%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CAT003-2 : 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 : n007.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 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 50 ( 29 unt; 0 nHn; 41 RR)
% Number of literals : 99 ( 98 equ; 52 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_domain1,axiom,
( codomain(X1) != domain(X2)
| domain(compose(X1,X2)) = domain(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain1) ).
cnf(star_property,axiom,
( codomain(X2) != domain(X3)
| codomain(X1) != domain(X2)
| compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',star_property) ).
cnf(domain_of_codomain_is_codomain,axiom,
domain(codomain(X1)) = codomain(X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',domain_of_codomain_is_codomain) ).
cnf(codomain_of_domain_is_domain,axiom,
codomain(domain(X1)) = domain(X1),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_of_domain_is_domain) ).
cnf(domain_composition,axiom,
compose(domain(X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',domain_composition) ).
cnf(codomain_composition,axiom,
compose(X1,codomain(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_composition) ).
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
cnf(endomorphism,hypothesis,
( compose(compose(a,b),X3) != X2
| codomain(compose(a,b)) != domain(X3)
| compose(compose(a,b),X1) != X2
| codomain(compose(a,b)) != domain(X1)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',endomorphism) ).
cnf(codomain_domain2,axiom,
( codomain(X1) != domain(X2)
| codomain(compose(X1,X2)) = codomain(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain2) ).
cnf(codomain_of_b_equals_domain_of_g,hypothesis,
codomain(b) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
cnf(codomain_of_b_equals_domain_of_h,hypothesis,
codomain(b) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
cnf(bh_equals_bg,hypothesis,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_bg) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
cnf(c_0_13,plain,
( codomain(X1) != domain(X2)
| domain(compose(X1,X2)) = domain(X1) ),
inference(fof_simplification,[status(thm)],[codomain_domain1]) ).
cnf(c_0_14,plain,
( codomain(X2) != domain(X3)
| codomain(X1) != domain(X2)
| compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3) ),
inference(fof_simplification,[status(thm)],[star_property]) ).
cnf(c_0_15,plain,
( codomain(X1) != domain(X2)
| domain(compose(X1,X2)) = domain(X1) ),
c_0_13 ).
cnf(c_0_16,plain,
( codomain(X2) != domain(X3)
| codomain(X1) != domain(X2)
| compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3) ),
c_0_14 ).
cnf(c_0_17,axiom,
domain(codomain(X1)) = codomain(X1),
domain_of_codomain_is_codomain ).
cnf(c_0_18,axiom,
codomain(domain(X1)) = domain(X1),
codomain_of_domain_is_domain ).
cnf(c_0_19,plain,
( codomain(X1) != domain(X2)
| codomain(X2) != domain(X3)
| codomain(compose(X1,X2)) != domain(X3)
| domain(compose(X1,compose(X2,X3))) = domain(compose(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
compose(domain(X1),X1) = X1,
domain_composition ).
cnf(c_0_21,plain,
domain(domain(X1)) = domain(X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,axiom,
compose(X1,codomain(X1)) = X1,
codomain_composition ).
cnf(c_0_23,hypothesis,
codomain(a) = domain(b),
codomain_of_a_equals_domain_of_b ).
cnf(c_0_24,hypothesis,
( compose(compose(a,b),X3) != X2
| codomain(compose(a,b)) != domain(X3)
| compose(compose(a,b),X1) != X2
| codomain(compose(a,b)) != domain(X1)
| X1 = X3 ),
inference(fof_simplification,[status(thm)],[endomorphism]) ).
cnf(c_0_25,plain,
( codomain(X1) != domain(X2)
| codomain(compose(X1,X2)) = codomain(X2) ),
inference(fof_simplification,[status(thm)],[codomain_domain2]) ).
cnf(c_0_26,plain,
( codomain(X1) != domain(X2)
| codomain(compose(X1,domain(X2))) != domain(X2)
| domain(compose(X1,domain(X2))) = domain(compose(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_21])]) ).
cnf(c_0_27,hypothesis,
compose(a,domain(b)) = a,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,hypothesis,
codomain(b) = domain(g),
codomain_of_b_equals_domain_of_g ).
cnf(c_0_29,hypothesis,
codomain(b) = domain(h),
codomain_of_b_equals_domain_of_h ).
cnf(c_0_30,hypothesis,
( compose(compose(a,b),X3) != X2
| codomain(compose(a,b)) != domain(X3)
| compose(compose(a,b),X1) != X2
| codomain(compose(a,b)) != domain(X1)
| X1 = X3 ),
c_0_24 ).
cnf(c_0_31,plain,
( codomain(X1) != domain(X2)
| codomain(compose(X1,X2)) = codomain(X2) ),
c_0_25 ).
cnf(c_0_32,hypothesis,
domain(compose(a,b)) = domain(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23])]) ).
cnf(c_0_33,hypothesis,
compose(b,h) = compose(b,g),
bh_equals_bg ).
cnf(c_0_34,hypothesis,
domain(g) = domain(h),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,hypothesis,
( codomain(compose(a,b)) != domain(X1)
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X1) != compose(compose(a,b),X2)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( codomain(X1) != domain(X2)
| codomain(X2) != domain(X3)
| codomain(compose(X1,X2)) != domain(X3)
| codomain(compose(X1,compose(X2,X3))) = codomain(X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_37,hypothesis,
compose(domain(a),compose(a,b)) = compose(a,b),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_38,hypothesis,
codomain(compose(b,h)) = codomain(g),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_29]),c_0_34])]) ).
cnf(c_0_39,hypothesis,
( codomain(X2) != domain(X3)
| codomain(compose(a,b)) != domain(X1)
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X1) != compose(compose(a,b),compose(X2,X3))
| X1 = compose(X2,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_40,hypothesis,
codomain(compose(a,b)) = domain(h),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_29]),c_0_20]),c_0_23]),c_0_23]),c_0_18])]) ).
cnf(c_0_41,hypothesis,
codomain(g) = codomain(h),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_29])]) ).
cnf(c_0_42,hypothesis,
( codomain(X2) != domain(X3)
| domain(h) != domain(X1)
| domain(h) != domain(X2)
| compose(compose(a,b),X1) != compose(compose(a,b),compose(X2,X3))
| X1 = compose(X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
cnf(c_0_43,hypothesis,
compose(g,codomain(h)) = g,
inference(spm,[status(thm)],[c_0_22,c_0_41]) ).
cnf(c_0_44,hypothesis,
( domain(h) != domain(X1)
| compose(compose(a,b),X1) != compose(compose(a,b),g)
| X1 = g ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]),c_0_41]),c_0_17])]) ).
cnf(c_0_45,hypothesis,
( domain(h) != domain(X1)
| compose(compose(a,b),X1) != compose(a,compose(b,h))
| X1 = g ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_16]),c_0_33]),c_0_29]),c_0_34]),c_0_23])]) ).
cnf(c_0_46,negated_conjecture,
g != h,
inference(fof_simplification,[status(thm)],[prove_g_equals_h]) ).
cnf(c_0_47,hypothesis,
( domain(h) != domain(X1)
| compose(a,compose(b,X1)) != compose(a,compose(b,h))
| X1 = g ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_16]),c_0_29]),c_0_23])]) ).
cnf(c_0_48,negated_conjecture,
g != h,
c_0_46 ).
cnf(c_0_49,hypothesis,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:53:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 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
% 0.19/0.47 % Version: 3.5.1
% 0.19/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.47 % Starting sh5l with 300s (1) cores
% 0.19/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1254454 completed with status 0
% 0.19/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.47 % No SInE strategy applied
% 0.19/0.47 % Search class: FHUPM-FFSS21-SFFFFFNN
% 0.19/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.19/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.19/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.19/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1254460 completed with status 0
% 0.19/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.19/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.47 % No SInE strategy applied
% 0.19/0.47 % Search class: FHUPM-FFSS21-SFFFFFNN
% 0.19/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.19/0.47 % Preprocessing time : 0.001 s
% 0.19/0.47 % Presaturation interreduction done
% 0.19/0.47
% 0.19/0.47 % Proof found!
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.47 % Parsed axioms : 13
% 0.19/0.47 % Removed by relevancy pruning/SinE : 0
% 0.19/0.47 % Initial clauses : 13
% 0.19/0.47 % Removed in clause preprocessing : 0
% 0.19/0.47 % Initial clauses in saturation : 13
% 0.19/0.47 % Processed clauses : 338
% 0.19/0.47 % ...of these trivial : 13
% 0.19/0.47 % ...subsumed : 192
% 0.19/0.47 % ...remaining for further processing : 133
% 0.19/0.47 % Other redundant clauses eliminated : 1
% 0.19/0.47 % Clauses deleted for lack of memory : 0
% 0.19/0.47 % Backward-subsumed : 4
% 0.19/0.47 % Backward-rewritten : 6
% 0.19/0.47 % Generated clauses : 2149
% 0.19/0.47 % ...of the previous two non-redundant : 1623
% 0.19/0.47 % ...aggressively subsumed : 0
% 0.19/0.47 % Contextual simplify-reflections : 5
% 0.19/0.47 % Paramodulations : 2143
% 0.19/0.47 % Factorizations : 0
% 0.19/0.47 % NegExts : 0
% 0.19/0.47 % Equation resolutions : 6
% 0.19/0.47 % Disequality decompositions : 0
% 0.19/0.47 % Total rewrite steps : 3222
% 0.19/0.47 % ...of those cached : 3095
% 0.19/0.47 % Propositional unsat checks : 0
% 0.19/0.47 % Propositional check models : 0
% 0.19/0.47 % Propositional check unsatisfiable : 0
% 0.19/0.47 % Propositional clauses : 0
% 0.19/0.47 % Propositional clauses after purity: 0
% 0.19/0.47 % Propositional unsat core size : 0
% 0.19/0.47 % Propositional preprocessing time : 0.000
% 0.19/0.47 % Propositional encoding time : 0.000
% 0.19/0.47 % Propositional solver time : 0.000
% 0.19/0.47 % Success case prop preproc time : 0.000
% 0.19/0.47 % Success case prop encoding time : 0.000
% 0.19/0.47 % Success case prop solver time : 0.000
% 0.19/0.47 % Current number of processed clauses : 109
% 0.19/0.47 % Positive orientable unit clauses : 28
% 0.19/0.47 % Positive unorientable unit clauses: 0
% 0.19/0.47 % Negative unit clauses : 1
% 0.19/0.47 % Non-unit-clauses : 80
% 0.19/0.47 % Current number of unprocessed clauses: 1296
% 0.19/0.47 % ...number of literals in the above : 4945
% 0.19/0.47 % Current number of archived formulas : 0
% 0.19/0.47 % Current number of archived clauses : 23
% 0.19/0.47 % Clause-clause subsumption calls (NU) : 846
% 0.19/0.47 % Rec. Clause-clause subsumption calls : 810
% 0.19/0.47 % Non-unit clause-clause subsumptions : 201
% 0.19/0.47 % Unit Clause-clause subsumption calls : 0
% 0.19/0.47 % Rewrite failures with RHS unbound : 0
% 0.19/0.47 % BW rewrite match attempts : 5
% 0.19/0.47 % BW rewrite match successes : 5
% 0.19/0.47 % Condensation attempts : 0
% 0.19/0.47 % Condensation successes : 0
% 0.19/0.47 % Termbank termtop insertions : 38136
% 0.19/0.47 % Search garbage collected termcells : 22
% 0.19/0.47
% 0.19/0.47 % -------------------------------------------------
% 0.19/0.47 % User time : 0.021 s
% 0.19/0.47 % System time : 0.004 s
% 0.19/0.47 % Total time : 0.025 s
% 0.19/0.47 % Maximum resident set size: 3588 pages
% 0.19/0.47
% 0.19/0.47 % -------------------------------------------------
% 0.19/0.47 % User time : 0.091 s
% 0.19/0.47 % System time : 0.011 s
% 0.19/0.47 % Total time : 0.102 s
% 0.19/0.47 % Maximum resident set size: 4864 pages
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------