%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT005-1 : 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 : n008.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 12:07:58 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 16 unt; 0 nHn; 26 RR)
% Number of literals : 56 ( 7 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 42 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity2,axiom,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity2) ).
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(ad_defined,hypothesis,
defined(a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ad_defined) ).
cnf(d_is_identity_map,hypothesis,
identity_map(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_identity_map) ).
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(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_a_is_d,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
cnf(c_0_9,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
inference(fof_simplification,[status(thm)],[identity2]) ).
cnf(c_0_10,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
inference(fof_simplification,[status(thm)],[associative_property2]) ).
cnf(c_0_11,plain,
( ~ identity_map(X2)
| ~ defined(X1,X2)
| product(X1,X2,X1) ),
c_0_9 ).
cnf(c_0_12,hypothesis,
defined(a,d),
ad_defined ).
cnf(c_0_13,hypothesis,
identity_map(d),
d_is_identity_map ).
cnf(c_0_14,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
c_0_10 ).
cnf(c_0_15,hypothesis,
product(a,d,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,hypothesis,
( ~ defined(a,X1)
| defined(d,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain ).
cnf(c_0_18,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[composition_is_well_defined]) ).
cnf(c_0_19,hypothesis,
defined(d,domain(a)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_21,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[identity1]) ).
cnf(c_0_22,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_18 ).
cnf(c_0_23,hypothesis,
product(d,domain(a),d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( ~ identity_map(X1)
| ~ defined(X1,X2)
| product(X1,X2,X2) ),
c_0_21 ).
cnf(c_0_25,negated_conjecture,
domain(a) != d,
inference(fof_simplification,[status(thm)],[prove_domain_of_a_is_d]) ).
cnf(c_0_26,hypothesis,
( ~ product(d,domain(a),X1)
| X1 = d ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
product(d,domain(a),domain(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_19]),c_0_13])]) ).
cnf(c_0_28,negated_conjecture,
domain(a) != d,
c_0_25 ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.53 % Computer : n008.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Mon Sep 21 13:56:26 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.58 Running first-order theorem proving
% 0.14/0.58 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
% 0.14/0.60 % Version: 3.5.1
% 0.14/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.60 % Starting sh5l with 300s (1) cores
% 0.14/0.60 % new_bool_1 with pid 1151842 completed with status 0
% 0.14/0.60 % Result found by new_bool_1
% 0.14/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.60 % Search class: FHUSS-FFSF11-SFFFFFNN
% 0.14/0.60 % partial match(1): FHUSS-FFSF21-SFFFFFNN
% 0.14/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.60 % SubtermCWHack with pid 1151848 completed with status 0
% 0.14/0.60 % Result found by SubtermCWHack
% 0.14/0.60 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.60 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.60 % Search class: FHUSS-FFSF11-SFFFFFNN
% 0.14/0.60 % partial match(1): FHUSS-FFSF21-SFFFFFNN
% 0.14/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.60 % Preprocessing time : 0.001 s
% 0.14/0.60
% 0.14/0.60 % Proof found!
% 0.14/0.60 % SZS status Unsatisfiable
% 0.14/0.60 % SZS output start CNFRefutation
% See solution above
% 0.14/0.60 % Parsed axioms : 21
% 0.14/0.60 % Removed by relevancy pruning/SinE : 4
% 0.14/0.60 % Initial clauses : 17
% 0.14/0.60 % Removed in clause preprocessing : 0
% 0.14/0.60 % Initial clauses in saturation : 17
% 0.14/0.60 % Processed clauses : 63
% 0.14/0.60 % ...of these trivial : 3
% 0.14/0.60 % ...subsumed : 7
% 0.14/0.60 % ...remaining for further processing : 53
% 0.14/0.60 % Other redundant clauses eliminated : 0
% 0.14/0.60 % Clauses deleted for lack of memory : 0
% 0.14/0.60 % Backward-subsumed : 0
% 0.14/0.60 % Backward-rewritten : 0
% 0.14/0.60 % Generated clauses : 169
% 0.14/0.60 % ...of the previous two non-redundant : 125
% 0.14/0.60 % ...aggressively subsumed : 0
% 0.14/0.60 % Contextual simplify-reflections : 0
% 0.14/0.60 % Paramodulations : 169
% 0.14/0.60 % Factorizations : 0
% 0.14/0.60 % NegExts : 0
% 0.14/0.60 % Equation resolutions : 0
% 0.14/0.60 % Disequality decompositions : 0
% 0.14/0.60 % Total rewrite steps : 65
% 0.14/0.60 % ...of those cached : 44
% 0.14/0.60 % Propositional unsat checks : 0
% 0.14/0.60 % Propositional check models : 0
% 0.14/0.60 % Propositional check unsatisfiable : 0
% 0.14/0.60 % Propositional clauses : 0
% 0.14/0.60 % Propositional clauses after purity: 0
% 0.14/0.60 % Propositional unsat core size : 0
% 0.14/0.60 % Propositional preprocessing time : 0.000
% 0.14/0.60 % Propositional encoding time : 0.000
% 0.14/0.60 % Propositional solver time : 0.000
% 0.14/0.60 % Success case prop preproc time : 0.000
% 0.14/0.60 % Success case prop encoding time : 0.000
% 0.14/0.60 % Success case prop solver time : 0.000
% 0.14/0.60 % Current number of processed clauses : 53
% 0.14/0.60 % Positive orientable unit clauses : 22
% 0.14/0.60 % Positive unorientable unit clauses: 0
% 0.14/0.60 % Negative unit clauses : 1
% 0.14/0.60 % Non-unit-clauses : 30
% 0.14/0.60 % Current number of unprocessed clauses: 79
% 0.14/0.60 % ...number of literals in the above : 225
% 0.14/0.60 % Current number of archived formulas : 0
% 0.14/0.60 % Current number of archived clauses : 0
% 0.14/0.60 % Clause-clause subsumption calls (NU) : 70
% 0.14/0.60 % Rec. Clause-clause subsumption calls : 67
% 0.14/0.60 % Non-unit clause-clause subsumptions : 7
% 0.14/0.60 % Unit Clause-clause subsumption calls : 0
% 0.14/0.60 % Rewrite failures with RHS unbound : 0
% 0.14/0.60 % BW rewrite match attempts : 5
% 0.14/0.60 % BW rewrite match successes : 0
% 0.14/0.60 % Condensation attempts : 0
% 0.14/0.60 % Condensation successes : 0
% 0.14/0.60 % Termbank termtop insertions : 2334
% 0.14/0.60 % Search garbage collected termcells : 66
% 0.14/0.60
% 0.14/0.60 % -------------------------------------------------
% 0.14/0.60 % User time : 0.004 s
% 0.14/0.60 % System time : 0.002 s
% 0.14/0.60 % Total time : 0.006 s
% 0.14/0.60 % Maximum resident set size: 3648 pages
% 0.14/0.60
% 0.14/0.60 % -------------------------------------------------
% 0.14/0.60 % User time : 0.009 s
% 0.14/0.60 % System time : 0.003 s
% 0.14/0.60 % Total time : 0.012 s
% 0.14/0.60 % Maximum resident set size: 4864 pages
% 0.14/0.60 % E exiting
%------------------------------------------------------------------------------