%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL003+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:04:09 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 30 ( 11 ~; 10 |; 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(X1,X2) = X2
=> join(converse(X1),converse(X2)) = converse(X2) )
& ( join(converse(X1),converse(X2)) = converse(X2)
=> join(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( join(X1,X2) = X2
=> join(converse(X1),converse(X2)) = converse(X2) )
& ( join(converse(X1),converse(X2)) = converse(X2)
=> join(X1,X2) = 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(esk1_0,esk2_0) != 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(converse(esk1_0),converse(esk2_0)) != converse(esk2_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X31,X32] : join(X31,X32) = join(X32,X31),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_7,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_8,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X48,X49] : converse(join(X48,X49)) = join(converse(X48),converse(X49)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_10,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]) ).
fof(c_0_11,plain,
! [X47] : converse(converse(X47)) = X47,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_12,negated_conjecture,
( join(converse(esk2_0),converse(esk1_0)) = converse(esk2_0)
| join(esk2_0,esk1_0) = esk2_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_13,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( join(converse(esk2_0),converse(esk1_0)) != converse(esk2_0)
| join(esk2_0,esk1_0) != esk2_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_8]),c_0_8]) ).
cnf(c_0_15,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( converse(join(esk2_0,esk1_0)) = converse(esk2_0)
| join(esk2_0,esk1_0) = esk2_0 ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( converse(join(esk2_0,esk1_0)) != converse(esk2_0)
| join(esk2_0,esk1_0) != esk2_0 ),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
join(esk2_0,esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL003+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:42:33 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------