%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL008+3 : 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 : n020.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 05:04:12 PM UTC 2026
% Result : Theorem 9.58s 6.36s
% Output : CNFRefutation 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 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 : 49 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_5,plain,
! [X60,X61] : converse(composition(X60,X61)) = composition(converse(X61),converse(X60)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_6,plain,
! [X57] : converse(converse(X57)) = X57,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
fof(c_0_7,plain,
! [X58,X59] : converse(join(X58,X59)) = join(converse(X58),converse(X59)),
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]) ).
cnf(c_0_10,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X54,X55,X56] : composition(join(X54,X55),X56) = join(composition(X54,X56),composition(X55,X56)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_12,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_10,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_11]) ).
cnf(c_0_15,plain,
join(composition(X1,converse(X2)),converse(X3)) = converse(join(composition(X2,converse(X1)),X3)),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_16,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
fof(c_0_17,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_18,plain,
converse(join(composition(X1,converse(X2)),composition(X1,X3))) = converse(composition(X1,join(converse(X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_8]),c_0_15]),c_0_16]) ).
fof(c_0_19,negated_conjecture,
composition(esk1_0,join(esk2_0,esk3_0)) != join(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_20,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_18]),c_0_9]) ).
cnf(c_0_21,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_19]) ).
cnf(c_0_22,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_20,c_0_9]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL008+3 : 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
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:40:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 9.58/6.36 % Version : CSE_E---1.7
% 9.58/6.36 % Problem : theBenchmark.p
% 9.58/6.36 % SZS status Theorem for theBenchmark.p
% 9.58/6.36 % SZS output start CNFRefutation
% See solution above
% 9.68/6.40 % Total time : 4.370s
%------------------------------------------------------------------------------