%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 02:03:51 PM UTC 2026
% Result : Theorem 0.44s 0.54s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(goals,conjecture,
! [X1,X2,X3] : composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_5,plain,
! [X18,X19] : converse(composition(X18,X19)) = composition(converse(X19),converse(X18)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_6,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
fof(c_0_7,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_8,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X12,X13,X14] : composition(join(X12,X13),X14) = join(composition(X12,X14),composition(X13,X14)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3] : composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_12,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
composition(esk1_0,join(esk2_0,esk3_0)) != join(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_16,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
composition(esk1_0,join(esk2_0,esk3_0)) != join(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
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_16,c_0_17]),c_0_12]),c_0_8]),c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.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 04:00:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.44/0.54 % Version: 3.5.1
% 0.44/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.44/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.44/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.44/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.44/0.54 % Starting sh5l with 300s (1) cores
% 0.44/0.54 % new_bool_3 with pid 3361172 completed with status 0
% 0.44/0.54 % Result found by new_bool_3
% 0.44/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.44/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.44/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.44/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.44/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.44/0.54 % Search class: FUUPM-FFMF21-DFFFFFNN
% 0.44/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.44/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.44/0.54 % SubtermCWHack with pid 3361179 completed with status 0
% 0.44/0.54 % Result found by SubtermCWHack
% 0.44/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.44/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.44/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.44/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.44/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.44/0.54 % Search class: FUUPM-FFMF21-DFFFFFNN
% 0.44/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.44/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.44/0.54 % Preprocessing time : 0.002 s
% 0.44/0.54
% 0.44/0.54 % Proof found!
% 0.44/0.54 % SZS status Theorem
% 0.44/0.54 % SZS output start CNFRefutation
% See solution above
% 0.44/0.54 % Parsed axioms : 17
% 0.44/0.54 % Removed by relevancy pruning/SinE : 3
% 0.44/0.54 % Initial clauses : 14
% 0.44/0.54 % Removed in clause preprocessing : 0
% 0.44/0.54 % Initial clauses in saturation : 14
% 0.44/0.54 % Processed clauses : 474
% 0.44/0.54 % ...of these trivial : 211
% 0.44/0.54 % ...subsumed : 187
% 0.44/0.54 % ...remaining for further processing : 76
% 0.44/0.54 % Other redundant clauses eliminated : 0
% 0.44/0.54 % Clauses deleted for lack of memory : 0
% 0.44/0.54 % Backward-subsumed : 0
% 0.44/0.54 % Backward-rewritten : 1
% 0.44/0.54 % Generated clauses : 2554
% 0.44/0.54 % ...of the previous two non-redundant : 2271
% 0.44/0.54 % ...aggressively subsumed : 0
% 0.44/0.54 % Contextual simplify-reflections : 0
% 0.44/0.54 % Paramodulations : 2554
% 0.44/0.54 % Factorizations : 0
% 0.44/0.54 % NegExts : 0
% 0.44/0.54 % Equation resolutions : 0
% 0.44/0.54 % Disequality decompositions : 0
% 0.44/0.54 % Total rewrite steps : 1849
% 0.44/0.54 % ...of those cached : 975
% 0.44/0.54 % Propositional unsat checks : 0
% 0.44/0.54 % Propositional check models : 0
% 0.44/0.54 % Propositional check unsatisfiable : 0
% 0.44/0.54 % Propositional clauses : 0
% 0.44/0.54 % Propositional clauses after purity: 0
% 0.44/0.54 % Propositional unsat core size : 0
% 0.44/0.54 % Propositional preprocessing time : 0.000
% 0.44/0.54 % Propositional encoding time : 0.000
% 0.44/0.54 % Propositional solver time : 0.000
% 0.44/0.54 % Success case prop preproc time : 0.000
% 0.44/0.54 % Success case prop encoding time : 0.000
% 0.44/0.54 % Success case prop solver time : 0.000
% 0.44/0.54 % Current number of processed clauses : 75
% 0.44/0.54 % Positive orientable unit clauses : 59
% 0.44/0.54 % Positive unorientable unit clauses: 16
% 0.44/0.54 % Negative unit clauses : 0
% 0.44/0.54 % Non-unit-clauses : 0
% 0.44/0.54 % Current number of unprocessed clauses: 1811
% 0.44/0.54 % ...number of literals in the above : 1811
% 0.44/0.54 % Current number of archived formulas : 0
% 0.44/0.54 % Current number of archived clauses : 1
% 0.44/0.54 % Clause-clause subsumption calls (NU) : 0
% 0.44/0.54 % Rec. Clause-clause subsumption calls : 0
% 0.44/0.54 % Non-unit clause-clause subsumptions : 0
% 0.44/0.54 % Unit Clause-clause subsumption calls : 65
% 0.44/0.54 % Rewrite failures with RHS unbound : 0
% 0.44/0.54 % BW rewrite match attempts : 132
% 0.44/0.54 % BW rewrite match successes : 33
% 0.44/0.54 % Condensation attempts : 0
% 0.44/0.54 % Condensation successes : 0
% 0.44/0.54 % Termbank termtop insertions : 31602
% 0.44/0.54 % Search garbage collected termcells : 33
% 0.44/0.54
% 0.44/0.54 % -------------------------------------------------
% 0.44/0.54 % User time : 0.052 s
% 0.44/0.54 % System time : 0.008 s
% 0.44/0.54 % Total time : 0.059 s
% 0.44/0.54 % Maximum resident set size: 3908 pages
% 0.44/0.54
% 0.44/0.54 % -------------------------------------------------
% 0.44/0.54 % User time : 0.054 s
% 0.44/0.54 % System time : 0.014 s
% 0.44/0.54 % Total time : 0.068 s
% 0.44/0.54 % Maximum resident set size: 4864 pages
% 0.44/0.54 % E exiting
%------------------------------------------------------------------------------