%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : REL003+1 : 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 : n020.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 02:04:12 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 23 ( 7 ~; 7 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X1,X2] :
( ( join(converse(X1),converse(X2)) = converse(X2)
=> join(X1,X2) = X2 )
& ( join(X1,X2) = X2
=> join(converse(X1),converse(X2)) = converse(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( join(converse(X1),converse(X2)) = converse(X2)
=> join(X1,X2) = X2 )
& ( join(X1,X2) = X2
=> join(converse(X1),converse(X2)) = converse(X2) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_5,negated_conjecture,
( ( join(converse(esk1_0),converse(esk2_0)) != converse(esk2_0)
| join(esk1_0,esk2_0) != esk2_0 )
& ( join(converse(esk1_0),converse(esk2_0)) != converse(esk2_0)
| join(converse(esk1_0),converse(esk2_0)) = converse(esk2_0) )
& ( join(esk1_0,esk2_0) = esk2_0
| join(esk1_0,esk2_0) != esk2_0 )
& ( join(esk1_0,esk2_0) = esk2_0
| join(converse(esk1_0),converse(esk2_0)) = converse(esk2_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).
fof(c_0_6,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
fof(c_0_7,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_8,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_9,negated_conjecture,
( join(esk1_0,esk2_0) = esk2_0
| join(converse(esk1_0),converse(esk2_0)) = converse(esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( join(esk2_0,esk1_0) = esk2_0
| converse(join(esk2_0,esk1_0)) = converse(esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( join(converse(esk1_0),converse(esk2_0)) != converse(esk2_0)
| join(esk1_0,esk2_0) != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
join(esk2_0,esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_12])]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_10]),c_0_15]),c_0_11]),c_0_10]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:58:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1952896 completed with status 0
% 0.10/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FGHPM-FFSF21-MFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.10/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.43 % SubtermCWHack with pid 1952900 completed with status 0
% 0.10/0.43 % Result found by SubtermCWHack
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.43 % No SInE strategy applied
% 0.10/0.43 % Search class: FGHPM-FFSF21-MFFFFFNN
% 0.10/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Theorem
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 14
% 0.10/0.43 % Removed by relevancy pruning/SinE : 0
% 0.10/0.43 % Initial clauses : 17
% 0.10/0.43 % Removed in clause preprocessing : 3
% 0.10/0.43 % Initial clauses in saturation : 14
% 0.10/0.43 % Processed clauses : 22
% 0.10/0.43 % ...of these trivial : 0
% 0.10/0.43 % ...subsumed : 4
% 0.10/0.43 % ...remaining for further processing : 17
% 0.10/0.43 % Other redundant clauses eliminated : 0
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 0
% 0.10/0.43 % Backward-rewritten : 2
% 0.10/0.43 % Generated clauses : 68
% 0.10/0.43 % ...of the previous two non-redundant : 53
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 0
% 0.10/0.43 % Paramodulations : 68
% 0.10/0.43 % Factorizations : 0
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 0
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 51
% 0.10/0.43 % ...of those cached : 24
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 15
% 0.10/0.43 % Positive orientable unit clauses : 14
% 0.10/0.43 % Positive unorientable unit clauses: 1
% 0.10/0.43 % Negative unit clauses : 0
% 0.10/0.43 % Non-unit-clauses : 0
% 0.10/0.43 % Current number of unprocessed clauses: 45
% 0.10/0.43 % ...number of literals in the above : 49
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 3
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.43 % Non-unit clause-clause subsumptions : 0
% 0.10/0.43 % Unit Clause-clause subsumption calls : 0
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 4
% 0.10/0.43 % BW rewrite match successes : 4
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 1317
% 0.10/0.43 % Search garbage collected termcells : 50
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.004 s
% 0.10/0.43 % System time : 0.003 s
% 0.10/0.43 % Total time : 0.006 s
% 0.10/0.43 % Maximum resident set size: 3648 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.013 s
% 0.10/0.43 % System time : 0.009 s
% 0.10/0.43 % Total time : 0.022 s
% 0.10/0.43 % Maximum resident set size: 4864 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------