%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET027+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 : n024.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 05:06:56 PM UTC 2026
% Result : Theorem 1.11s 1.73s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 35 ( 11 ~; 14 |; 6 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 28 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(prove_transitivity_of_subset,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).
fof(c_0_2,plain,
! [X11,X12,X13,X14,X15] :
( ( ~ subset(X11,X12)
| ~ member(X13,X11)
| member(X13,X12) )
& ( member(esk1_2(X14,X15),X14)
| subset(X14,X15) )
& ( ~ member(esk1_2(X14,X15),X15)
| subset(X14,X15) ) ),
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_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
inference(assume_negation,[status(cth)],[prove_transitivity_of_subset]) ).
cnf(c_0_4,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_6,negated_conjecture,
( subset(esk2_0,esk3_0)
& subset(esk3_0,esk4_0)
& ~ subset(esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_7,plain,
( member(esk1_2(X1,X2),X3)
| subset(X1,X2)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( member(esk1_2(esk2_0,X1),esk3_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,negated_conjecture,
( member(esk1_2(esk2_0,X1),X2)
| subset(esk2_0,X1)
| ~ subset(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_13,negated_conjecture,
( member(esk1_2(esk2_0,X1),esk4_0)
| subset(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
~ subset(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.16 % Problem : SET027+3 : TPTP v9.2.1. Released v2.2.0.
% 0.05/0.16 % 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
% 0.06/0.36 % Computer : n024.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8042.1875MB
% 0.06/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Mon May 4 21:04:42 EDT 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.37 % start to proof: theBenchmark
% 1.11/1.73 % Version : CSE_E---1.7
% 1.11/1.73 % Problem : theBenchmark.p
% 1.11/1.73 % SZS status Theorem for theBenchmark.p
% 1.11/1.73 % SZS output start CNFRefutation
% See solution above
% 1.11/1.73 % Total time : 1.363s
%------------------------------------------------------------------------------