%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:37:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 24 unt; 5 nHn; 27 RR)
% Number of literals : 71 ( 22 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_multiply,axiom,
( multiply(X1,X2) != X3
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(prove_d_in_O2,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
cnf(closure_of_inverse,axiom,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
cnf(b_in_O2,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
cnf(a_times_c_is_d,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
cnf(inverse_inverse,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_inverse) ).
cnf(property_of_O2,axiom,
( multiply(X1,element_in_O2(X1,X2)) = X2
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
cnf(an_element_in_O2,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
cnf(c_0_12,plain,
( multiply(X1,X2) != X3
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
inference(fof_simplification,[status(thm)],[closure_of_multiply]) ).
cnf(c_0_13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_14,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_15,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_16,plain,
( multiply(X1,X2) != X3
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_12 ).
cnf(c_0_17,negated_conjecture,
~ subgroup_member(d),
inference(fof_simplification,[status(thm)],[prove_d_in_O2]) ).
cnf(c_0_18,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
inference(fof_simplification,[status(thm)],[closure_of_inverse]) ).
cnf(c_0_19,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
multiply(b,inverse(a)) = c,
b_times_a_inverse_is_c ).
cnf(c_0_21,plain,
( ~ subgroup_member(X1)
| ~ subgroup_member(X2)
| subgroup_member(multiply(X1,X2)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
subgroup_member(b),
b_in_O2 ).
cnf(c_0_23,negated_conjecture,
multiply(a,c) = d,
a_times_c_is_d ).
cnf(c_0_24,negated_conjecture,
~ subgroup_member(d),
c_0_17 ).
cnf(c_0_25,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
c_0_18 ).
cnf(c_0_26,axiom,
inverse(inverse(X1)) = X1,
inverse_inverse ).
cnf(c_0_27,negated_conjecture,
multiply(inverse(b),c) = inverse(a),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ subgroup_member(inverse(a))
| subgroup_member(c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_24]) ).
cnf(c_0_30,axiom,
( multiply(X1,element_in_O2(X1,X2)) = X2
| subgroup_member(X2)
| subgroup_member(X1) ),
property_of_O2 ).
cnf(c_0_31,plain,
( ~ subgroup_member(inverse(X1))
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(inverse(b))
| subgroup_member(inverse(a)) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
~ subgroup_member(a),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
multiply(inverse(a),d) = c,
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_35,plain,
( subgroup_member(X1)
| subgroup_member(X2)
| multiply(inverse(X1),X2) = element_in_O2(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( ~ subgroup_member(c)
| ~ subgroup_member(inverse(b)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_37,axiom,
( subgroup_member(element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
an_element_in_O2 ).
cnf(c_0_38,negated_conjecture,
element_in_O2(a,d) = c,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
~ subgroup_member(c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_25]),c_0_22])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_33]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.43 % Version: 3.5.1
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.43 % Starting sh5l with 300s (1) cores
% 0.14/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1624571 completed with status 0
% 0.14/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.43 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.14/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.43 % SubtermCWHack with pid 1624576 completed with status 0
% 0.14/0.43 % Result found by SubtermCWHack
% 0.14/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.43 % No SInE strategy applied
% 0.14/0.43 % Search class: FGUSM-FFSS21-SFFFFFNN
% 0.14/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.43 % Preprocessing time : 0.001 s
% 0.14/0.43
% 0.14/0.43 % Proof found!
% 0.14/0.43 % SZS status Unsatisfiable
% 0.14/0.43 % SZS output start CNFRefutation
% See solution above
% 0.14/0.43 % Parsed axioms : 16
% 0.14/0.43 % Removed by relevancy pruning/SinE : 0
% 0.14/0.43 % Initial clauses : 16
% 0.14/0.43 % Removed in clause preprocessing : 0
% 0.14/0.43 % Initial clauses in saturation : 16
% 0.14/0.43 % Processed clauses : 101
% 0.14/0.43 % ...of these trivial : 2
% 0.14/0.43 % ...subsumed : 40
% 0.14/0.43 % ...remaining for further processing : 59
% 0.14/0.43 % Other redundant clauses eliminated : 1
% 0.14/0.43 % Clauses deleted for lack of memory : 0
% 0.14/0.43 % Backward-subsumed : 4
% 0.14/0.43 % Backward-rewritten : 3
% 0.14/0.43 % Generated clauses : 508
% 0.14/0.43 % ...of the previous two non-redundant : 337
% 0.14/0.43 % ...aggressively subsumed : 0
% 0.14/0.43 % Contextual simplify-reflections : 1
% 0.14/0.43 % Paramodulations : 507
% 0.14/0.43 % Factorizations : 0
% 0.14/0.43 % NegExts : 0
% 0.14/0.43 % Equation resolutions : 1
% 0.14/0.43 % Disequality decompositions : 0
% 0.14/0.43 % Total rewrite steps : 439
% 0.14/0.43 % ...of those cached : 304
% 0.14/0.43 % Propositional unsat checks : 0
% 0.14/0.43 % Propositional check models : 0
% 0.14/0.43 % Propositional check unsatisfiable : 0
% 0.14/0.43 % Propositional clauses : 0
% 0.14/0.43 % Propositional clauses after purity: 0
% 0.14/0.43 % Propositional unsat core size : 0
% 0.14/0.43 % Propositional preprocessing time : 0.000
% 0.14/0.43 % Propositional encoding time : 0.000
% 0.14/0.43 % Propositional solver time : 0.000
% 0.14/0.43 % Success case prop preproc time : 0.000
% 0.14/0.43 % Success case prop encoding time : 0.000
% 0.14/0.43 % Success case prop solver time : 0.000
% 0.14/0.43 % Current number of processed clauses : 51
% 0.14/0.43 % Positive orientable unit clauses : 32
% 0.14/0.43 % Positive unorientable unit clauses: 0
% 0.14/0.43 % Negative unit clauses : 6
% 0.14/0.43 % Non-unit-clauses : 13
% 0.14/0.43 % Current number of unprocessed clauses: 249
% 0.14/0.43 % ...number of literals in the above : 575
% 0.14/0.43 % Current number of archived formulas : 0
% 0.14/0.43 % Current number of archived clauses : 7
% 0.14/0.43 % Clause-clause subsumption calls (NU) : 78
% 0.14/0.43 % Rec. Clause-clause subsumption calls : 72
% 0.14/0.43 % Non-unit clause-clause subsumptions : 9
% 0.14/0.43 % Unit Clause-clause subsumption calls : 30
% 0.14/0.43 % Rewrite failures with RHS unbound : 0
% 0.14/0.43 % BW rewrite match attempts : 4
% 0.14/0.43 % BW rewrite match successes : 2
% 0.14/0.43 % Condensation attempts : 0
% 0.14/0.43 % Condensation successes : 0
% 0.14/0.43 % Termbank termtop insertions : 5188
% 0.14/0.43 % Search garbage collected termcells : 10
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.006 s
% 0.14/0.43 % System time : 0.002 s
% 0.14/0.43 % Total time : 0.009 s
% 0.14/0.43 % Maximum resident set size: 3640 pages
% 0.14/0.43
% 0.14/0.43 % -------------------------------------------------
% 0.14/0.43 % User time : 0.023 s
% 0.14/0.43 % System time : 0.012 s
% 0.14/0.43 % Total time : 0.035 s
% 0.14/0.43 % Maximum resident set size: 4864 pages
% 0.14/0.43 % E exiting
%------------------------------------------------------------------------------