%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU159+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 : n010.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 02:51:09 PM UTC 2026
% Result : Theorem 23.01s 3.37s
% Output : Proof 23.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 131 ( 40 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 137 ( 48 ~; 59 |; 24 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 4 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(f2_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)],[f2]) ).
fof(f2_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])],[f2_nnf]) ).
cnf(c2,plain,
( X3 = X1
| X3 = X0
| ~ in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3_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)],[f3]) ).
fof(f3_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])],[f3_nnf]) ).
cnf(c12,plain,
( in(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p69,plain,
( subset(unordered_pair(X0,X1),X2)
| sk1(unordered_pair(X0,X1),X2) = X1
| sk1(unordered_pair(X0,X1),X2) = X0 ),
inference(resolution,[status(thm)],[p25,c12]) ).
cnf(c13,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p409,plain,
( ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2)
| subset(unordered_pair(X0,X1),X2)
| sk1(unordered_pair(X0,X1),X2) = X1 ),
inference(superposition,[status(thm)],[p69,c13]) ).
cnf(p2686,plain,
( ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2)
| sk1(unordered_pair(X0,X1),X2) = X1 ),
inference(factoring,[status(thm)],[p409]) ).
cnf(c11,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f6,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B,C] :
( ( in(B,C)
& in(A,C)
& ~ subset(unordered_pair(A,B),C) )
| ( ( ~ in(B,C)
| ~ in(A,C) )
& subset(unordered_pair(A,B),C) ) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( in(sk3,sk4)
& in(sk2,sk4)
& ~ subset(unordered_pair(sk2,sk3),sk4) )
| ( ( ~ in(sk3,sk4)
| ~ in(sk2,sk4) )
& subset(unordered_pair(sk2,sk3),sk4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f6_nnf]) ).
cnf(c17,plain,
( in(sk2,sk4)
| subset(unordered_pair(sk2,sk3),sk4) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p28,plain,
( in(sk2,sk4)
| in(X0,sk4)
| ~ in(X0,unordered_pair(sk2,sk3)) ),
inference(resolution,[status(thm)],[c11,c17]) ).
cnf(c3,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p33,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p30]) ).
cnf(p73,plain,
( in(sk2,sk4)
| in(sk2,sk4) ),
inference(resolution,[status(thm)],[p28,p33]) ).
cnf(p76,plain,
in(sk2,sk4),
inference(factoring,[status(thm)],[p73]) ).
cnf(p2718,plain,
( subset(unordered_pair(sk2,X0),sk4)
| sk1(unordered_pair(sk2,X0),sk4) = X0 ),
inference(resolution,[status(thm)],[p2686,p76]) ).
cnf(p2787,plain,
( ~ in(X0,sk4)
| subset(unordered_pair(sk2,X0),sk4)
| subset(unordered_pair(sk2,X0),sk4) ),
inference(superposition,[status(thm)],[p2718,c13]) ).
cnf(p3023,plain,
( ~ in(X0,sk4)
| subset(unordered_pair(sk2,X0),sk4) ),
inference(factoring,[status(thm)],[p2787]) ).
cnf(c18,plain,
( in(sk3,sk4)
| subset(unordered_pair(sk2,sk3),sk4) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p29,plain,
( in(sk3,sk4)
| in(X0,sk4)
| ~ in(X0,unordered_pair(sk2,sk3)) ),
inference(resolution,[status(thm)],[c11,c18]) ).
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/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]) ).
cnf(p36,plain,
in(X0,unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c1,p33]) ).
cnf(p82,plain,
( in(sk3,sk4)
| in(sk3,sk4) ),
inference(resolution,[status(thm)],[p29,p36]) ).
cnf(p84,plain,
in(sk3,sk4),
inference(factoring,[status(thm)],[p82]) ).
cnf(p3026,plain,
subset(unordered_pair(sk2,sk3),sk4),
inference(resolution,[status(thm)],[p3023,p84]) ).
cnf(c19,plain,
( ~ subset(unordered_pair(sk2,sk3),sk4)
| ~ in(sk3,sk4)
| ~ in(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p78,plain,
( ~ subset(unordered_pair(sk2,sk3),sk4)
| ~ in(sk3,sk4) ),
inference(resolution,[status(thm)],[p76,c19]) ).
cnf(p86,plain,
~ subset(unordered_pair(sk2,sk3),sk4),
inference(resolution,[status(thm)],[p84,p78]) ).
cnf(p3052,plain,
$false,
inference(resolution,[status(thm)],[p3026,p86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU159+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:59:28 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.01/3.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.01/3.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------