%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP035-3 : 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 : n020.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 12:41:26 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 22 unt; 0 nHn; 28 RR)
% Number of literals : 76 ( 7 equ; 40 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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(left_identity,axiom,
product(identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
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(right_identity,axiom,
product(X1,identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
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_function1,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(b_is_in_subgroup,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
cnf(prove_c_is_in_subgroup,negated_conjecture,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(a_is_in_subgroup,hypothesis,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
cnf(c_0_11,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_12,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_11 ).
cnf(c_0_13,axiom,
product(identity,X1,X1),
left_identity ).
cnf(c_0_14,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[total_function2]) ).
cnf(c_0_15,plain,
( ~ product(X4,X3,X2)
| ~ product(X1,X4,identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
product(X1,inverse(X1),identity),
right_inverse ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_14 ).
cnf(c_0_18,axiom,
product(X1,identity,X1),
right_identity ).
cnf(c_0_19,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_20,axiom,
product(X1,X2,multiply(X1,X2)),
total_function1 ).
cnf(c_0_21,plain,
( ~ product(inverse(X1),X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( ~ product(X2,identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ product(X1,inverse(X2),X3)
| ~ subgroup_member(X2)
| ~ subgroup_member(X1)
| subgroup_member(X3) ),
c_0_19 ).
cnf(c_0_24,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_25,plain,
product(X1,identity,inverse(inverse(X1))),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_26,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_27,plain,
( ~ subgroup_member(X1)
| subgroup_member(identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,hypothesis,
subgroup_member(b),
b_is_in_subgroup ).
cnf(c_0_29,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,hypothesis,
subgroup_member(identity),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
( ~ product(X3,X2,X1)
| ~ subgroup_member(X3)
| ~ subgroup_member(inverse(X2))
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_32,plain,
( ~ subgroup_member(X1)
| subgroup_member(inverse(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_13]),c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
~ subgroup_member(c),
inference(fof_simplification,[status(thm)],[prove_c_is_in_subgroup]) ).
cnf(c_0_34,plain,
( ~ product(X2,X3,X1)
| ~ subgroup_member(X3)
| ~ subgroup_member(X2)
| subgroup_member(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_36,hypothesis,
subgroup_member(a),
a_is_in_subgroup ).
cnf(c_0_37,negated_conjecture,
~ subgroup_member(c),
c_0_33 ).
cnf(c_0_38,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_28])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP035-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n020.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
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:56:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.41 % Version: 3.5.1
% 0.13/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.41 % Starting sh5l with 300s (1) cores
% 0.13/0.41 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1083408 completed with status 0
% 0.13/0.41 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.41 % No SInE strategy applied
% 0.13/0.41 % Search class: FHUSM-FFSS21-SFFFFFNN
% 0.13/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.13/0.41 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.41 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.41 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1083413 completed with status 0
% 0.13/0.41 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.41 % No SInE strategy applied
% 0.13/0.41 % Search class: FHUSM-FFSS21-SFFFFFNN
% 0.13/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.41 % Preprocessing time : 0.001 s
% 0.13/0.41 % Presaturation interreduction done
% 0.13/0.41
% 0.13/0.41 % Proof found!
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation
% See solution above
% 0.13/0.41 % Parsed axioms : 13
% 0.13/0.41 % Removed by relevancy pruning/SinE : 0
% 0.13/0.41 % Initial clauses : 13
% 0.13/0.41 % Removed in clause preprocessing : 0
% 0.13/0.41 % Initial clauses in saturation : 13
% 0.13/0.41 % Processed clauses : 70
% 0.13/0.41 % ...of these trivial : 2
% 0.13/0.41 % ...subsumed : 9
% 0.13/0.41 % ...remaining for further processing : 59
% 0.13/0.41 % Other redundant clauses eliminated : 0
% 0.13/0.41 % Clauses deleted for lack of memory : 0
% 0.13/0.41 % Backward-subsumed : 0
% 0.13/0.41 % Backward-rewritten : 2
% 0.13/0.41 % Generated clauses : 141
% 0.13/0.41 % ...of the previous two non-redundant : 81
% 0.13/0.41 % ...aggressively subsumed : 0
% 0.13/0.41 % Contextual simplify-reflections : 0
% 0.13/0.41 % Paramodulations : 141
% 0.13/0.41 % Factorizations : 0
% 0.13/0.41 % NegExts : 0
% 0.13/0.41 % Equation resolutions : 0
% 0.13/0.41 % Disequality decompositions : 0
% 0.13/0.41 % Total rewrite steps : 80
% 0.13/0.41 % ...of those cached : 61
% 0.13/0.41 % Propositional unsat checks : 0
% 0.13/0.41 % Propositional check models : 0
% 0.13/0.41 % Propositional check unsatisfiable : 0
% 0.13/0.41 % Propositional clauses : 0
% 0.13/0.41 % Propositional clauses after purity: 0
% 0.13/0.41 % Propositional unsat core size : 0
% 0.13/0.41 % Propositional preprocessing time : 0.000
% 0.13/0.41 % Propositional encoding time : 0.000
% 0.13/0.41 % Propositional solver time : 0.000
% 0.13/0.41 % Success case prop preproc time : 0.000
% 0.13/0.41 % Success case prop encoding time : 0.000
% 0.13/0.41 % Success case prop solver time : 0.000
% 0.13/0.41 % Current number of processed clauses : 44
% 0.13/0.41 % Positive orientable unit clauses : 17
% 0.13/0.41 % Positive unorientable unit clauses: 0
% 0.13/0.41 % Negative unit clauses : 1
% 0.13/0.41 % Non-unit-clauses : 26
% 0.13/0.41 % Current number of unprocessed clauses: 33
% 0.13/0.41 % ...number of literals in the above : 79
% 0.13/0.41 % Current number of archived formulas : 0
% 0.13/0.41 % Current number of archived clauses : 15
% 0.13/0.41 % Clause-clause subsumption calls (NU) : 168
% 0.13/0.41 % Rec. Clause-clause subsumption calls : 144
% 0.13/0.41 % Non-unit clause-clause subsumptions : 9
% 0.13/0.41 % Unit Clause-clause subsumption calls : 0
% 0.13/0.41 % Rewrite failures with RHS unbound : 0
% 0.13/0.41 % BW rewrite match attempts : 21
% 0.13/0.41 % BW rewrite match successes : 2
% 0.13/0.41 % Condensation attempts : 0
% 0.13/0.41 % Condensation successes : 0
% 0.13/0.41 % Termbank termtop insertions : 1690
% 0.13/0.41 % Search garbage collected termcells : 27
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.003 s
% 0.13/0.41 % System time : 0.003 s
% 0.13/0.41 % Total time : 0.006 s
% 0.13/0.41 % Maximum resident set size: 3592 pages
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.017 s
% 0.13/0.41 % System time : 0.010 s
% 0.13/0.41 % Total time : 0.027 s
% 0.13/0.41 % Maximum resident set size: 4864 pages
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------