%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU119+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n008.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 05:10:40 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 122 ( 30 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 144 ( 60 ~; 56 |; 23 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 66 ( 2 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t3_xboole_0,conjecture,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(c_0_5,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_6,plain,
! [X31,X32,X33] :
( ( X31 != empty_set
| ~ in(X32,X31) )
& ( in(esk1_1(X33),X33)
| X33 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t3_xboole_0])]) ).
cnf(c_0_8,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X35,X36,X37,X38,X39,X40,X41,X42] :
( ( in(X38,X35)
| ~ in(X38,X37)
| X37 != set_intersection2(X35,X36) )
& ( in(X38,X36)
| ~ in(X38,X37)
| X37 != set_intersection2(X35,X36) )
& ( ~ in(X39,X35)
| ~ in(X39,X36)
| in(X39,X37)
| X37 != set_intersection2(X35,X36) )
& ( ~ in(esk2_3(X40,X41,X42),X42)
| ~ in(esk2_3(X40,X41,X42),X40)
| ~ in(esk2_3(X40,X41,X42),X41)
| X42 = set_intersection2(X40,X41) )
& ( in(esk2_3(X40,X41,X42),X40)
| in(esk2_3(X40,X41,X42),X42)
| X42 = set_intersection2(X40,X41) )
& ( in(esk2_3(X40,X41,X42),X41)
| in(esk2_3(X40,X41,X42),X42)
| X42 = set_intersection2(X40,X41) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X53] :
( ( in(esk7_0,esk5_0)
| ~ disjoint(esk5_0,esk6_0) )
& ( in(esk7_0,esk6_0)
| ~ disjoint(esk5_0,esk6_0) )
& ( disjoint(esk5_0,esk6_0)
| ~ disjoint(esk5_0,esk6_0) )
& ( in(esk7_0,esk5_0)
| ~ in(X53,esk5_0)
| ~ in(X53,esk6_0) )
& ( in(esk7_0,esk6_0)
| ~ in(X53,esk5_0)
| ~ in(X53,esk6_0) )
& ( disjoint(esk5_0,esk6_0)
| ~ in(X53,esk5_0)
| ~ in(X53,esk6_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_7])])])])]) ).
cnf(c_0_11,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(esk2_3(X1,X2,X3),X2)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X44,X45] :
( ( ~ disjoint(X44,X45)
| set_intersection2(X44,X45) = empty_set )
& ( set_intersection2(X44,X45) != empty_set
| disjoint(X44,X45) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_14,negated_conjecture,
( in(esk7_0,esk5_0)
| ~ in(X1,esk5_0)
| ~ in(X1,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( set_intersection2(X1,X2) = empty_set
| in(esk2_3(X1,X2,empty_set),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X29,X30] : set_intersection2(X29,X30) = set_intersection2(X30,X29),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_17,negated_conjecture,
( in(esk7_0,esk5_0)
| ~ disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( set_intersection2(X1,esk5_0) = empty_set
| in(esk7_0,esk5_0)
| ~ in(esk2_3(X1,esk5_0,empty_set),esk6_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( in(esk7_0,esk5_0)
| set_intersection2(esk5_0,esk6_0) != empty_set ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( disjoint(esk5_0,esk6_0)
| ~ in(X1,esk5_0)
| ~ in(X1,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
in(esk7_0,esk5_0),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_11]),c_0_22]) ).
cnf(c_0_25,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( disjoint(esk5_0,esk6_0)
| ~ in(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( set_intersection2(esk5_0,esk6_0) = empty_set
| ~ in(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( in(esk7_0,esk6_0)
| ~ in(X1,esk5_0)
| ~ in(X1,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_11]),c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( in(esk7_0,esk6_0)
| ~ disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,negated_conjecture,
( set_intersection2(X1,esk6_0) = empty_set
| ~ in(esk2_3(X1,esk6_0,empty_set),esk5_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( in(esk7_0,esk6_0)
| set_intersection2(esk5_0,esk6_0) != empty_set ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_35,negated_conjecture,
set_intersection2(esk5_0,esk6_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_11]) ).
cnf(c_0_36,negated_conjecture,
in(esk7_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_36]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU119+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.14/0.32 % Computer : n008.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:44:28 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------