%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET945+1 : TPTP v9.2.1. Released v3.2.0.
% 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 05:09:01 PM UTC 2026
% Result : Theorem 1.14s 1.71s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 3 unt; 0 def)
% Number of atoms : 127 ( 19 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 157 ( 66 ~; 62 |; 20 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 99 ( 5 sgn 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_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(t98_zfmisc_1,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> disjoint(X3,X2) )
=> disjoint(union(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(c_0_5,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_6,plain,
! [X34,X35,X36,X37,X38,X39,X40,X41] :
( ( in(X37,X34)
| ~ in(X37,X36)
| X36 != set_intersection2(X34,X35) )
& ( in(X37,X35)
| ~ in(X37,X36)
| X36 != set_intersection2(X34,X35) )
& ( ~ in(X38,X34)
| ~ in(X38,X35)
| in(X38,X36)
| X36 != set_intersection2(X34,X35) )
& ( ~ in(esk1_3(X39,X40,X41),X41)
| ~ in(esk1_3(X39,X40,X41),X39)
| ~ in(esk1_3(X39,X40,X41),X40)
| X41 = set_intersection2(X39,X40) )
& ( in(esk1_3(X39,X40,X41),X39)
| in(esk1_3(X39,X40,X41),X41)
| X41 = set_intersection2(X39,X40) )
& ( in(esk1_3(X39,X40,X41),X40)
| in(esk1_3(X39,X40,X41),X41)
| X41 = set_intersection2(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)],[d3_xboole_0])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> disjoint(X3,X2) )
=> disjoint(union(X1),X2) ),
inference(assume_negation,[status(cth)],[t98_zfmisc_1]) ).
fof(c_0_8,plain,
! [X43,X44,X45,X47,X48,X49,X50,X52] :
( ( in(X45,esk2_3(X43,X44,X45))
| ~ in(X45,X44)
| X44 != union(X43) )
& ( in(esk2_3(X43,X44,X45),X43)
| ~ in(X45,X44)
| X44 != union(X43) )
& ( ~ in(X47,X48)
| ~ in(X48,X43)
| in(X47,X44)
| X44 != union(X43) )
& ( ~ in(esk3_2(X49,X50),X50)
| ~ in(esk3_2(X49,X50),X52)
| ~ in(X52,X49)
| X50 = union(X49) )
& ( in(esk3_2(X49,X50),esk4_2(X49,X50))
| in(esk3_2(X49,X50),X50)
| X50 = union(X49) )
& ( in(esk4_2(X49,X50),X49)
| in(esk3_2(X49,X50),X50)
| X50 = union(X49) ) ),
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)],[d4_tarski])])])])])]) ).
fof(c_0_9,plain,
! [X59,X60,X62,X63,X64] :
( ( disjoint(X59,X60)
| in(esk7_2(X59,X60),set_intersection2(X59,X60)) )
& ( ~ in(X64,set_intersection2(X62,X63))
| ~ disjoint(X62,X63) ) ),
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])])])])]) ).
cnf(c_0_10,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
! [X67] :
( ( ~ in(X67,esk8_0)
| disjoint(X67,esk9_0) )
& ~ disjoint(union(esk8_0),esk9_0) ),
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_12,plain,
( in(esk2_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( disjoint(X1,esk9_0)
| ~ in(X1,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(esk2_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( disjoint(esk2_3(esk8_0,union(esk8_0),X1),esk9_0)
| ~ in(X1,union(esk8_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( in(X1,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(X1,esk2_3(esk8_0,union(esk8_0),X2))
| ~ in(X2,union(esk8_0))
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( in(X1,esk2_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( disjoint(X1,X2)
| in(esk7_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( ~ in(X1,union(esk8_0))
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( disjoint(X1,X2)
| in(esk7_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X57,X58] :
( ~ disjoint(X57,X58)
| disjoint(X58,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
cnf(c_0_30,negated_conjecture,
( disjoint(X1,union(esk8_0))
| ~ in(esk7_2(X1,union(esk8_0)),esk9_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( disjoint(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_32,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
disjoint(esk9_0,union(esk8_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ disjoint(union(esk8_0),esk9_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SET945+1 : TPTP v9.2.1. Released v3.2.0.
% 0.05/0.13 % 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
% 0.06/0.33 % Computer : n024.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8042.1875MB
% 0.06/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon May 4 21:39:42 EDT 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.34 % start to proof: theBenchmark
% 1.14/1.71 % Version : CSE_E---1.7
% 1.14/1.71 % Problem : theBenchmark.p
% 1.14/1.71 % SZS status Theorem for theBenchmark.p
% 1.14/1.71 % SZS output start CNFRefutation
% See solution above
% 1.14/1.71 % Total time : 1.361s
%------------------------------------------------------------------------------