%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET597+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 : n011.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 05:08:05 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 104 ( 29 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 112 ( 44 ~; 47 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 2 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th56,conjecture,
! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ( subset(X2,X4)
& subset(X3,X4) )
=> subset(X1,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th56) ).
fof(subset_of_union,axiom,
! [X1,X2] : subset(X1,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_of_union) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(union_subset,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(union(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_subset) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( X1 = union(X2,X3)
<=> ( subset(X2,X1)
& subset(X3,X1)
& ! [X4] :
( ( subset(X2,X4)
& subset(X3,X4) )
=> subset(X1,X4) ) ) ),
inference(assume_negation,[status(cth)],[prove_th56]) ).
fof(c_0_6,negated_conjecture,
! [X58] :
( ( subset(esk4_0,esk6_0)
| ~ subset(esk4_0,esk3_0)
| ~ subset(esk5_0,esk3_0)
| esk3_0 != union(esk4_0,esk5_0) )
& ( subset(esk5_0,esk6_0)
| ~ subset(esk4_0,esk3_0)
| ~ subset(esk5_0,esk3_0)
| esk3_0 != union(esk4_0,esk5_0) )
& ( ~ subset(esk3_0,esk6_0)
| ~ subset(esk4_0,esk3_0)
| ~ subset(esk5_0,esk3_0)
| esk3_0 != union(esk4_0,esk5_0) )
& ( subset(esk4_0,esk3_0)
| esk3_0 = union(esk4_0,esk5_0) )
& ( subset(esk5_0,esk3_0)
| esk3_0 = union(esk4_0,esk5_0) )
& ( ~ subset(esk4_0,X58)
| ~ subset(esk5_0,X58)
| subset(esk3_0,X58)
| esk3_0 = union(esk4_0,esk5_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_7,plain,
! [X28,X29] : subset(X28,union(X28,X29)),
inference(variable_rename,[status(thm)],[subset_of_union]) ).
fof(c_0_8,plain,
! [X44,X45] : union(X44,X45) = union(X45,X44),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_9,negated_conjecture,
( subset(esk3_0,X1)
| esk3_0 = union(esk4_0,esk5_0)
| ~ subset(esk4_0,X1)
| ~ subset(esk5_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
subset(X1,union(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X42,X43] :
( ( subset(X42,X43)
| X42 != X43 )
& ( subset(X43,X42)
| X42 != X43 )
& ( ~ subset(X42,X43)
| ~ subset(X43,X42)
| X42 = X43 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_13,negated_conjecture,
( union(esk4_0,esk5_0) = esk3_0
| subset(esk3_0,union(esk5_0,X1))
| ~ subset(esk4_0,union(esk5_0,X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( union(esk4_0,esk5_0) = esk3_0
| subset(esk3_0,union(esk4_0,esk5_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
fof(c_0_17,plain,
! [X30,X31,X32] :
( ~ subset(X30,X31)
| ~ subset(X32,X31)
| subset(union(X30,X32),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_subset])]) ).
cnf(c_0_18,negated_conjecture,
( subset(esk5_0,esk3_0)
| esk3_0 = union(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( subset(esk4_0,esk3_0)
| esk3_0 = union(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( union(esk4_0,esk5_0) = esk3_0
| ~ subset(union(esk4_0,esk5_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( subset(union(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
subset(esk5_0,esk3_0),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
subset(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( subset(esk5_0,esk6_0)
| ~ subset(esk4_0,esk3_0)
| ~ subset(esk5_0,esk3_0)
| esk3_0 != union(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( subset(esk4_0,esk6_0)
| ~ subset(esk4_0,esk3_0)
| ~ subset(esk5_0,esk3_0)
| esk3_0 != union(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( ~ subset(esk3_0,esk6_0)
| ~ subset(esk4_0,esk3_0)
| ~ subset(esk5_0,esk3_0)
| esk3_0 != union(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
union(esk4_0,esk5_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
( subset(esk5_0,esk6_0)
| union(esk4_0,esk5_0) != esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_23])]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
( subset(esk4_0,esk6_0)
| union(esk4_0,esk5_0) != esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_23])]),c_0_22])]) ).
cnf(c_0_30,negated_conjecture,
( union(esk4_0,esk5_0) != esk3_0
| ~ subset(esk3_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_23])]),c_0_22])]) ).
cnf(c_0_31,negated_conjecture,
( subset(esk3_0,X1)
| ~ subset(esk5_0,X1)
| ~ subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
subset(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
subset(esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_27])]) ).
cnf(c_0_34,negated_conjecture,
~ subset(esk3_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_27])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET597+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
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:28:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------