%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL009+2 : 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 : 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 02:03:51 PM UTC 2026
% Result : Theorem 0.24s 0.64s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 23 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 2 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 47 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X1,X2,X3] :
( join(X1,X2) = X2
=> ( join(composition(X3,X1),composition(X3,X2)) = composition(X3,X2)
& join(composition(X1,X3),composition(X2,X3)) = composition(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
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(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( join(X1,X2) = X2
=> ( join(composition(X3,X1),composition(X3,X2)) = composition(X3,X2)
& join(composition(X1,X3),composition(X2,X3)) = composition(X2,X3) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X13,X14] : converse(composition(X13,X14)) = composition(converse(X14),converse(X13)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_8,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
fof(c_0_9,negated_conjecture,
( ( join(composition(esk3_0,esk1_0),composition(esk3_0,esk2_0)) != composition(esk3_0,esk2_0)
| join(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) != composition(esk2_0,esk3_0) )
& join(esk1_0,esk2_0) = esk2_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X15,X16] : join(X15,X16) = join(X16,X15),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
fof(c_0_11,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_12,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X10,X11,X12] : composition(join(X10,X11),X12) = join(composition(X10,X12),composition(X11,X12)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_15,negated_conjecture,
join(esk1_0,esk2_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( join(composition(esk3_0,esk1_0),composition(esk3_0,esk2_0)) != composition(esk3_0,esk2_0)
| join(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) != composition(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
join(esk2_0,esk1_0) = esk2_0,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,negated_conjecture,
join(composition(esk3_0,esk2_0),composition(esk3_0,esk1_0)) != composition(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19]),c_0_16]),c_0_21]),c_0_16])]) ).
cnf(c_0_25,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_22,c_0_23]),c_0_17]),c_0_12]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n007.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 03:56:05 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 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
% 0.24/0.64 % Version: 3.5.1
% 0.24/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.64 % Starting sh5l with 300s (1) cores
% 0.24/0.64 % new_bool_3 with pid 122564 completed with status 0
% 0.24/0.64 % Result found by new_bool_3
% 0.24/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.64 % Search class: FUHPM-FFMF21-DFFFFFNN
% 0.24/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.64 % SubtermCWHack with pid 122572 completed with status 0
% 0.24/0.64 % Result found by SubtermCWHack
% 0.24/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.64 % Search class: FUHPM-FFMF21-DFFFFFNN
% 0.24/0.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.64 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.64 % Preprocessing time : 0.002 s
% 0.24/0.64
% 0.24/0.64 % Proof found!
% 0.24/0.64 % SZS status Theorem
% 0.24/0.64 % SZS output start CNFRefutation
% See solution above
% 0.24/0.64 % Parsed axioms : 17
% 0.24/0.64 % Removed by relevancy pruning/SinE : 3
% 0.24/0.64 % Initial clauses : 15
% 0.24/0.64 % Removed in clause preprocessing : 0
% 0.24/0.64 % Initial clauses in saturation : 15
% 0.24/0.64 % Processed clauses : 640
% 0.24/0.64 % ...of these trivial : 332
% 0.24/0.64 % ...subsumed : 208
% 0.24/0.64 % ...remaining for further processing : 100
% 0.24/0.64 % Other redundant clauses eliminated : 0
% 0.24/0.64 % Clauses deleted for lack of memory : 0
% 0.24/0.64 % Backward-subsumed : 0
% 0.24/0.64 % Backward-rewritten : 4
% 0.24/0.64 % Generated clauses : 3805
% 0.24/0.64 % ...of the previous two non-redundant : 3433
% 0.24/0.64 % ...aggressively subsumed : 0
% 0.24/0.64 % Contextual simplify-reflections : 0
% 0.24/0.64 % Paramodulations : 3805
% 0.24/0.64 % Factorizations : 0
% 0.24/0.64 % NegExts : 0
% 0.24/0.64 % Equation resolutions : 0
% 0.24/0.64 % Disequality decompositions : 0
% 0.24/0.64 % Total rewrite steps : 2998
% 0.24/0.64 % ...of those cached : 1705
% 0.24/0.64 % Propositional unsat checks : 0
% 0.24/0.64 % Propositional check models : 0
% 0.24/0.64 % Propositional check unsatisfiable : 0
% 0.24/0.64 % Propositional clauses : 0
% 0.24/0.64 % Propositional clauses after purity: 0
% 0.24/0.64 % Propositional unsat core size : 0
% 0.24/0.64 % Propositional preprocessing time : 0.000
% 0.24/0.64 % Propositional encoding time : 0.000
% 0.24/0.64 % Propositional solver time : 0.000
% 0.24/0.64 % Success case prop preproc time : 0.000
% 0.24/0.64 % Success case prop encoding time : 0.000
% 0.24/0.64 % Success case prop solver time : 0.000
% 0.24/0.64 % Current number of processed clauses : 96
% 0.24/0.64 % Positive orientable unit clauses : 78
% 0.24/0.64 % Positive unorientable unit clauses: 18
% 0.24/0.64 % Negative unit clauses : 0
% 0.24/0.64 % Non-unit-clauses : 0
% 0.24/0.64 % Current number of unprocessed clauses: 2802
% 0.24/0.64 % ...number of literals in the above : 2802
% 0.24/0.64 % Current number of archived formulas : 0
% 0.24/0.64 % Current number of archived clauses : 4
% 0.24/0.64 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.64 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.64 % Non-unit clause-clause subsumptions : 0
% 0.24/0.64 % Unit Clause-clause subsumption calls : 71
% 0.24/0.64 % Rewrite failures with RHS unbound : 0
% 0.24/0.64 % BW rewrite match attempts : 212
% 0.24/0.64 % BW rewrite match successes : 59
% 0.24/0.64 % Condensation attempts : 0
% 0.24/0.64 % Condensation successes : 0
% 0.24/0.64 % Termbank termtop insertions : 48115
% 0.24/0.64 % Search garbage collected termcells : 57
% 0.24/0.64
% 0.24/0.64 % -------------------------------------------------
% 0.24/0.64 % User time : 0.072 s
% 0.24/0.64 % System time : 0.011 s
% 0.24/0.64 % Total time : 0.084 s
% 0.24/0.64 % Maximum resident set size: 3396 pages
% 0.24/0.64
% 0.24/0.64 % -------------------------------------------------
% 0.24/0.64 % User time : 0.075 s
% 0.24/0.64 % System time : 0.015 s
% 0.24/0.64 % Total time : 0.090 s
% 0.24/0.64 % Maximum resident set size: 4608 pages
% 0.24/0.64 % E exiting
%------------------------------------------------------------------------------