%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU154+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n031.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 05:10:49 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 110 ( 37 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 117 ( 43 ~; 48 |; 16 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 4 sgn 47 !; 0 ?)
% 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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(l28_zfmisc_1,conjecture,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(c_0_8,plain,
! [X53,X54,X55,X56,X57,X58,X59,X60] :
( ( in(X56,X53)
| ~ in(X56,X55)
| X55 != set_intersection2(X53,X54) )
& ( in(X56,X54)
| ~ in(X56,X55)
| X55 != set_intersection2(X53,X54) )
& ( ~ in(X57,X53)
| ~ in(X57,X54)
| in(X57,X55)
| X55 != set_intersection2(X53,X54) )
& ( ~ in(esk3_3(X58,X59,X60),X60)
| ~ in(esk3_3(X58,X59,X60),X58)
| ~ in(esk3_3(X58,X59,X60),X59)
| X60 = set_intersection2(X58,X59) )
& ( in(esk3_3(X58,X59,X60),X58)
| in(esk3_3(X58,X59,X60),X60)
| X60 = set_intersection2(X58,X59) )
& ( in(esk3_3(X58,X59,X60),X59)
| in(esk3_3(X58,X59,X60),X60)
| X60 = set_intersection2(X58,X59) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_10,plain,
! [X47,X48,X49,X50,X51] :
( ( ~ subset(X47,X48)
| ~ in(X49,X47)
| in(X49,X48) )
& ( in(esk2_2(X50,X51),X50)
| subset(X50,X51) )
& ( ~ in(esk2_2(X50,X51),X51)
| subset(X50,X51) ) ),
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_tarski])])])])])]) ).
fof(c_0_11,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ in(X42,X41)
| X42 = X40
| X41 != singleton(X40) )
& ( X43 != X40
| in(X43,X41)
| X41 != singleton(X40) )
& ( ~ in(esk1_2(X44,X45),X45)
| esk1_2(X44,X45) != X44
| X45 = singleton(X44) )
& ( in(esk1_2(X44,X45),X45)
| esk1_2(X44,X45) = X44
| X45 = singleton(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)],[d1_tarski])])])])])]) ).
cnf(c_0_12,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X36,X37] : set_intersection2(X36,X37) = set_intersection2(X37,X36),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_15,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l28_zfmisc_1])]) ).
fof(c_0_17,plain,
! [X38,X39] :
( ( subset(X38,X39)
| X38 != X39 )
& ( subset(X39,X38)
| X38 != X39 )
& ( ~ subset(X38,X39)
| ~ subset(X39,X38)
| X38 = X39 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(c_0_18,plain,
! [X72] : subset(empty_set,X72),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_19,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk2_2(set_intersection2(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_15]) ).
fof(c_0_22,negated_conjecture,
( ~ in(esk4_0,esk5_0)
& ~ disjoint(singleton(esk4_0),esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_23,plain,
! [X62,X63] :
( ( ~ disjoint(X62,X63)
| set_intersection2(X62,X63) = empty_set )
& ( set_intersection2(X62,X63) != empty_set
| disjoint(X62,X63) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_24,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk2_2(set_intersection2(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( esk2_2(set_intersection2(X1,singleton(X2)),X3) = X2
| subset(set_intersection2(X1,singleton(X2)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
~ disjoint(singleton(esk4_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( subset(set_intersection2(X1,singleton(X2)),X3)
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
set_intersection2(esk5_0,singleton(esk4_0)) != empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]) ).
cnf(c_0_33,plain,
( set_intersection2(X1,singleton(X2)) = empty_set
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
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
% 0.00/0.12 % Problem : SEU154+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.13/0.32 % Computer : n031.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:47:23 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % 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
%------------------------------------------------------------------------------