%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET920+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 38.04s 5.28s
% Output : Proof 38.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 92 ( 42 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 38 ~; 35 |; 27 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 4 sgn 36 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B,D] :
( ( ( in(sk1(A,B,C),B)
& in(sk1(A,B,C),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(sk1(A,B,C),B)
| ~ in(sk1(A,B,C),A) )
& in(sk1(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,[sk1])],[f4_nnf]) ).
cnf(c12,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f8,conjecture,
! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C] :
( ~ in(A,C)
& set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ~ in(sk4,sk6)
& set_intersection2(unordered_pair(sk4,sk5),sk6) = unordered_pair(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f8_nnf]) ).
cnf(c24,plain,
set_intersection2(unordered_pair(sk4,sk5),sk6) = unordered_pair(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/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(p28,plain,
unordered_pair(sk4,sk5) = set_intersection2(sk6,unordered_pair(sk4,sk5)),
inference(superposition,[status(thm)],[c24,c2]) ).
cnf(p74,plain,
( in(X0,sk6)
| ~ in(X0,unordered_pair(sk4,sk5)) ),
inference(resolution,[status(thm)],[c12,p28]) ).
fof(f3,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( ( sk0(A,B,C) = B
| sk0(A,B,C) = A )
& ~ in(sk0(A,B,C),C) )
| ( sk0(A,B,C) != B
& sk0(A,B,C) != A
& in(sk0(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,[sk0])],[f3_nnf]) ).
cnf(c4,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p33,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
cnf(p36,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p33]) ).
cnf(p78,plain,
in(sk4,sk6),
inference(resolution,[status(thm)],[p74,p36]) ).
cnf(c25,plain,
~ in(sk4,sk6),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p81,plain,
$false,
inference(resolution,[status(thm)],[p78,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET920+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:22:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 38.04/5.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.04/5.28 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------