%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP037-3 : 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 : n001.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 12:37:31 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.53s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 37 ( 17 unt; 0 nHn; 28 RR)
% Number of literals : 69 ( 15 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 55 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_product_and_inverse,axiom,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
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(right_inverse,axiom,
product(X1,inverse(X1),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(another_right_identity,hypothesis,
( ~ subgroup_member(X1)
| product(X1,another_identity,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_identity) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
cnf(product_right_cancellation,hypothesis,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| X4 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(left_inverse,axiom,
product(inverse(X1),X1,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(another_right_inverse,hypothesis,
( ~ subgroup_member(X1)
| product(X1,another_inverse(X1),another_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',another_right_inverse) ).
cnf(prove_two_inverses_are_equal,negated_conjecture,
inverse(a) != another_inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_two_inverses_are_equal) ).
cnf(c_0_10,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_11,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_12,plain,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_10 ).
cnf(c_0_13,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_14,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_11 ).
cnf(c_0_15,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_16,hypothesis,
( ~ subgroup_member(X1)
| product(X1,another_identity,X1) ),
inference(fof_simplification,[status(thm)],[another_right_identity]) ).
cnf(c_0_17,plain,
( ~ subgroup_member(X1)
| subgroup_member(identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,hypothesis,
subgroup_member(a),
a_is_in_subgroup ).
cnf(c_0_19,plain,
( ~ product(identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
( ~ subgroup_member(X1)
| product(X1,another_identity,X1) ),
c_0_16 ).
cnf(c_0_21,hypothesis,
subgroup_member(identity),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,hypothesis,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| X4 = X2 ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_23,axiom,
product(inverse(X1),X1,identity),
left_inverse ).
cnf(c_0_24,hypothesis,
identity = another_identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,hypothesis,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| X4 = X2 ),
c_0_22 ).
cnf(c_0_26,plain,
product(inverse(X1),X1,another_identity),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,hypothesis,
( ~ subgroup_member(X1)
| product(X1,another_inverse(X1),another_identity) ),
inference(fof_simplification,[status(thm)],[another_right_inverse]) ).
cnf(c_0_28,hypothesis,
( ~ product(inverse(X2),X1,another_identity)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,hypothesis,
( ~ subgroup_member(X1)
| product(X1,another_inverse(X1),another_identity) ),
c_0_27 ).
cnf(c_0_30,plain,
product(X1,inverse(X1),another_identity),
inference(rw,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
inverse(a) != another_inverse(a),
inference(fof_simplification,[status(thm)],[prove_two_inverses_are_equal]) ).
cnf(c_0_32,hypothesis,
( ~ subgroup_member(inverse(X1))
| another_inverse(inverse(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,hypothesis,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
inverse(a) != another_inverse(a),
c_0_31 ).
cnf(c_0_35,hypothesis,
( ~ subgroup_member(X1)
| another_inverse(X1) = inverse(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 20:00:43 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.27/0.53 % Version: 3.5.1
% 0.27/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.53 % Starting sh5l with 300s (1) cores
% 0.27/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1264252 completed with status 0
% 0.27/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.27/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.53 % No SInE strategy applied
% 0.27/0.53 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.27/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.27/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.53 % new_bool_1 with pid 1264260 completed with status 0
% 0.27/0.53 % Result found by new_bool_1
% 0.27/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.53 % No SInE strategy applied
% 0.27/0.53 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.27/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.27/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.27/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.27/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.27/0.53 % Preprocessing time : 0.001 s
% 0.27/0.53 % Presaturation interreduction done
% 0.27/0.53
% 0.27/0.53 % Proof found!
% 0.27/0.53 % SZS status Unsatisfiable
% 0.27/0.53 % SZS output start CNFRefutation
% See solution above
% 0.27/0.53 % Parsed axioms : 19
% 0.27/0.53 % Removed by relevancy pruning/SinE : 0
% 0.27/0.53 % Initial clauses : 19
% 0.27/0.53 % Removed in clause preprocessing : 0
% 0.27/0.53 % Initial clauses in saturation : 19
% 0.27/0.53 % Processed clauses : 70
% 0.27/0.53 % ...of these trivial : 2
% 0.27/0.53 % ...subsumed : 5
% 0.27/0.53 % ...remaining for further processing : 63
% 0.27/0.53 % Other redundant clauses eliminated : 0
% 0.27/0.53 % Clauses deleted for lack of memory : 0
% 0.27/0.53 % Backward-subsumed : 3
% 0.27/0.53 % Backward-rewritten : 6
% 0.27/0.53 % Generated clauses : 119
% 0.27/0.53 % ...of the previous two non-redundant : 89
% 0.27/0.53 % ...aggressively subsumed : 0
% 0.27/0.53 % Contextual simplify-reflections : 0
% 0.27/0.53 % Paramodulations : 119
% 0.27/0.53 % Factorizations : 0
% 0.27/0.53 % NegExts : 0
% 0.27/0.53 % Equation resolutions : 0
% 0.27/0.53 % Disequality decompositions : 0
% 0.27/0.53 % Total rewrite steps : 58
% 0.27/0.53 % ...of those cached : 44
% 0.27/0.53 % Propositional unsat checks : 0
% 0.27/0.53 % Propositional check models : 0
% 0.27/0.53 % Propositional check unsatisfiable : 0
% 0.27/0.53 % Propositional clauses : 0
% 0.27/0.53 % Propositional clauses after purity: 0
% 0.27/0.53 % Propositional unsat core size : 0
% 0.27/0.53 % Propositional preprocessing time : 0.000
% 0.27/0.53 % Propositional encoding time : 0.000
% 0.27/0.53 % Propositional solver time : 0.000
% 0.27/0.53 % Success case prop preproc time : 0.000
% 0.27/0.53 % Success case prop encoding time : 0.000
% 0.27/0.53 % Success case prop solver time : 0.000
% 0.27/0.53 % Current number of processed clauses : 35
% 0.27/0.53 % Positive orientable unit clauses : 14
% 0.27/0.53 % Positive unorientable unit clauses: 0
% 0.27/0.53 % Negative unit clauses : 1
% 0.27/0.53 % Non-unit-clauses : 20
% 0.27/0.53 % Current number of unprocessed clauses: 44
% 0.27/0.53 % ...number of literals in the above : 124
% 0.27/0.53 % Current number of archived formulas : 0
% 0.27/0.53 % Current number of archived clauses : 28
% 0.27/0.53 % Clause-clause subsumption calls (NU) : 129
% 0.27/0.53 % Rec. Clause-clause subsumption calls : 107
% 0.27/0.53 % Non-unit clause-clause subsumptions : 5
% 0.27/0.53 % Unit Clause-clause subsumption calls : 8
% 0.27/0.53 % Rewrite failures with RHS unbound : 0
% 0.27/0.53 % BW rewrite match attempts : 16
% 0.27/0.53 % BW rewrite match successes : 4
% 0.27/0.53 % Condensation attempts : 0
% 0.27/0.53 % Condensation successes : 0
% 0.27/0.53 % Termbank termtop insertions : 1589
% 0.27/0.53 % Search garbage collected termcells : 40
% 0.27/0.53
% 0.27/0.53 % -------------------------------------------------
% 0.27/0.53 % User time : 0.003 s
% 0.27/0.53 % System time : 0.004 s
% 0.27/0.53 % Total time : 0.007 s
% 0.27/0.53 % Maximum resident set size: 3644 pages
% 0.27/0.53
% 0.27/0.53 % -------------------------------------------------
% 0.27/0.53 % User time : 0.030 s
% 0.27/0.53 % System time : 0.013 s
% 0.27/0.53 % Total time : 0.042 s
% 0.27/0.53 % Maximum resident set size: 4608 pages
% 0.27/0.53 % E exiting
%------------------------------------------------------------------------------