%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET596+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 05:08:04 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 59 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 16 |; 9 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th55,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& intersection(X2,X3) = empty_set )
=> intersection(X1,X3) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th55) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(intersection_of_subset,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(intersection(X1,X3),intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subset) ).
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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& intersection(X2,X3) = empty_set )
=> intersection(X1,X3) = empty_set ),
inference(assume_negation,[status(cth)],[prove_th55]) ).
fof(c_0_7,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_8,plain,
! [X29,X30,X31] :
( ~ subset(X29,X30)
| subset(intersection(X29,X31),intersection(X30,X31)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_of_subset])]) ).
fof(c_0_9,negated_conjecture,
( subset(esk4_0,esk5_0)
& intersection(esk5_0,esk6_0) = empty_set
& intersection(esk4_0,esk6_0) != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X32] : ~ member(X32,empty_set),
inference(variable_rename,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X36,X37,X38,X39,X40] :
( ( ~ subset(X36,X37)
| ~ member(X38,X36)
| member(X38,X37) )
& ( member(esk1_2(X39,X40),X39)
| subset(X39,X40) )
& ( ~ member(esk1_2(X39,X40),X40)
| subset(X39,X40) ) ),
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_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,plain,
( subset(intersection(X1,X3),intersection(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
intersection(esk5_0,esk6_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X44,X45] : intersection(X44,X45) = intersection(X45,X44),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( subset(intersection(X1,esk6_0),empty_set)
| ~ subset(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
intersection(esk4_0,esk6_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( intersection(X1,esk6_0) = empty_set
| ~ subset(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
intersection(esk6_0,esk4_0) != empty_set,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( intersection(esk6_0,X1) = empty_set
| ~ subset(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET596+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n010.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 02:28:36 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 : 1.371s
%------------------------------------------------------------------------------