%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:44:17 PM UTC 2026
% Result : Theorem 49.91s 8.84s
% Output : Proof 49.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 136 ( 70 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 157 ( 59 ~; 51 |; 41 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 4 sgn 51 !; 6 ?)
% 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/sandbox/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(c20,plain,
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f9,conjecture,
! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(f9_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [A,B,C] :
( A != B
& in(B,C)
& set_intersection2(unordered_pair(A,B),C) = singleton(A) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
( sk5 != sk6
& in(sk6,sk7)
& set_intersection2(unordered_pair(sk5,sk6),sk7) = singleton(sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7])],[f9_nnf]) ).
cnf(c30,plain,
set_intersection2(unordered_pair(sk5,sk6),sk7) = singleton(sk5),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p36,plain,
singleton(sk5) = set_intersection2(sk7,unordered_pair(sk5,sk6)),
inference(superposition,[status(thm)],[c30,c2]) ).
cnf(p188,plain,
( ~ in(X0,unordered_pair(sk5,sk6))
| ~ in(X0,sk7)
| in(X0,singleton(sk5)) ),
inference(resolution,[status(thm)],[c20,p36]) ).
cnf(c31,plain,
in(sk6,sk7),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p194,plain,
( ~ in(sk6,unordered_pair(sk5,sk6))
| in(sk6,singleton(sk5)) ),
inference(resolution,[status(thm)],[p188,c31]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f1_nnf,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f4_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D = B
| D = A )
& ~ in(D,C) )
| ( D != B
& D != A
& in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B,D] :
( ( ( ( sk1(A,B,C) = B
| sk1(A,B,C) = A )
& ~ in(sk1(A,B,C),C) )
| ( sk1(A,B,C) != B
& sk1(A,B,C) != A
& in(sk1(A,B,C),C) )
| C = unordered_pair(A,B) )
& ( ( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c10,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p53,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(p57,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p53]) ).
cnf(p62,plain,
in(X0,unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c1,p57]) ).
cnf(p197,plain,
in(sk6,singleton(sk5)),
inference(resolution,[status(thm)],[p194,p62]) ).
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/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(c3,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p37,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p199,plain,
sk6 = sk5,
inference(resolution,[status(thm)],[p197,p37]) ).
cnf(c32,plain,
sk5 != sk6,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p201,plain,
sk5 != sk5,
inference(demodulation,[status(thm)],[p199,c32]) ).
cnf(p240,plain,
$false,
inference(equality_resolution,[status(thm)],[p201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET918+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 12:22:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 49.91/8.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.91/8.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------