c_0_37,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| X4 = X2 ),
c_0_32 ).
cnf(c_0_38,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| product(X1,element_in_O2(X1,X2),X2) ),
property_of_O2 ).
cnf(c_0_39,plain,
( ~ product(inverse(X1),X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,hypothesis,
product(inverse(d),a,inverse(c)),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_41,hypothesis,
~ subgroup_member(d),
inference(fof_simplification,[status(thm)],[d_in_subgroup]) ).
cnf(c_0_42,hypothesis,
~ subgroup_member(a),
inference(fof_simplification,[status(thm)],[a_in_subgroup]) ).
cnf(c_0_43,plain,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_36 ).
cnf(c_0_44,hypothesis,
product(b,inverse(a),c),
b_times_a_inverse_is_c ).
cnf(c_0_45,plain,
( ~ product(X2,X1,X3)
| subgroup_member(X3)
| subgroup_member(X2)
| X1 = element_in_O2(X2,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,hypothesis,
product(d,inverse(c),a),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,hypothesis,
~ subgroup_member(d),
c_0_41 ).
cnf(c_0_48,hypothesis,
~ subgroup_member(a),
c_0_42 ).
cnf(c_0_49,plain,
( ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| subgroup_member(multiply(X1,inverse(X2))) ),
inference(spm,[status(thm)],[c_0_43,c_0_27]) ).
cnf(c_0_50,negated_conjecture,
inverse(inverse(X1)) = X1,
prove_inverse_is_self_cancelling ).
cnf(c_0_51,hypothesis,
( ~ product(b,X1,c)
| X1 = inverse(a) ),
inference(spm,[status(thm)],[c_0_37,c_0_44]) ).
cnf(c_0_52,plain,
product(X1,multiply(inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_53,axiom,
( subgroup_member(X1)
| subgroup_member(X2)
| subgroup_member(element_in_O2(X1,X2)) ),
an_element_in_O2 ).
cnf(c_0_54,hypothesis,
element_in_O2(d,a) = inverse(c),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
inference(fof_simplification,[status(thm)],[closure_of_inverse]) ).
cnf(c_0_56,negated_conjecture,
( ~ subgroup_member(X1)
| ~ subgroup_member(inverse(X2))
| subgroup_member(multiply(X1,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,hypothesis,
multiply(inverse(b),c) = inverse(a),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,hypothesis,
subgroup_member(inverse(c)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48]),c_0_47]) ).
cnf(c_0_59,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
c_0_55 ).
cnf(c_0_60,negated_conjecture,
( ~ subgroup_member(inverse(b))
| subgroup_member(inverse(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_61,hypothesis,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_62,negated_conjecture,
( ~ subgroup_member(inverse(X1))
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_50]) ).
cnf(c_0_63,negated_conjecture,
subgroup_member(inverse(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_61])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 19:55:49 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 0.16/0.44 % Version: 3.5.1
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.44 % Starting sh5l with 300s (1) cores
% 0.16/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 788187 completed with status 0
% 0.16/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.44 % No SInE strategy applied
% 0.16/0.44 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.16/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.44 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.16/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.16/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.16/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 788193 completed with status 0
% 0.16/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.44 % No SInE strategy applied
% 0.16/0.44 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.16/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.44 % Preprocessing time : 0.001 s
% 0.16/0.44 % Presaturation interreduction done
% 0.16/0.44
% 0.16/0.44 % Proof found!
% 0.16/0.44 % SZS status Unsatisfiable
% 0.16/0.44 % SZS output start CNFRefutation
% See solution above
% 0.16/0.44 % Parsed axioms : 21
% 0.16/0.44 % Removed by relevancy pruning/SinE : 0
% 0.16/0.44 % Initial clauses : 21
% 0.16/0.44 % Removed in clause preprocessing : 0
% 0.16/0.44 % Initial clauses in saturation : 21
% 0.16/0.44 % Processed clauses : 170
% 0.16/0.44 % ...of these trivial : 3
% 0.16/0.44 % ...subsumed : 54
% 0.16/0.44 % ...remaining for further processing : 113
% 0.16/0.44 % Other redundant clauses eliminated : 0
% 0.16/0.44 % Clauses deleted for lack of memory : 0
% 0.16/0.44 % Backward-subsumed : 0
% 0.16/0.44 % Backward-rewritten : 2
% 0.16/0.44 % Generated clauses : 334
% 0.16/0.44 % ...of the previous two non-redundant : 197
% 0.16/0.44 % ...aggressively subsumed : 0
% 0.16/0.44 % Contextual simplify-reflections : 0
% 0.16/0.44 % Paramodulations : 334
% 0.16/0.44 % Factorizations : 0
% 0.16/0.44 % NegExts : 0
% 0.16/0.44 % Equation resolutions : 0
% 0.16/0.44 % Disequality decompositions : 0
% 0.16/0.44 % Total rewrite steps : 192
% 0.16/0.44 % ...of those cached : 158
% 0.16/0.44 % Propositional unsat checks : 0
% 0.16/0.44 % Propositional check models : 0
% 0.16/0.44 % Propositional check unsatisfiable : 0
% 0.16/0.44 % Propositional clauses : 0
% 0.16/0.44 % Propositional clauses after purity: 0
% 0.16/0.44 % Propositional unsat core size : 0
% 0.16/0.44 % Propositional preprocessing time : 0.000
% 0.16/0.44 % Propositional encoding time : 0.000
% 0.16/0.44 % Propositional solver time : 0.000
% 0.16/0.44 % Success case prop preproc time : 0.000
% 0.16/0.44 % Success case prop encoding time : 0.000
% 0.16/0.44 % Success case prop solver time : 0.000
% 0.16/0.44 % Current number of processed clauses : 90
% 0.16/0.44 % Positive orientable unit clauses : 29
% 0.16/0.44 % Positive unorientable unit clauses: 0
% 0.16/0.44 % Negative unit clauses : 2
% 0.16/0.44 % Non-unit-clauses : 59
% 0.16/0.44 % Current number of unprocessed clauses: 67
% 0.16/0.44 % ...number of literals in the above : 178
% 0.16/0.44 % Current number of archived formulas : 0
% 0.16/0.44 % Current number of archived clauses : 23
% 0.16/0.44 % Clause-clause subsumption calls (NU) : 795
% 0.16/0.44 % Rec. Clause-clause subsumption calls : 646
% 0.16/0.44 % Non-unit clause-clause subsumptions : 42
% 0.16/0.44 % Unit Clause-clause subsumption calls : 2
% 0.16/0.44 % Rewrite failures with RHS unbound : 0
% 0.16/0.44 % BW rewrite match attempts : 21
% 0.16/0.44 % BW rewrite match successes : 2
% 0.16/0.44 % Condensation attempts : 0
% 0.16/0.44 % Condensation successes : 0
% 0.16/0.44 % Termbank termtop insertions : 3876
% 0.16/0.44 % Search garbage collected termcells : 36
% 0.16/0.44
% 0.16/0.44 % -------------------------------------------------
% 0.16/0.44 % User time : 0.006 s
% 0.16/0.44 % System time : 0.004 s
% 0.16/0.44 % Total time : 0.010 s
% 0.16/0.44 % Maximum resident set size: 3644 pages
% 0.16/0.44
% 0.16/0.44 % -------------------------------------------------
% 0.16/0.44 % User time : 0.030 s
% 0.16/0.44 % System time : 0.013 s
% 0.16/0.44 % Total time : 0.043 s
% 0.16/0.44 % Maximum resident set size: 4864 pages
% 0.16/0.44 % E exiting
%------------------------------------------------------------------------------