%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET574+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n019.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 05:08:01 PM UTC 2026
% Result : Theorem 0.24s 1.61s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 34 ( 13 ~; 10 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 17 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th13,conjecture,
! [X1,X2,X3] :
( ( member(X1,X2)
& member(X1,X3) )
=> intersect(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th13) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(i_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( member(X1,X2)
& member(X1,X3) )
=> intersect(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th13]) ).
fof(i_0_4,plain,
! [X12,X13,X15,X16,X17] :
( ( member(esk1_2(X12,X13),X12)
| ~ intersect(X12,X13) )
& ( member(esk1_2(X12,X13),X13)
| ~ intersect(X12,X13) )
& ( ~ member(X17,X15)
| ~ member(X17,X16)
| intersect(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[intersect_defn])])])])])]) ).
fof(i_0_5,plain,
! [X18,X19] :
( ~ intersect(X18,X19)
| intersect(X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).
fof(i_0_6,negated_conjecture,
( member(esk2_0,esk3_0)
& member(esk2_0,esk4_0)
& ~ intersect(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_3])])]) ).
cnf(i_0_7,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_8,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_9,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_10,plain,
( intersect(X2,X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_11,negated_conjecture,
~ intersect(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_12,negated_conjecture,
member(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_13,negated_conjecture,
member(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_14,plain,
$false,
inference(scs_inference,[],[i_0_11,i_0_13,i_0_12,i_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET574+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n019.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 02:27:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.24/1.61 % Version : CSE_E---1.7
% 0.24/1.61 % Problem : theBenchmark.p
% 0.24/1.61 % SZS status Theorem for theBenchmark.p
% 0.24/1.61 % SZS output start CNFRefutation
% See solution above
% 0.24/1.63 % Total time : 1.270s
%------------------------------------------------------------------------------