%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT008-1 : 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 : n017.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 12:07:59 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 73 ( 32 unt; 0 nHn; 55 RR)
% Number of literals : 139 ( 9 equ; 69 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 120 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity1,axiom,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
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(mapping_from_x_to_its_domain,axiom,
defined(X1,domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
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(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(domain_is_an_identity_map,axiom,
identity_map(domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
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(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(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(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(ab_defined,hypothesis,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_defined) ).
cnf(associative_property1,axiom,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
cnf(prove_domain_of_a_equals_codomain_of_b,negated_conjecture,
domain(a) != codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_equals_codomain_of_b) ).
cnf(c_0_15,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[identity1]) ).
cnf(c_0_16,plain,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom3]) ).
cnf(c_0_17,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
c_0_15 ).
cnf(c_0_18,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain ).
cnf(c_0_19,plain,
( ~ defined(X4,X3)
| ~ product(X1,X2,X3)
| defined(X4,X1) ),
c_0_16 ).
cnf(c_0_20,plain,
( ~ identity_map(X1)
| product(X1,domain(X1),domain(X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( ~ defined(X1,domain(X2))
| ~ identity_map(X2)
| defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
inference(fof_simplification,[status(thm)],[associative_property2]) ).
cnf(c_0_23,plain,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
inference(fof_simplification,[status(thm)],[category_theory_axiom6]) ).
cnf(c_0_24,plain,
( ~ identity_map(X1)
| defined(X1,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_25,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_26,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
c_0_22 ).
cnf(c_0_27,axiom,
product(X1,domain(X1),X1),
product_on_domain ).
cnf(c_0_28,plain,
( ~ identity_map(X2)
| ~ defined(X2,X3)
| ~ defined(X1,X2)
| defined(X1,X3) ),
c_0_23 ).
cnf(c_0_29,axiom,
defined(codomain(X1),X1),
mapping_from_codomain_of_x_to_x ).
cnf(c_0_30,axiom,
identity_map(codomain(X1)),
codomain_is_an_identity_map ).
cnf(c_0_31,plain,
defined(domain(X1),domain(X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ defined(X1,X2)
| defined(domain(X1),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ defined(X1,codomain(X2))
| defined(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_34,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[composition_is_well_defined]) ).
cnf(c_0_35,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
inference(fof_simplification,[status(thm)],[identity2]) ).
cnf(c_0_36,axiom,
product(codomain(X1),X1,X1),
product_on_codomain ).
cnf(c_0_37,plain,
( ~ identity_map(X1)
| defined(domain(X1),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_38,plain,
( ~ defined(X1,X2)
| product(domain(X1),X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_32]),c_0_25])]) ).
cnf(c_0_39,plain,
defined(codomain(codomain(X1)),X1),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_40,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_34 ).
cnf(c_0_41,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
c_0_35 ).
cnf(c_0_42,plain,
( ~ defined(X1,X2)
| defined(X1,codomain(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_43,plain,
defined(domain(codomain(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_37]),c_0_30])]) ).
cnf(c_0_44,plain,
( ~ defined(X2,X3)
| ~ defined(X1,X3)
| defined(X1,domain(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_45,hypothesis,
defined(a,b),
ab_defined ).
cnf(c_0_46,plain,
( ~ defined(X1,codomain(codomain(X2)))
| defined(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_30])]) ).
cnf(c_0_47,plain,
( ~ identity_map(X1)
| defined(codomain(domain(X1)),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_48,plain,
( ~ product(codomain(X2),X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_49,plain,
( ~ defined(X1,X2)
| product(X1,codomain(X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_30])]) ).
cnf(c_0_50,plain,
( ~ defined(X1,domain(codomain(X2)))
| defined(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_25])]) ).
cnf(c_0_51,hypothesis,
( ~ defined(X1,b)
| defined(a,domain(X1)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
defined(codomain(domain(codomain(codomain(X1)))),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30])]) ).
cnf(c_0_53,plain,
codomain(codomain(X1)) = codomain(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_39])]) ).
cnf(c_0_54,hypothesis,
( ~ defined(codomain(X1),b)
| defined(a,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
defined(codomain(domain(codomain(domain(codomain(X1))))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_52]),c_0_53]) ).
cnf(c_0_56,plain,
( ~ defined(X1,codomain(X2))
| defined(domain(X1),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_57,hypothesis,
defined(a,domain(codomain(domain(codomain(b))))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,hypothesis,
defined(a,domain(codomain(b))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_52]),c_0_53]) ).
cnf(c_0_59,plain,
( ~ defined(X1,codomain(domain(X2)))
| ~ identity_map(X2)
| defined(domain(X1),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_56]) ).
cnf(c_0_60,hypothesis,
defined(a,codomain(domain(codomain(b)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_57]),c_0_30])]) ).
cnf(c_0_61,plain,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
inference(fof_simplification,[status(thm)],[associative_property1]) ).
cnf(c_0_62,plain,
( ~ defined(X1,codomain(X2))
| product(domain(X1),X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_56]),c_0_25])]) ).
cnf(c_0_63,hypothesis,
defined(a,codomain(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_58]),c_0_30])]) ).
cnf(c_0_64,hypothesis,
defined(domain(a),codomain(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_30])]) ).
cnf(c_0_65,plain,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
c_0_61 ).
cnf(c_0_66,hypothesis,
product(domain(a),b,b),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,negated_conjecture,
domain(a) != codomain(b),
inference(fof_simplification,[status(thm)],[prove_domain_of_a_equals_codomain_of_b]) ).
cnf(c_0_68,plain,
( ~ defined(X2,X3)
| ~ product(X2,codomain(X3),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_69,hypothesis,
product(domain(a),codomain(b),codomain(b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_64]),c_0_25])]) ).
cnf(c_0_70,hypothesis,
defined(domain(a),b),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,negated_conjecture,
domain(a) != codomain(b),
c_0_67 ).
cnf(c_0_72,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.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 : Mon Sep 21 13:50:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % new_bool_3 with pid 2477504 completed with status 0
% 0.11/0.46 % Result found by new_bool_3
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FHUSM-FFSF11-SFFFFFNN
% 0.11/0.46 % partial match(1): FHUSM-FFSF21-SFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % SubtermCWHack with pid 2477510 completed with status 0
% 0.11/0.46 % Result found by SubtermCWHack
% 0.11/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.46 % Search class: FHUSM-FFSF11-SFFFFFNN
% 0.11/0.46 % partial match(1): FHUSM-FFSF21-SFFFFFNN
% 0.11/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Unsatisfiable
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 20
% 0.11/0.46 % Removed by relevancy pruning/SinE : 1
% 0.11/0.46 % Initial clauses : 19
% 0.11/0.46 % Removed in clause preprocessing : 0
% 0.11/0.46 % Initial clauses in saturation : 19
% 0.11/0.46 % Processed clauses : 326
% 0.11/0.46 % ...of these trivial : 39
% 0.11/0.46 % ...subsumed : 122
% 0.11/0.46 % ...remaining for further processing : 165
% 0.11/0.46 % Other redundant clauses eliminated : 0
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 0
% 0.11/0.46 % Backward-rewritten : 77
% 0.11/0.46 % Generated clauses : 1775
% 0.11/0.46 % ...of the previous two non-redundant : 1340
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 0
% 0.11/0.46 % Paramodulations : 1775
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 0
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 1272
% 0.11/0.46 % ...of those cached : 1089
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 88
% 0.11/0.46 % Positive orientable unit clauses : 21
% 0.11/0.46 % Positive unorientable unit clauses: 0
% 0.11/0.46 % Negative unit clauses : 1
% 0.11/0.46 % Non-unit-clauses : 66
% 0.11/0.46 % Current number of unprocessed clauses: 973
% 0.11/0.46 % ...number of literals in the above : 2490
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 77
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 735
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 696
% 0.11/0.46 % Non-unit clause-clause subsumptions : 122
% 0.11/0.46 % Unit Clause-clause subsumption calls : 26
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 139
% 0.11/0.46 % BW rewrite match successes : 40
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 19475
% 0.11/0.46 % Search garbage collected termcells : 59
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.015 s
% 0.11/0.46 % System time : 0.002 s
% 0.11/0.46 % Total time : 0.017 s
% 0.11/0.46 % Maximum resident set size: 3904 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.018 s
% 0.11/0.46 % System time : 0.007 s
% 0.11/0.46 % Total time : 0.024 s
% 0.11/0.46 % Maximum resident set size: 4864 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------