%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET196+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 : n010.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 05:07:34 PM UTC 2026
% Result : Theorem 1.17s 1.88s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 32 ( 12 ~; 12 |; 5 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(prove_intersection_is_subset,conjecture,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_is_subset) ).
fof(c_0_3,plain,
! [X18,X19,X20] :
( ( member(X20,X18)
| ~ member(X20,intersection(X18,X19)) )
& ( member(X20,X19)
| ~ member(X20,intersection(X18,X19)) )
& ( ~ member(X20,X18)
| ~ member(X20,X19)
| member(X20,intersection(X18,X19)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_4,plain,
! [X21,X22,X23,X24,X25] :
( ( ~ subset(X21,X22)
| ~ member(X23,X21)
| member(X23,X22) )
& ( member(esk1_2(X24,X25),X24)
| subset(X24,X25) )
& ( ~ member(esk1_2(X24,X25),X25)
| subset(X24,X25) ) ),
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,
~ ! [X1,X2] : subset(intersection(X1,X2),X1),
inference(assume_negation,[status(cth)],[prove_intersection_is_subset]) ).
cnf(c_0_6,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
~ subset(intersection(esk3_0,esk4_0),esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
~ subset(intersection(esk3_0,esk4_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20 % Problem : SET196+3 : TPTP v9.2.1. Released v2.2.0.
% 0.02/0.20 % 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
% 0.12/0.47 % Computer : n010.cluster.edu
% 0.12/0.47 % Model : x86_64 x86_64
% 0.12/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.47 % Memory : 8042.1875MB
% 0.12/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.47 % CPULimit : 300
% 0.12/0.47 % WCLimit : 300
% 0.12/0.47 % DateTime : Tue May 5 02:15:06 EDT 2026
% 0.12/0.48 % CPUTime :
% 0.12/0.49 % start to proof: theBenchmark
% 1.17/1.88 % Version : CSE_E---1.7
% 1.17/1.88 % Problem : theBenchmark.p
% 1.17/1.88 % SZS status Theorem for theBenchmark.p
% 1.17/1.88 % SZS output start CNFRefutation
% See solution above
% 1.17/1.88 % Total time : 1.383s
%------------------------------------------------------------------------------