%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT003-1 : 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 : 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 12:07:57 PM UTC 2026
% Result : Unsatisfiable 5.22s 1.63s
% Output : CNFRefutation 5.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of clauses : 72 ( 31 unt; 0 nHn; 66 RR)
% Number of literals : 149 ( 12 equ; 80 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 133 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associative_property1,axiom,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(associative_property2,axiom,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(ga_equals_d,hypothesis,
product(g,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ga_equals_d) ).
cnf(category_theory_axiom1,axiom,
( ~ defined(X3,X4)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| defined(X1,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom1) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_equals_c) ).
cnf(identity1,axiom,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
cnf(category_theory_axiom3,axiom,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
cnf(ha_equals_d,hypothesis,
product(h,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_equals_d) ).
cnf(category_theory_axiom6,axiom,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
cnf(closure_of_composition,axiom,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
cnf(category_theory_axiom5,axiom,
( ~ product(X4,X1,X6)
| ~ product(X4,X3,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X1,domain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
cnf(composition_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
cnf(cancellation_for_product,hypothesis,
( ~ product(X3,c,X2)
| ~ product(X1,c,X2)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
inference(fof_simplification,[status(thm)],[associative_property1]) ).
cnf(c_0_18,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
inference(fof_simplification,[status(thm)],[associative_property2]) ).
cnf(c_0_19,plain,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
c_0_17 ).
cnf(c_0_20,hypothesis,
product(g,a,d),
ga_equals_d ).
cnf(c_0_21,plain,
( ~ defined(X3,X4)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| defined(X1,X5) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom1]) ).
cnf(c_0_22,hypothesis,
product(a,b,c),
ab_equals_c ).
cnf(c_0_23,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
c_0_18 ).
cnf(c_0_24,hypothesis,
defined(g,a),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ defined(X3,X4)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| defined(X1,X5) ),
c_0_21 ).
cnf(c_0_26,hypothesis,
defined(a,b),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_27,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[identity1]) ).
cnf(c_0_28,hypothesis,
( ~ product(X2,X1,g)
| defined(X1,a) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
product(X1,domain(X1),X1),
product_on_domain ).
cnf(c_0_30,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,b,X2)
| defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
c_0_27 ).
cnf(c_0_32,hypothesis,
defined(domain(g),a),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_34,plain,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom3]) ).
cnf(c_0_35,hypothesis,
product(h,a,d),
ha_equals_d ).
cnf(c_0_36,plain,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom6]) ).
cnf(c_0_37,hypothesis,
( ~ product(X1,a,a)
| defined(X1,c) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_38,hypothesis,
product(domain(g),a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_39,plain,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
c_0_34 ).
cnf(c_0_40,hypothesis,
defined(h,a),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_41,plain,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
c_0_36 ).
cnf(c_0_42,hypothesis,
defined(domain(g),c),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
( ~ product(X1,X2,a)
| defined(h,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
inference(fof_simplification,[status(thm)],[closure_of_composition]) ).
cnf(c_0_45,hypothesis,
( ~ defined(X1,domain(g))
| defined(X1,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33])]) ).
cnf(c_0_46,hypothesis,
defined(h,domain(g)),
inference(spm,[status(thm)],[c_0_43,c_0_38]) ).
cnf(c_0_47,plain,
( ~ product(X4,X1,X6)
| ~ product(X4,X3,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X5) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom5]) ).
cnf(c_0_48,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
c_0_44 ).
cnf(c_0_49,hypothesis,
defined(h,c),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain ).
cnf(c_0_51,plain,
( ~ product(X4,X1,X6)
| ~ product(X4,X3,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X5) ),
c_0_47 ).
cnf(c_0_52,hypothesis,
product(h,c,compose(h,c)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,hypothesis,
defined(g,c),
inference(spm,[status(thm)],[c_0_45,c_0_50]) ).
cnf(c_0_54,hypothesis,
( ~ product(X3,X2,c)
| ~ product(h,X3,X1)
| product(X1,X2,compose(h,c)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,hypothesis,
product(g,c,compose(g,c)),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_56,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[composition_is_well_defined]) ).
cnf(c_0_57,hypothesis,
( ~ product(a,X1,c)
| product(d,X1,compose(h,c)) ),
inference(spm,[status(thm)],[c_0_54,c_0_35]) ).
cnf(c_0_58,hypothesis,
( ~ product(X3,X2,c)
| ~ product(g,X3,X1)
| product(X1,X2,compose(g,c)) ),
inference(spm,[status(thm)],[c_0_51,c_0_55]) ).
cnf(c_0_59,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_56 ).
cnf(c_0_60,hypothesis,
product(d,b,compose(h,c)),
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_61,hypothesis,
( ~ product(a,X1,c)
| product(d,X1,compose(g,c)) ),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_62,hypothesis,
( ~ product(X3,c,X2)
| ~ product(X1,c,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[cancellation_for_product]) ).
cnf(c_0_63,hypothesis,
( ~ product(d,b,X1)
| X1 = compose(h,c) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,hypothesis,
product(d,b,compose(g,c)),
inference(spm,[status(thm)],[c_0_61,c_0_22]) ).
cnf(c_0_65,hypothesis,
( ~ product(X3,c,X2)
| ~ product(X1,c,X2)
| X1 = X3 ),
c_0_62 ).
cnf(c_0_66,hypothesis,
compose(g,c) = compose(h,c),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
h != g,
inference(fof_simplification,[status(thm)],[prove_h_equals_g]) ).
cnf(c_0_68,hypothesis,
( ~ product(X1,c,compose(h,c))
| X1 = h ),
inference(spm,[status(thm)],[c_0_65,c_0_52]) ).
cnf(c_0_69,hypothesis,
product(g,c,compose(h,c)),
inference(rw,[status(thm)],[c_0_55,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
h != g,
c_0_67 ).
cnf(c_0_71,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n005.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 13:55:18 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.54 Running first-order theorem proving
% 0.24/0.54 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
% 5.22/1.63 % Version: 3.5.1
% 5.22/1.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.22/1.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.22/1.63 % Starting new_bool_3 with 300s (1) cores
% 5.22/1.63 % Starting new_bool_1 with 300s (1) cores
% 5.22/1.63 % Starting sh5l with 300s (1) cores
% 5.22/1.63 % new_bool_1 with pid 3648497 completed with status 9
% 5.22/1.63 % new_bool_3 with pid 3648496 completed with status 9
% 5.22/1.63 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3648495 completed with status 0
% 5.22/1.63 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.22/1.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.22/1.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.22/1.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.22/1.63 % No SInE strategy applied
% 5.22/1.63 % Search class: FHUSM-FFSS21-SFFFFFNN
% 5.22/1.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.22/1.63 % Starting SubtermCWHack with 136s (1) cores
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 5.22/1.63 % Starting new_bool_3 with 136s (1) cores
% 5.22/1.63 % Starting new_bool_1 with 136s (1) cores
% 5.22/1.63 % new_bool_1 with pid 3648505 completed with status 0
% 5.22/1.63 % Result found by new_bool_1
% 5.22/1.63 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.22/1.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.22/1.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.22/1.63 % No SInE strategy applied
% 5.22/1.63 % Search class: FHUSM-FFSS21-SFFFFFNN
% 5.22/1.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.22/1.63 % Starting SubtermCWHack with 136s (1) cores
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.22/1.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 5.22/1.63 % Starting new_bool_3 with 136s (1) cores
% 5.22/1.63 % Starting new_bool_1 with 136s (1) cores
% 5.22/1.63 % Preprocessing time : 0.002 s
% 5.22/1.63 % Presaturation interreduction done
% 5.22/1.63
% 5.22/1.63 % Proof found!
% 5.22/1.63 % SZS status Unsatisfiable
% 5.22/1.63 % SZS output start CNFRefutation
% See solution above
% 5.22/1.63 % Parsed axioms : 23
% 5.22/1.63 % Removed by relevancy pruning/SinE : 0
% 5.22/1.63 % Initial clauses : 23
% 5.22/1.63 % Removed in clause preprocessing : 0
% 5.22/1.63 % Initial clauses in saturation : 23
% 5.22/1.63 % Processed clauses : 11447
% 5.22/1.63 % ...of these trivial : 640
% 5.22/1.63 % ...subsumed : 6878
% 5.22/1.63 % ...remaining for further processing : 3929
% 5.22/1.63 % Other redundant clauses eliminated : 0
% 5.22/1.63 % Clauses deleted for lack of memory : 0
% 5.22/1.63 % Backward-subsumed : 47
% 5.22/1.63 % Backward-rewritten : 1964
% 5.22/1.63 % Generated clauses : 31421
% 5.22/1.63 % ...of the previous two non-redundant : 24641
% 5.22/1.63 % ...aggressively subsumed : 0
% 5.22/1.63 % Contextual simplify-reflections : 0
% 5.22/1.63 % Paramodulations : 31421
% 5.22/1.63 % Factorizations : 0
% 5.22/1.63 % NegExts : 0
% 5.22/1.63 % Equation resolutions : 0
% 5.22/1.63 % Disequality decompositions : 0
% 5.22/1.63 % Total rewrite steps : 30673
% 5.22/1.63 % ...of those cached : 29701
% 5.22/1.63 % Propositional unsat checks : 0
% 5.22/1.63 % Propositional check models : 0
% 5.22/1.63 % Propositional check unsatisfiable : 0
% 5.22/1.63 % Propositional clauses : 0
% 5.22/1.63 % Propositional clauses after purity: 0
% 5.22/1.63 % Propositional unsat core size : 0
% 5.22/1.63 % Propositional preprocessing time : 0.000
% 5.22/1.63 % Propositional encoding time : 0.000
% 5.22/1.63 % Propositional solver time : 0.000
% 5.22/1.63 % Success case prop preproc time : 0.000
% 5.22/1.63 % Success case prop encoding time : 0.000
% 5.22/1.63 % Success case prop solver time : 0.000
% 5.22/1.63 % Current number of processed clauses : 1895
% 5.22/1.63 % Positive orientable unit clauses : 116
% 5.22/1.63 % Positive unorientable unit clauses: 0
% 5.22/1.63 % Negative unit clauses : 1
% 5.22/1.63 % Non-unit-clauses : 1778
% 5.22/1.63 % Current number of unprocessed clauses: 9827
% 5.22/1.63 % ...number of literals in the above : 21153
% 5.22/1.63 % Current number of archived formulas : 0
% 5.22/1.63 % Current number of archived clauses : 2034
% 5.22/1.63 % Clause-clause subsumption calls (NU) : 1192876
% 5.22/1.63 % Rec. Clause-clause subsumption calls : 1042629
% 5.22/1.63 % Non-unit clause-clause subsumptions : 6925
% 5.22/1.63 % Unit Clause-clause subsumption calls : 2503
% 5.22/1.63 % Rewrite failures with RHS unbound : 0
% 5.22/1.63 % BW rewrite match attempts : 1448
% 5.22/1.63 % BW rewrite match successes : 191
% 5.22/1.63 % Condensation attempts : 0
% 5.22/1.63 % Condensation successes : 0
% 5.22/1.63 % Termbank termtop insertions : 391140
% 5.22/1.63 % Search garbage collected termcells : 62
% 5.22/1.63
% 5.22/1.63 % -------------------------------------------------
% 5.22/1.63 % User time : 1.003 s
% 5.22/1.63 % System time : 0.022 s
% 5.22/1.63 % Total time : 1.025 s
% 5.22/1.63 % Maximum resident set size: 3648 pages
% 5.22/1.63
% 5.22/1.63 % -------------------------------------------------
% 5.22/1.63 % User time : 4.995 s
% 5.22/1.63 % System time : 0.201 s
% 5.22/1.63 % Total time : 5.196 s
% 5.22/1.63 % Maximum resident set size: 4864 pages
% 5.22/1.63 % E exiting
%------------------------------------------------------------------------------