%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:07:55 PM UTC 2026
% Result : Unsatisfiable 13.37s 7.77s
% Output : CNFRefutation 13.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of clauses : 73 ( 30 unt; 0 nHn; 67 RR)
% Number of literals : 152 ( 13 equ; 82 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 : 136 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associative_property1,axiom,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(category_theory_axiom3,axiom,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
cnf(bg_equals_d,hypothesis,
product(b,g,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_equals_d) ).
cnf(category_theory_axiom4,axiom,
( ~ defined(X4,X3)
| ~ product(X4,X1,X5)
| ~ product(X1,X2,X3)
| defined(X5,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).
cnf(ab_equals_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
cnf(identity2,axiom,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
cnf(product_on_codomain,axiom,
product(codomain(X1),X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
cnf(associative_property2,axiom,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(bh_equals_d,hypothesis,
product(b,h,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_d) ).
cnf(category_theory_axiom6,axiom,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
cnf(codomain_is_an_identity_map,axiom,
identity_map(codomain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
cnf(mapping_from_codomain_of_x_to_x,axiom,
defined(codomain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
cnf(closure_of_composition,axiom,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
cnf(category_theory_axiom2,axiom,
( ~ product(X2,X4,X6)
| ~ product(X3,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).
cnf(composition_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
cnf(cancellation_for_product,hypothesis,
( ~ product(c,X3,X2)
| ~ product(c,X1,X2)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox/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(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom3]) ).
cnf(c_0_19,plain,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
c_0_17 ).
cnf(c_0_20,hypothesis,
product(b,g,d),
bg_equals_d ).
cnf(c_0_21,plain,
( ~ defined(X4,X3)
| ~ product(X4,X1,X5)
| ~ product(X1,X2,X3)
| defined(X5,X2) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom4]) ).
cnf(c_0_22,hypothesis,
product(a,b,c),
ab_equals_c ).
cnf(c_0_23,plain,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
c_0_18 ).
cnf(c_0_24,hypothesis,
defined(b,g),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ defined(X4,X3)
| ~ product(X4,X1,X5)
| ~ product(X1,X2,X3)
| defined(X5,X2) ),
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(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
inference(fof_simplification,[status(thm)],[identity2]) ).
cnf(c_0_28,hypothesis,
( ~ product(X1,X2,g)
| defined(b,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
product(codomain(X1),X1,X1),
product_on_codomain ).
cnf(c_0_30,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
inference(fof_simplification,[status(thm)],[associative_property2]) ).
cnf(c_0_31,hypothesis,
product(b,h,d),
bh_equals_d ).
cnf(c_0_32,plain,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom6]) ).
cnf(c_0_33,hypothesis,
( ~ product(X3,X2,b)
| ~ product(a,X3,X1)
| defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
c_0_27 ).
cnf(c_0_35,hypothesis,
defined(b,codomain(g)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map ).
cnf(c_0_37,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
c_0_30 ).
cnf(c_0_38,hypothesis,
defined(b,h),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_39,plain,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
c_0_32 ).
cnf(c_0_40,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x ).
cnf(c_0_41,hypothesis,
( ~ product(b,X1,b)
| defined(c,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_42,hypothesis,
product(b,codomain(g),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_43,hypothesis,
( ~ product(X2,X1,b)
| defined(X1,h) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
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,plain,
( ~ defined(X1,codomain(X2))
| defined(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_36])]) ).
cnf(c_0_46,hypothesis,
defined(c,codomain(g)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,hypothesis,
defined(codomain(g),h),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_48,plain,
( ~ product(X2,X4,X6)
| ~ product(X3,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X5) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom2]) ).
cnf(c_0_49,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
c_0_44 ).
cnf(c_0_50,hypothesis,
defined(c,g),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,hypothesis,
( ~ defined(X1,codomain(g))
| defined(X1,h) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_36])]) ).
cnf(c_0_52,plain,
( ~ product(X2,X4,X6)
| ~ product(X3,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X5) ),
c_0_48 ).
cnf(c_0_53,hypothesis,
product(c,g,compose(c,g)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,hypothesis,
defined(c,h),
inference(spm,[status(thm)],[c_0_51,c_0_46]) ).
cnf(c_0_55,hypothesis,
( ~ product(X1,X3,c)
| ~ product(X3,g,X2)
| product(X1,X2,compose(c,g)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,hypothesis,
product(c,h,compose(c,h)),
inference(spm,[status(thm)],[c_0_49,c_0_54]) ).
cnf(c_0_57,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[composition_is_well_defined]) ).
cnf(c_0_58,hypothesis,
( ~ product(X1,b,c)
| product(X1,d,compose(c,g)) ),
inference(spm,[status(thm)],[c_0_55,c_0_20]) ).
cnf(c_0_59,hypothesis,
( ~ product(X1,X3,c)
| ~ product(X3,h,X2)
| product(X1,X2,compose(c,h)) ),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_60,hypothesis,
( ~ product(c,X3,X2)
| ~ product(c,X1,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[cancellation_for_product]) ).
cnf(c_0_61,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_57 ).
cnf(c_0_62,hypothesis,
product(a,d,compose(c,g)),
inference(spm,[status(thm)],[c_0_58,c_0_22]) ).
cnf(c_0_63,hypothesis,
( ~ product(X1,b,c)
| product(X1,d,compose(c,h)) ),
inference(spm,[status(thm)],[c_0_59,c_0_31]) ).
cnf(c_0_64,hypothesis,
( ~ product(c,X3,X2)
| ~ product(c,X1,X2)
| X1 = X3 ),
c_0_60 ).
cnf(c_0_65,hypothesis,
( ~ product(a,d,X1)
| X1 = compose(c,g) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,hypothesis,
product(a,d,compose(c,h)),
inference(spm,[status(thm)],[c_0_63,c_0_22]) ).
cnf(c_0_67,hypothesis,
( ~ product(c,X1,compose(c,g))
| X1 = g ),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_68,hypothesis,
compose(c,g) = compose(c,h),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
h != g,
inference(fof_simplification,[status(thm)],[prove_h_equals_g]) ).
cnf(c_0_70,hypothesis,
( ~ product(c,X1,compose(c,h))
| X1 = g ),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
h != g,
c_0_69 ).
cnf(c_0_72,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_56]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/5.47 % Computer : n005.cluster.edu
% 0.19/5.47 % Model : x86_64 x86_64
% 0.19/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.47 % Memory : 8046.5625MB
% 0.19/5.47 % OS : Linux 6.8.0-71-generic
% 0.19/5.47 % CPULimit : 300
% 0.19/5.47 % WCLimit : 300
% 0.19/5.47 % DateTime : Mon Sep 21 13:54:53 UTC 2026
% 0.19/5.47 % CPUTime :
% 0.19/5.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.55 Running first-order theorem proving
% 0.24/5.55 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
% 13.37/7.77 % Version: 3.5.1
% 13.37/7.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.37/7.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.37/7.77 % Starting new_bool_3 with 300s (1) cores
% 13.37/7.77 % Starting new_bool_1 with 300s (1) cores
% 13.37/7.77 % Starting sh5l with 300s (1) cores
% 13.37/7.77 % new_bool_3 with pid 3647217 completed with status 9
% 13.37/7.77 % new_bool_1 with pid 3647218 completed with status 9
% 13.37/7.77 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3647216 completed with status 0
% 13.37/7.77 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.37/7.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.37/7.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.37/7.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.37/7.77 % No SInE strategy applied
% 13.37/7.77 % Search class: FHUSM-FFSS21-SFFFFFNN
% 13.37/7.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.37/7.77 % Starting SubtermCWHack with 136s (1) cores
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 13.37/7.77 % Starting new_bool_3 with 136s (1) cores
% 13.37/7.77 % Starting new_bool_1 with 136s (1) cores
% 13.37/7.77 % new_bool_1 with pid 3647224 completed with status 0
% 13.37/7.77 % Result found by new_bool_1
% 13.37/7.77 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.37/7.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.37/7.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.37/7.77 % No SInE strategy applied
% 13.37/7.77 % Search class: FHUSM-FFSS21-SFFFFFNN
% 13.37/7.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.37/7.77 % Starting SubtermCWHack with 136s (1) cores
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.37/7.77 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 13.37/7.77 % Starting new_bool_3 with 136s (1) cores
% 13.37/7.77 % Starting new_bool_1 with 136s (1) cores
% 13.37/7.77 % Preprocessing time : 0.002 s
% 13.37/7.77 % Presaturation interreduction done
% 13.37/7.77
% 13.37/7.77 % Proof found!
% 13.37/7.77 % SZS status Unsatisfiable
% 13.37/7.77 % SZS output start CNFRefutation
% See solution above
% 13.37/7.77 % Parsed axioms : 23
% 13.37/7.77 % Removed by relevancy pruning/SinE : 0
% 13.37/7.77 % Initial clauses : 23
% 13.37/7.77 % Removed in clause preprocessing : 0
% 13.37/7.77 % Initial clauses in saturation : 23
% 13.37/7.77 % Processed clauses : 12078
% 13.37/7.77 % ...of these trivial : 609
% 13.37/7.77 % ...subsumed : 7280
% 13.37/7.77 % ...remaining for further processing : 4189
% 13.37/7.77 % Other redundant clauses eliminated : 0
% 13.37/7.77 % Clauses deleted for lack of memory : 0
% 13.37/7.77 % Backward-subsumed : 71
% 13.37/7.77 % Backward-rewritten : 2058
% 13.37/7.77 % Generated clauses : 33234
% 13.37/7.77 % ...of the previous two non-redundant : 26239
% 13.37/7.77 % ...aggressively subsumed : 0
% 13.37/7.77 % Contextual simplify-reflections : 0
% 13.37/7.77 % Paramodulations : 33234
% 13.37/7.77 % Factorizations : 0
% 13.37/7.77 % NegExts : 0
% 13.37/7.77 % Equation resolutions : 0
% 13.37/7.77 % Disequality decompositions : 0
% 13.37/7.77 % Total rewrite steps : 29869
% 13.37/7.77 % ...of those cached : 28868
% 13.37/7.77 % Propositional unsat checks : 0
% 13.37/7.77 % Propositional check models : 0
% 13.37/7.77 % Propositional check unsatisfiable : 0
% 13.37/7.77 % Propositional clauses : 0
% 13.37/7.77 % Propositional clauses after purity: 0
% 13.37/7.77 % Propositional unsat core size : 0
% 13.37/7.77 % Propositional preprocessing time : 0.000
% 13.37/7.77 % Propositional encoding time : 0.000
% 13.37/7.77 % Propositional solver time : 0.000
% 13.37/7.77 % Success case prop preproc time : 0.000
% 13.37/7.77 % Success case prop encoding time : 0.000
% 13.37/7.77 % Success case prop solver time : 0.000
% 13.37/7.77 % Current number of processed clauses : 2037
% 13.37/7.77 % Positive orientable unit clauses : 126
% 13.37/7.77 % Positive unorientable unit clauses: 0
% 13.37/7.77 % Negative unit clauses : 1
% 13.37/7.77 % Non-unit-clauses : 1910
% 13.37/7.77 % Current number of unprocessed clauses: 10594
% 13.37/7.77 % ...number of literals in the above : 22718
% 13.37/7.77 % Current number of archived formulas : 0
% 13.37/7.77 % Current number of archived clauses : 2152
% 13.37/7.77 % Clause-clause subsumption calls (NU) : 1268344
% 13.37/7.77 % Rec. Clause-clause subsumption calls : 1123422
% 13.37/7.77 % Non-unit clause-clause subsumptions : 7351
% 13.37/7.77 % Unit Clause-clause subsumption calls : 2142
% 13.37/7.77 % Rewrite failures with RHS unbound : 0
% 13.37/7.77 % BW rewrite match attempts : 1378
% 13.37/7.77 % BW rewrite match successes : 187
% 13.37/7.77 % Condensation attempts : 0
% 13.37/7.77 % Condensation successes : 0
% 13.37/7.77 % Termbank termtop insertions : 418778
% 13.37/7.77 % Search garbage collected termcells : 62
% 13.37/7.77
% 13.37/7.77 % -------------------------------------------------
% 13.37/7.77 % User time : 2.112 s
% 13.37/7.77 % System time : 0.039 s
% 13.37/7.77 % Total time : 2.152 s
% 13.37/7.77 % Maximum resident set size: 3596 pages
% 13.37/7.77
% 13.37/7.77 % -------------------------------------------------
% 13.37/7.77 % User time : 10.987 s
% 13.37/7.77 % System time : 0.288 s
% 13.37/7.77 % Total time : 11.275 s
% 13.37/7.77 % Maximum resident set size: 4608 pages
% 13.37/7.77 % E exiting
%------------------------------------------------------------------------------