%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET916+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 : n022.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 05:08:57 PM UTC 2026
% Result : Theorem 1.77s 1.88s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 4 unt; 0 def)
% Number of atoms : 114 ( 34 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 140 ( 56 ~; 55 |; 24 &)
% ( 4 <=>; 1 =>; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 4 sgn 45 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(t57_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
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,
! [X47,X48,X49,X50,X51,X52,X53,X54] :
( ( in(X50,X47)
| ~ in(X50,X49)
| X49 != set_intersection2(X47,X48) )
& ( in(X50,X48)
| ~ in(X50,X49)
| X49 != set_intersection2(X47,X48) )
& ( ~ in(X51,X47)
| ~ in(X51,X48)
| in(X51,X49)
| X49 != set_intersection2(X47,X48) )
& ( ~ in(esk2_3(X52,X53,X54),X54)
| ~ in(esk2_3(X52,X53,X54),X52)
| ~ in(esk2_3(X52,X53,X54),X53)
| X54 = set_intersection2(X52,X53) )
& ( in(esk2_3(X52,X53,X54),X52)
| in(esk2_3(X52,X53,X54),X54)
| X54 = set_intersection2(X52,X53) )
& ( in(esk2_3(X52,X53,X54),X53)
| in(esk2_3(X52,X53,X54),X54)
| X54 = set_intersection2(X52,X53) ) ),
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_6,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_7,plain,
! [X38,X39,X40,X41,X42,X43,X44,X45] :
( ( ~ in(X41,X40)
| X41 = X38
| X41 = X39
| X40 != unordered_pair(X38,X39) )
& ( X42 != X38
| in(X42,X40)
| X40 != unordered_pair(X38,X39) )
& ( X42 != X39
| in(X42,X40)
| X40 != unordered_pair(X38,X39) )
& ( esk1_3(X43,X44,X45) != X43
| ~ in(esk1_3(X43,X44,X45),X45)
| X45 = unordered_pair(X43,X44) )
& ( esk1_3(X43,X44,X45) != X44
| ~ in(esk1_3(X43,X44,X45),X45)
| X45 = unordered_pair(X43,X44) )
& ( in(esk1_3(X43,X44,X45),X45)
| esk1_3(X43,X44,X45) = X43
| esk1_3(X43,X44,X45) = X44
| X45 = unordered_pair(X43,X44) ) ),
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)],[d2_tarski])])])])])]) ).
cnf(c_0_8,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X61,X62,X64,X65,X66] :
( ( disjoint(X61,X62)
| in(esk5_2(X61,X62),set_intersection2(X61,X62)) )
& ( ~ in(X66,set_intersection2(X64,X65))
| ~ disjoint(X64,X65) ) ),
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_6])])])])]) ).
cnf(c_0_10,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( disjoint(X1,X2)
| in(esk5_2(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,plain,
( esk5_2(X1,unordered_pair(X2,X3)) = X3
| esk5_2(X1,unordered_pair(X2,X3)) = X2
| disjoint(X1,unordered_pair(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t57_zfmisc_1])]) ).
fof(c_0_20,plain,
! [X59,X60] :
( ~ disjoint(X59,X60)
| disjoint(X60,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
cnf(c_0_21,plain,
( esk5_2(X1,unordered_pair(X2,X3)) = X3
| disjoint(X1,unordered_pair(X2,X3))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,negated_conjecture,
( ~ in(esk6_0,esk7_0)
& ~ in(esk8_0,esk7_0)
& ~ disjoint(unordered_pair(esk6_0,esk8_0),esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_23,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( disjoint(X1,unordered_pair(X2,X3))
| in(X2,X1)
| in(X3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
~ disjoint(unordered_pair(esk6_0,esk8_0),esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( disjoint(unordered_pair(X1,X2),X3)
| in(X2,X3)
| in(X1,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk8_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk6_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET916+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n022.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 02:39:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.77/1.88 % Version : CSE_E---1.7
% 1.77/1.88 % Problem : theBenchmark.p
% 1.77/1.88 % SZS status Theorem for theBenchmark.p
% 1.77/1.88 % SZS output start CNFRefutation
% See solution above
% 1.77/1.89 % Total time : 1.371s
%------------------------------------------------------------------------------