%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT002-1 : 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 12:07:57 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.78s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 46 ( 20 unt; 0 nHn; 46 RR)
% Number of literals : 89 ( 12 equ; 46 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 8 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(cg_equals_d,hypothesis,
product(c,g,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cg_equals_d) ).
cnf(ch_equals_d,hypothesis,
product(c,h,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ch_equals_d) ).
cnf(category_theory_axiom2,axiom,
( ~ product(X2,X4,X6)
| ~ product(X3,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).
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(ab_equals_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_equals_c) ).
cnf(cancellation_for_product1,hypothesis,
( ~ product(a,X3,X2)
| ~ product(a,X1,X2)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
cnf(cancellation_for_product2,hypothesis,
( ~ product(b,X3,X2)
| ~ product(b,X1,X2)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(c_0_10,plain,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
inference(fof_simplification,[status(thm)],[associative_property1]) ).
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,
( ~ product(X1,X2,X3)
| defined(X1,X2) ),
c_0_10 ).
cnf(c_0_13,hypothesis,
product(c,g,d),
cg_equals_d ).
cnf(c_0_14,plain,
( ~ defined(X3,X4)
| ~ product(X1,X2,X3)
| defined(X2,X4) ),
c_0_11 ).
cnf(c_0_15,hypothesis,
defined(c,g),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,hypothesis,
product(c,h,d),
ch_equals_d ).
cnf(c_0_17,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_18,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
inference(fof_simplification,[status(thm)],[closure_of_composition]) ).
cnf(c_0_19,hypothesis,
( ~ product(X2,X1,c)
| defined(X1,g) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
product(a,b,c),
ab_equals_c ).
cnf(c_0_21,hypothesis,
defined(c,h),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_22,plain,
( ~ product(X2,X4,X6)
| ~ product(X3,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X6,X5) ),
c_0_17 ).
cnf(c_0_23,plain,
( ~ defined(X1,X2)
| product(X1,X2,compose(X1,X2)) ),
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,hypothesis,
( ~ product(X2,X1,c)
| defined(X1,h) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_26,hypothesis,
( ~ product(X1,X3,c)
| ~ product(X3,g,X2)
| product(X1,X2,d) ),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_27,hypothesis,
product(b,g,compose(b,g)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
defined(b,h),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_29,hypothesis,
( ~ product(a,X3,X2)
| ~ product(a,X1,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[cancellation_for_product1]) ).
cnf(c_0_30,hypothesis,
( ~ product(X1,b,c)
| product(X1,compose(b,g),d) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
( ~ product(X1,X3,c)
| ~ product(X3,h,X2)
| product(X1,X2,d) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_32,hypothesis,
product(b,h,compose(b,h)),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_33,hypothesis,
( ~ product(a,X3,X2)
| ~ product(a,X1,X2)
| X1 = X3 ),
c_0_29 ).
cnf(c_0_34,hypothesis,
product(a,compose(b,g),d),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_35,hypothesis,
( ~ product(X1,b,c)
| product(X1,compose(b,h),d) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
( ~ product(b,X3,X2)
| ~ product(b,X1,X2)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[cancellation_for_product2]) ).
cnf(c_0_37,hypothesis,
( ~ product(a,X1,d)
| X1 = compose(b,g) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,hypothesis,
product(a,compose(b,h),d),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
cnf(c_0_39,hypothesis,
( ~ product(b,X3,X2)
| ~ product(b,X1,X2)
| X1 = X3 ),
c_0_36 ).
cnf(c_0_40,hypothesis,
compose(b,g) = compose(b,h),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
h != g,
inference(fof_simplification,[status(thm)],[prove_h_equals_g]) ).
cnf(c_0_42,hypothesis,
( ~ product(b,X1,compose(b,h))
| X1 = h ),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_43,hypothesis,
product(b,g,compose(b,h)),
inference(rw,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
h != g,
c_0_41 ).
cnf(c_0_45,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.39 % Computer : n016.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 21 13:59:59 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 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
% 0.15/5.78 % Version: 3.5.1
% 0.15/5.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.78 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.78 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.78 % Starting sh5l with 300s (1) cores
% 0.15/5.78 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2589444 completed with status 0
% 0.15/5.78 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.78 % No SInE strategy applied
% 0.15/5.78 % Search class: FHUSM-FFSS21-SFFFFFNN
% 0.15/5.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.78 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.15/5.78 % Starting new_bool_3 with 136s (1) cores
% 0.15/5.78 % Starting new_bool_1 with 136s (1) cores
% 0.15/5.78 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 2589451 completed with status 0
% 0.15/5.78 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 0.15/5.78 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.78 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.78 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.78 % No SInE strategy applied
% 0.15/5.78 % Search class: FHUSM-FFSS21-SFFFFFNN
% 0.15/5.78 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.78 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.78 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.15/5.78 % Preprocessing time : 0.001 s
% 0.15/5.78 % Presaturation interreduction done
% 0.15/5.78
% 0.15/5.78 % Proof found!
% 0.15/5.78 % SZS status Unsatisfiable
% 0.15/5.78 % SZS output start CNFRefutation
% See solution above
% 0.15/5.78 % Parsed axioms : 24
% 0.15/5.78 % Removed by relevancy pruning/SinE : 0
% 0.15/5.78 % Initial clauses : 24
% 0.15/5.78 % Removed in clause preprocessing : 0
% 0.15/5.78 % Initial clauses in saturation : 24
% 0.15/5.78 % Processed clauses : 3703
% 0.15/5.78 % ...of these trivial : 126
% 0.15/5.78 % ...subsumed : 1916
% 0.15/5.78 % ...remaining for further processing : 1661
% 0.15/5.78 % Other redundant clauses eliminated : 0
% 0.15/5.78 % Clauses deleted for lack of memory : 0
% 0.15/5.78 % Backward-subsumed : 14
% 0.15/5.78 % Backward-rewritten : 248
% 0.15/5.78 % Generated clauses : 14471
% 0.15/5.78 % ...of the previous two non-redundant : 10862
% 0.15/5.78 % ...aggressively subsumed : 0
% 0.15/5.78 % Contextual simplify-reflections : 0
% 0.15/5.78 % Paramodulations : 14471
% 0.15/5.78 % Factorizations : 0
% 0.15/5.78 % NegExts : 0
% 0.15/5.78 % Equation resolutions : 0
% 0.15/5.78 % Disequality decompositions : 0
% 0.15/5.78 % Total rewrite steps : 11029
% 0.15/5.78 % ...of those cached : 10491
% 0.15/5.78 % Propositional unsat checks : 0
% 0.15/5.78 % Propositional check models : 0
% 0.15/5.78 % Propositional check unsatisfiable : 0
% 0.15/5.78 % Propositional clauses : 0
% 0.15/5.78 % Propositional clauses after purity: 0
% 0.15/5.78 % Propositional unsat core size : 0
% 0.15/5.78 % Propositional preprocessing time : 0.000
% 0.15/5.78 % Propositional encoding time : 0.000
% 0.15/5.78 % Propositional solver time : 0.000
% 0.15/5.78 % Success case prop preproc time : 0.000
% 0.15/5.78 % Success case prop encoding time : 0.000
% 0.15/5.78 % Success case prop solver time : 0.000
% 0.15/5.78 % Current number of processed clauses : 1375
% 0.15/5.78 % Positive orientable unit clauses : 286
% 0.15/5.78 % Positive unorientable unit clauses: 0
% 0.15/5.78 % Negative unit clauses : 1
% 0.15/5.78 % Non-unit-clauses : 1088
% 0.15/5.78 % Current number of unprocessed clauses: 6694
% 0.15/5.78 % ...number of literals in the above : 13647
% 0.15/5.78 % Current number of archived formulas : 0
% 0.15/5.78 % Current number of archived clauses : 286
% 0.15/5.78 % Clause-clause subsumption calls (NU) : 167513
% 0.15/5.78 % Rec. Clause-clause subsumption calls : 145864
% 0.15/5.78 % Non-unit clause-clause subsumptions : 1930
% 0.15/5.78 % Unit Clause-clause subsumption calls : 2565
% 0.15/5.78 % Rewrite failures with RHS unbound : 0
% 0.15/5.78 % BW rewrite match attempts : 768
% 0.15/5.78 % BW rewrite match successes : 41
% 0.15/5.78 % Condensation attempts : 0
% 0.15/5.78 % Condensation successes : 0
% 0.15/5.78 % Termbank termtop insertions : 170926
% 0.15/5.78 % Search garbage collected termcells : 68
% 0.15/5.78
% 0.15/5.78 % -------------------------------------------------
% 0.15/5.78 % User time : 0.309 s
% 0.15/5.78 % System time : 0.015 s
% 0.15/5.78 % Total time : 0.323 s
% 0.15/5.78 % Maximum resident set size: 3648 pages
% 0.15/5.78
% 0.15/5.78 % -------------------------------------------------
% 0.15/5.78 % User time : 1.553 s
% 0.15/5.78 % System time : 0.060 s
% 0.15/5.78 % Total time : 1.613 s
% 0.15/5.78 % Maximum resident set size: 4864 pages
% 0.15/5.78 % E exiting
%------------------------------------------------------------------------------