%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:37:54 PM UTC 2026
% Result : Unsatisfiable 17.51s 3.08s
% Output : CNFRefutation 17.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 8 RR)
% Number of literals : 59 ( 58 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(inverse_product_lemma,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product_lemma) ).
cnf(inverse_of_identity,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_identity) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(inverse_involution,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_involution) ).
cnf(multiply_union2,axiom,
multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union2) ).
cnf(union_commutative,axiom,
union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_commutative) ).
cnf(multiply_union1,axiom,
multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union1) ).
cnf(multiply_intersection2,axiom,
multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection2) ).
cnf(intersection_commutative,axiom,
intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_commutative) ).
cnf(multiply_intersection1,axiom,
multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection1) ).
cnf(intersection_union_absorbtion,axiom,
intersection(union(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
cnf(union_associative,axiom,
union(X1,union(X2,X3)) = union(union(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_associative) ).
cnf(union_intersection_absorbtion,axiom,
union(intersection(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
cnf(prove_product,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
cnf(intersection_associative,axiom,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_associative) ).
cnf(positive_part,axiom,
positive_part(X1) = union(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',positive_part) ).
cnf(negative_part,axiom,
negative_part(X1) = intersection(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',negative_part) ).
cnf(c_0_17,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inverse_product_lemma ).
cnf(c_0_18,axiom,
inverse(identity) = identity,
inverse_of_identity ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,plain,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,axiom,
inverse(inverse(X1)) = X1,
inverse_involution ).
cnf(c_0_22,axiom,
multiply(union(X1,X2),X3) = union(multiply(X1,X3),multiply(X2,X3)),
multiply_union2 ).
cnf(c_0_23,axiom,
union(X1,X2) = union(X2,X1),
union_commutative ).
cnf(c_0_24,axiom,
multiply(X1,union(X2,X3)) = union(multiply(X1,X2),multiply(X1,X3)),
multiply_union1 ).
cnf(c_0_25,plain,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
union(X1,multiply(X2,X1)) = multiply(union(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
cnf(c_0_27,plain,
union(X1,multiply(X1,X2)) = multiply(X1,union(identity,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
multiply(intersection(X1,X2),X3) = intersection(multiply(X1,X3),multiply(X2,X3)),
multiply_intersection2 ).
cnf(c_0_29,axiom,
intersection(X1,X2) = intersection(X2,X1),
intersection_commutative ).
cnf(c_0_30,axiom,
multiply(X1,intersection(X2,X3)) = intersection(multiply(X1,X2),multiply(X1,X3)),
multiply_intersection1 ).
cnf(c_0_31,plain,
multiply(union(X1,identity),X1) = multiply(X1,union(identity,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
intersection(union(X1,X2),X2) = X2,
intersection_union_absorbtion ).
cnf(c_0_33,axiom,
union(X1,union(X2,X3)) = union(union(X1,X2),X3),
union_associative ).
cnf(c_0_34,plain,
intersection(X1,multiply(X2,X1)) = multiply(intersection(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_29]) ).
cnf(c_0_35,plain,
intersection(X1,multiply(X1,X2)) = multiply(X1,intersection(identity,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_36,plain,
multiply(union(identity,X1),X1) = multiply(X1,union(identity,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_37,axiom,
union(intersection(X1,X2),X2) = X2,
union_intersection_absorbtion ).
cnf(c_0_38,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
inference(fof_simplification,[status(thm)],[prove_product]) ).
cnf(c_0_39,axiom,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X1,X2),X3),
intersection_associative ).
cnf(c_0_40,plain,
intersection(X1,union(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_41,plain,
union(X1,union(X2,X3)) = union(X2,union(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_33]) ).
cnf(c_0_42,plain,
multiply(intersection(X1,identity),X1) = multiply(X1,intersection(identity,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
multiply(intersection(X1,identity),union(identity,X1)) = multiply(union(identity,X1),intersection(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34]) ).
cnf(c_0_44,plain,
union(X1,intersection(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_45,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
c_0_38 ).
cnf(c_0_46,axiom,
positive_part(X1) = union(X1,identity),
positive_part ).
cnf(c_0_47,axiom,
negative_part(X1) = intersection(X1,identity),
negative_part ).
cnf(c_0_48,plain,
intersection(X1,intersection(X2,union(X3,intersection(X1,X2)))) = intersection(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
union(X1,multiply(X2,union(identity,X3))) = union(X2,union(X1,multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_50,plain,
union(intersection(X1,identity),multiply(X1,intersection(identity,X1))) = multiply(union(identity,X1),intersection(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_43]) ).
cnf(c_0_51,plain,
union(X1,intersection(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_52,negated_conjecture,
multiply(union(a,identity),intersection(a,identity)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_53,plain,
intersection(X1,intersection(multiply(X1,X2),union(X3,multiply(X1,intersection(identity,X2))))) = multiply(X1,intersection(identity,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
cnf(c_0_54,plain,
union(X1,multiply(union(identity,X1),intersection(identity,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_25]),c_0_23]),c_0_51]) ).
cnf(c_0_55,plain,
intersection(X1,union(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_56,negated_conjecture,
multiply(union(identity,a),intersection(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_29]),c_0_23]) ).
cnf(c_0_57,plain,
multiply(union(identity,X1),intersection(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_36]),c_0_29]),c_0_35]),c_0_55]),c_0_25]),c_0_29]),c_0_40]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.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 20:00:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 17.51/3.08 % Version: 3.5.1
% 17.51/3.08 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.51/3.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.51/3.08 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.51/3.08 % Starting new_bool_3 with 300s (1) cores
% 17.51/3.08 % Starting new_bool_1 with 300s (1) cores
% 17.51/3.08 % Starting sh5l with 300s (1) cores
% 17.51/3.08 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1574457 completed with status 0
% 17.51/3.08 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.51/3.08 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.51/3.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.51/3.08 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.51/3.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.51/3.08 % No SInE strategy applied
% 17.51/3.08 % Search class: FUUPM-FFSF21-SFFFFFNN
% 17.51/3.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 17.51/3.08 % Starting SubtermCWHack with 136s (1) cores
% 17.51/3.08 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.51/3.08 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 17.51/3.08 % Starting new_bool_3 with 136s (1) cores
% 17.51/3.08 % Starting new_bool_1 with 136s (1) cores
% 17.51/3.08 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1574463 completed with status 0
% 17.51/3.08 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.51/3.08 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.51/3.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.51/3.08 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.51/3.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.51/3.08 % No SInE strategy applied
% 17.51/3.08 % Search class: FUUPM-FFSF21-SFFFFFNN
% 17.51/3.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 17.51/3.08 % Starting SubtermCWHack with 136s (1) cores
% 17.51/3.08 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.51/3.08 % Preprocessing time : 0.002 s
% 17.51/3.08 % Presaturation interreduction done
% 17.51/3.08
% 17.51/3.08 % Proof found!
% 17.51/3.08 % SZS status Unsatisfiable
% 17.51/3.08 % SZS output start CNFRefutation
% See solution above
% 17.51/3.08 % Parsed axioms : 21
% 17.51/3.08 % Removed by relevancy pruning/SinE : 0
% 17.51/3.08 % Initial clauses : 21
% 17.51/3.08 % Removed in clause preprocessing : 2
% 17.51/3.08 % Initial clauses in saturation : 19
% 17.51/3.08 % Processed clauses : 6085
% 17.51/3.08 % ...of these trivial : 2207
% 17.51/3.08 % ...subsumed : 3252
% 17.51/3.08 % ...remaining for further processing : 626
% 17.51/3.08 % Other redundant clauses eliminated : 0
% 17.51/3.08 % Clauses deleted for lack of memory : 0
% 17.51/3.08 % Backward-subsumed : 0
% 17.51/3.08 % Backward-rewritten : 71
% 17.51/3.08 % Generated clauses : 147323
% 17.51/3.08 % ...of the previous two non-redundant : 81190
% 17.51/3.08 % ...aggressively subsumed : 0
% 17.51/3.08 % Contextual simplify-reflections : 0
% 17.51/3.08 % Paramodulations : 147323
% 17.51/3.08 % Factorizations : 0
% 17.51/3.08 % NegExts : 0
% 17.51/3.08 % Equation resolutions : 0
% 17.51/3.08 % Disequality decompositions : 0
% 17.51/3.08 % Total rewrite steps : 219424
% 17.51/3.08 % ...of those cached : 185125
% 17.51/3.08 % Propositional unsat checks : 0
% 17.51/3.08 % Propositional check models : 0
% 17.51/3.08 % Propositional check unsatisfiable : 0
% 17.51/3.08 % Propositional clauses : 0
% 17.51/3.08 % Propositional clauses after purity: 0
% 17.51/3.08 % Propositional unsat core size : 0
% 17.51/3.08 % Propositional preprocessing time : 0.000
% 17.51/3.08 % Propositional encoding time : 0.000
% 17.51/3.08 % Propositional solver time : 0.000
% 17.51/3.08 % Success case prop preproc time : 0.000
% 17.51/3.08 % Success case prop encoding time : 0.000
% 17.51/3.08 % Success case prop solver time : 0.000
% 17.51/3.08 % Current number of processed clauses : 536
% 17.51/3.08 % Positive orientable unit clauses : 492
% 17.51/3.08 % Positive unorientable unit clauses: 44
% 17.51/3.08 % Negative unit clauses : 0
% 17.51/3.08 % Non-unit-clauses : 0
% 17.51/3.08 % Current number of unprocessed clauses: 74787
% 17.51/3.08 % ...number of literals in the above : 74787
% 17.51/3.08 % Current number of archived formulas : 0
% 17.51/3.08 % Current number of archived clauses : 92
% 17.51/3.08 % Clause-clause subsumption calls (NU) : 0
% 17.51/3.08 % Rec. Clause-clause subsumption calls : 0
% 17.51/3.08 % Non-unit clause-clause subsumptions : 0
% 17.51/3.08 % Unit Clause-clause subsumption calls : 171
% 17.51/3.08 % Rewrite failures with RHS unbound : 0
% 17.51/3.08 % BW rewrite match attempts : 2457
% 17.51/3.08 % BW rewrite match successes : 316
% 17.51/3.08 % Condensation attempts : 0
% 17.51/3.08 % Condensation successes : 0
% 17.51/3.08 % Termbank termtop insertions : 1855280
% 17.51/3.08 % Search garbage collected termcells : 2
% 17.51/3.08
% 17.51/3.08 % -------------------------------------------------
% 17.51/3.08 % User time : 2.408 s
% 17.51/3.08 % System time : 0.110 s
% 17.51/3.08 % Total time : 2.517 s
% 17.51/3.08 % Maximum resident set size: 3640 pages
% 17.51/3.08
% 17.51/3.08 % -------------------------------------------------
% 17.51/3.08 % User time : 11.736 s
% 17.51/3.08 % System time : 0.573 s
% 17.51/3.08 % Total time : 12.309 s
% 17.51/3.08 % Maximum resident set size: 4864 pages
% 17.51/3.08 % E exiting
%------------------------------------------------------------------------------