%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT009-1 : 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 : n016.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 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 17 unt; 0 nHn; 29 RR)
% Number of literals : 65 ( 7 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(ba_defined,hypothesis,
defined(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ba_defined) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
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(identity2,axiom,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity2) ).
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(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(identity1,axiom,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(prove_domain_of_ba_equals_domain_of_a,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
cnf(c_0_10,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
inference(fof_simplification,[status(thm)],[closure_of_composition]) ).
cnf(c_0_11,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
inference(fof_simplification,[status(thm)],[associative_property2]) ).
cnf(c_0_12,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
c_0_10 ).
cnf(c_0_13,hypothesis,
defined(b,a),
ba_defined ).
cnf(c_0_14,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
c_0_11 ).
cnf(c_0_15,hypothesis,
product(b,a,compose(b,a)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
product(X1,domain(X1),X1),
product_on_domain ).
cnf(c_0_17,hypothesis,
( ~ defined(compose(b,a),X1)
| defined(a,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain ).
cnf(c_0_19,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
inference(fof_simplification,[status(thm)],[identity2]) ).
cnf(c_0_20,plain,
( ~ defined(X1,X2)
| defined(domain(X1),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_21,hypothesis,
defined(a,domain(compose(b,a))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[composition_is_well_defined]) ).
cnf(c_0_23,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
c_0_19 ).
cnf(c_0_24,hypothesis,
defined(domain(a),domain(compose(b,a))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_26,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[identity1]) ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_22 ).
cnf(c_0_28,hypothesis,
product(domain(a),domain(compose(b,a)),domain(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
c_0_26 ).
cnf(c_0_30,negated_conjecture,
domain(compose(b,a)) != domain(a),
inference(fof_simplification,[status(thm)],[prove_domain_of_ba_equals_domain_of_a]) ).
cnf(c_0_31,hypothesis,
( ~ product(domain(a),domain(compose(b,a)),X1)
| X1 = domain(a) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,hypothesis,
product(domain(a),domain(compose(b,a)),domain(compose(b,a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_24]),c_0_25])]) ).
cnf(c_0_33,negated_conjecture,
domain(compose(b,a)) != domain(a),
c_0_30 ).
cnf(c_0_34,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 14:00:24 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.46 % Version: 3.5.1
% 0.13/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.46 % Starting sh5l with 300s (1) cores
% 0.13/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2590982 completed with status 0
% 0.13/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.46 % No SInE strategy applied
% 0.13/0.46 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.13/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.13/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.46 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 2590990 completed with status 0
% 0.13/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 0.13/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.46 % No SInE strategy applied
% 0.13/0.46 % Search class: FHUSM-FFSF21-SFFFFFNN
% 0.13/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 136s (1) cores
% 0.13/0.46 % Preprocessing time : 0.001 s
% 0.13/0.46 % Presaturation interreduction done
% 0.13/0.46
% 0.13/0.46 % Proof found!
% 0.13/0.46 % SZS status Unsatisfiable
% 0.13/0.46 % SZS output start CNFRefutation
% See solution above
% 0.13/0.46 % Parsed axioms : 20
% 0.13/0.46 % Removed by relevancy pruning/SinE : 0
% 0.13/0.46 % Initial clauses : 20
% 0.13/0.46 % Removed in clause preprocessing : 0
% 0.13/0.46 % Initial clauses in saturation : 20
% 0.13/0.46 % Processed clauses : 324
% 0.13/0.46 % ...of these trivial : 33
% 0.13/0.46 % ...subsumed : 28
% 0.13/0.46 % ...remaining for further processing : 263
% 0.13/0.46 % Other redundant clauses eliminated : 0
% 0.13/0.46 % Clauses deleted for lack of memory : 0
% 0.13/0.46 % Backward-subsumed : 0
% 0.13/0.46 % Backward-rewritten : 107
% 0.13/0.46 % Generated clauses : 1622
% 0.13/0.46 % ...of the previous two non-redundant : 1303
% 0.13/0.46 % ...aggressively subsumed : 0
% 0.13/0.46 % Contextual simplify-reflections : 0
% 0.13/0.46 % Paramodulations : 1622
% 0.13/0.46 % Factorizations : 0
% 0.13/0.46 % NegExts : 0
% 0.13/0.46 % Equation resolutions : 0
% 0.13/0.46 % Disequality decompositions : 0
% 0.13/0.46 % Total rewrite steps : 994
% 0.13/0.46 % ...of those cached : 804
% 0.13/0.46 % Propositional unsat checks : 0
% 0.13/0.46 % Propositional check models : 0
% 0.13/0.46 % Propositional check unsatisfiable : 0
% 0.13/0.46 % Propositional clauses : 0
% 0.13/0.46 % Propositional clauses after purity: 0
% 0.13/0.46 % Propositional unsat core size : 0
% 0.13/0.46 % Propositional preprocessing time : 0.000
% 0.13/0.46 % Propositional encoding time : 0.000
% 0.13/0.46 % Propositional solver time : 0.000
% 0.13/0.46 % Success case prop preproc time : 0.000
% 0.13/0.46 % Success case prop encoding time : 0.000
% 0.13/0.46 % Success case prop solver time : 0.000
% 0.13/0.46 % Current number of processed clauses : 136
% 0.13/0.46 % Positive orientable unit clauses : 52
% 0.13/0.46 % Positive unorientable unit clauses: 0
% 0.13/0.46 % Negative unit clauses : 1
% 0.13/0.46 % Non-unit-clauses : 83
% 0.13/0.46 % Current number of unprocessed clauses: 859
% 0.13/0.46 % ...number of literals in the above : 1534
% 0.13/0.46 % Current number of archived formulas : 0
% 0.13/0.46 % Current number of archived clauses : 127
% 0.13/0.46 % Clause-clause subsumption calls (NU) : 819
% 0.13/0.46 % Rec. Clause-clause subsumption calls : 744
% 0.13/0.46 % Non-unit clause-clause subsumptions : 28
% 0.13/0.46 % Unit Clause-clause subsumption calls : 7
% 0.13/0.46 % Rewrite failures with RHS unbound : 0
% 0.13/0.46 % BW rewrite match attempts : 194
% 0.13/0.46 % BW rewrite match successes : 32
% 0.13/0.46 % Condensation attempts : 0
% 0.13/0.46 % Condensation successes : 0
% 0.13/0.46 % Termbank termtop insertions : 23241
% 0.13/0.46 % Search garbage collected termcells : 56
% 0.13/0.46
% 0.13/0.46 % -------------------------------------------------
% 0.13/0.46 % User time : 0.029 s
% 0.13/0.46 % System time : 0.007 s
% 0.13/0.46 % Total time : 0.036 s
% 0.13/0.46 % Maximum resident set size: 3340 pages
% 0.13/0.46
% 0.13/0.46 % -------------------------------------------------
% 0.13/0.46 % User time : 0.146 s
% 0.13/0.46 % System time : 0.017 s
% 0.13/0.46 % Total time : 0.163 s
% 0.13/0.46 % Maximum resident set size: 4608 pages
% 0.13/0.46 % E exiting
%------------------------------------------------------------------------------