%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:51:08 PM UTC 2026
% Result : Theorem 36.61s 5.75s
% Output : Proof 36.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 12 unt; 0 def)
% Number of atoms : 155 ( 44 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 167 ( 61 ~; 62 |; 34 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 108 ( 5 sgn 55 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f5_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,A,B,D] :
( ( ( in(sk2(A,B,C),B)
& in(sk2(A,B,C),A)
& ~ in(sk2(A,B,C),C) )
| ( ( ~ in(sk2(A,B,C),B)
| ~ in(sk2(A,B,C),A) )
& in(sk2(A,B,C),C) )
| C = set_intersection2(A,B) )
& ( ( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c14,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p70,plain,
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c14]) ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk1(A,B),B)
& in(sk1(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c12,plain,
( in(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p74,plain,
( subset(set_intersection2(X0,X1),X2)
| in(sk1(set_intersection2(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[p70,c12]) ).
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c5,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p47,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
cnf(p91,plain,
( sk1(set_intersection2(singleton(X0),X1),X2) = X0
| subset(set_intersection2(singleton(X0),X1),X2) ),
inference(resolution,[status(thm)],[p74,p47]) ).
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p72,plain,
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(resolution,[status(thm)],[c14,c1]) ).
cnf(p75,plain,
( subset(set_intersection2(X0,X1),X2)
| in(sk1(set_intersection2(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[p72,c12]) ).
cnf(p197,plain,
( subset(set_intersection2(singleton(X0),X1),X2)
| in(X0,X1)
| subset(set_intersection2(singleton(X0),X1),X2) ),
inference(superposition,[status(thm)],[p91,p75]) ).
cnf(p2476,plain,
( in(X0,X1)
| subset(set_intersection2(singleton(X0),X1),X2) ),
inference(factoring,[status(thm)],[p197]) ).
fof(f2,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f17,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f17_nnf,plain,
! [A] : subset(empty_set,A),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A] : subset(empty_set,A),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c36,plain,
subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p43,plain,
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[status(thm)],[c4,c36]) ).
cnf(p2479,plain,
( empty_set = set_intersection2(singleton(X0),X1)
| in(X0,X1) ),
inference(resolution,[status(thm)],[p2476,p43]) ).
cnf(p2505,plain,
( set_intersection2(X1,singleton(X0)) = empty_set
| in(X0,X1) ),
inference(superposition,[status(thm)],[p2479,c1]) ).
fof(f6,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f6_nnf,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c24,plain,
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p42,plain,
( set_intersection2(X1,X0) != empty_set
| disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c1,c24]) ).
cnf(p2773,plain,
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(resolution,[status(thm)],[p2505,p42]) ).
fof(f12,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f12_neg,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [A,B] :
( ~ disjoint(singleton(A),B)
& ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ~ disjoint(singleton(sk3),sk4)
& ~ in(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f12_nnf]) ).
cnf(c31,plain,
~ disjoint(singleton(sk3),sk4),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p2784,plain,
in(sk3,sk4),
inference(resolution,[status(thm)],[p2773,c31]) ).
cnf(c30,plain,
~ in(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p2789,plain,
$false,
inference(resolution,[status(thm)],[p2784,c30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 13:04:23 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 36.61/5.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.61/5.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------