%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET626+3 : TPTP v9.2.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 05:08:10 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 19 |; 7 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(prove_th102,conjecture,
! [X1,X2,X3] :
( intersect(X1,intersection(X2,X3))
=> intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th102) ).
fof(symmetry_of_intersect,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(c_0_4,plain,
! [X23,X24,X26,X27,X28] :
( ( member(esk1_2(X23,X24),X23)
| ~ intersect(X23,X24) )
& ( member(esk1_2(X23,X24),X24)
| ~ intersect(X23,X24) )
& ( ~ member(X28,X26)
| ~ member(X28,X27)
| intersect(X26,X27) ) ),
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(c_0_5,plain,
! [X20,X21,X22] :
( ( member(X22,X20)
| ~ member(X22,intersection(X20,X21)) )
& ( member(X22,X21)
| ~ member(X22,intersection(X20,X21)) )
& ( ~ member(X22,X20)
| ~ member(X22,X21)
| member(X22,intersection(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_6,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( intersect(X1,intersection(X2,X3))
=> intersect(X1,X2) ),
inference(assume_negation,[status(cth)],[prove_th102]) ).
cnf(c_0_11,plain,
( intersect(X1,X2)
| ~ intersect(X2,X3)
| ~ member(esk1_2(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,intersection(X2,X3)),X2)
| ~ intersect(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_13,negated_conjecture,
( intersect(esk3_0,intersection(esk4_0,esk5_0))
& ~ intersect(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_14,plain,
! [X31,X32] :
( ~ intersect(X31,X32)
| intersect(X32,X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).
cnf(c_0_15,plain,
( intersect(X1,X2)
| ~ intersect(X2,intersection(X1,X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
intersect(esk3_0,intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( intersect(X2,X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
intersect(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ intersect(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET626+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:30:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------