%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET589+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 : n017.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 05:08:03 PM UTC 2026
% Result : Theorem 1.41s 1.78s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 37 ( 15 ~; 12 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subset) ).
fof(difference_subset2,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X3,X2),difference(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_subset2) ).
fof(prove_th48,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(difference(X1,X4),difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th48) ).
fof(difference_subset1,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X1,X3),difference(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_subset1) ).
fof(c_0_4,plain,
! [X25,X26,X27] :
( ~ subset(X25,X26)
| ~ subset(X26,X27)
| subset(X25,X27) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_subset])]) ).
fof(c_0_5,plain,
! [X31,X32,X33] :
( ~ subset(X31,X32)
| subset(difference(X33,X32),difference(X33,X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_subset2])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(difference(X1,X4),difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_th48]) ).
cnf(c_0_7,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( subset(difference(X3,X2),difference(X3,X1))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X28,X29,X30] :
( ~ subset(X28,X29)
| subset(difference(X28,X30),difference(X29,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_subset1])]) ).
fof(c_0_10,negated_conjecture,
( subset(esk2_0,esk3_0)
& subset(esk4_0,esk5_0)
& ~ subset(difference(esk2_0,esk5_0),difference(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( subset(X1,difference(X2,X3))
| ~ subset(X1,difference(X2,X4))
| ~ subset(X3,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( subset(difference(X1,X3),difference(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
~ subset(difference(esk2_0,esk5_0),difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( subset(difference(X1,X2),difference(X3,X4))
| ~ subset(X4,X2)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET589+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
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:26:58 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.41/1.78 % Version : CSE_E---1.7
% 1.41/1.78 % Problem : theBenchmark.p
% 1.41/1.78 % SZS status Theorem for theBenchmark.p
% 1.41/1.78 % SZS output start CNFRefutation
% See solution above
% 1.41/1.78 % Total time : 1.371s
%------------------------------------------------------------------------------