%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET625+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 : n025.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 56 ( 22 ~; 20 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th101,conjecture,
! [X1,X2,X3] :
( ( intersect(X1,X2)
& subset(X2,X3) )
=> intersect(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th101) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
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(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( intersect(X1,X2)
& subset(X2,X3) )
=> intersect(X1,X3) ),
inference(assume_negation,[status(cth)],[prove_th101]) ).
fof(c_0_4,plain,
! [X22,X23,X24,X25,X26] :
( ( ~ subset(X22,X23)
| ~ member(X24,X22)
| member(X24,X23) )
& ( member(esk2_2(X25,X26),X25)
| subset(X25,X26) )
& ( ~ member(esk2_2(X25,X26),X26)
| subset(X25,X26) ) ),
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)],[subset_defn])])])])])]) ).
fof(c_0_5,negated_conjecture,
( intersect(esk3_0,esk4_0)
& subset(esk4_0,esk5_0)
& ~ intersect(esk3_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,plain,
! [X16,X17,X19,X20,X21] :
( ( member(esk1_2(X16,X17),X16)
| ~ intersect(X16,X17) )
& ( member(esk1_2(X16,X17),X17)
| ~ intersect(X16,X17) )
& ( ~ member(X21,X19)
| ~ member(X21,X20)
| intersect(X19,X20) ) ),
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])])])])])]) ).
cnf(c_0_7,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( intersect(X1,esk5_0)
| ~ member(X2,esk4_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( intersect(X1,esk5_0)
| ~ member(esk1_2(X2,esk4_0),X1)
| ~ intersect(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
~ intersect(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
( intersect(X1,esk5_0)
| ~ intersect(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
intersect(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET625+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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 : n025.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 02:30:13 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % 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 : 1.370s
%------------------------------------------------------------------------------