%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU159+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 27.55s 3.86s
% Output : Proof 27.55s
% 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/sandbox/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(p26,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/sandbox/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(p70,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)],[p26,c12]) ).
cnf(c13,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p410,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)],[p70,c13]) ).
cnf(p2712,plain,
( ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2)
| sk1(unordered_pair(X0,X1),X2) = X1 ),
inference(factoring,[status(thm)],[p410]) ).
cnf(c11,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f7,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_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)],[f7_neg]) ).
fof(f7_sk,plain,
( ( in(sk5,sk6)
& in(sk4,sk6)
& ~ subset(unordered_pair(sk4,sk5),sk6) )
| ( ( ~ in(sk5,sk6)
| ~ in(sk4,sk6) )
& subset(unordered_pair(sk4,sk5),sk6) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f7_nnf]) ).
cnf(c18,plain,
( in(sk4,sk6)
| subset(unordered_pair(sk4,sk5),sk6) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p29,plain,
( in(sk4,sk6)
| in(X0,sk6)
| ~ in(X0,unordered_pair(sk4,sk5)) ),
inference(resolution,[status(thm)],[c11,c18]) ).
cnf(c3,plain,
( X3 != X0
| in(X3,X2)
| X2 != unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p31,plain,
( X0 != X1
| in(X0,unordered_pair(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p34,plain,
in(X0,unordered_pair(X0,X1)),
inference(equality_resolution,[status(thm)],[p31]) ).
cnf(p74,plain,
( in(sk4,sk6)
| in(sk4,sk6) ),
inference(resolution,[status(thm)],[p29,p34]) ).
cnf(p77,plain,
in(sk4,sk6),
inference(factoring,[status(thm)],[p74]) ).
cnf(p2719,plain,
( subset(unordered_pair(sk4,X0),sk6)
| sk1(unordered_pair(sk4,X0),sk6) = X0 ),
inference(resolution,[status(thm)],[p2712,p77]) ).
cnf(p2788,plain,
( ~ in(X0,sk6)
| subset(unordered_pair(sk4,X0),sk6)
| subset(unordered_pair(sk4,X0),sk6) ),
inference(superposition,[status(thm)],[p2719,c13]) ).
cnf(p3007,plain,
( ~ in(X0,sk6)
| subset(unordered_pair(sk4,X0),sk6) ),
inference(factoring,[status(thm)],[p2788]) ).
cnf(c19,plain,
( in(sk5,sk6)
| subset(unordered_pair(sk4,sk5),sk6) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p30,plain,
( in(sk5,sk6)
| in(X0,sk6)
| ~ in(X0,unordered_pair(sk4,sk5)) ),
inference(resolution,[status(thm)],[c11,c19]) ).
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]) ).
cnf(p37,plain,
in(X0,unordered_pair(X1,X0)),
inference(superposition,[status(thm)],[c1,p34]) ).
cnf(p83,plain,
( in(sk5,sk6)
| in(sk5,sk6) ),
inference(resolution,[status(thm)],[p30,p37]) ).
cnf(p85,plain,
in(sk5,sk6),
inference(factoring,[status(thm)],[p83]) ).
cnf(p3010,plain,
subset(unordered_pair(sk4,sk5),sk6),
inference(resolution,[status(thm)],[p3007,p85]) ).
cnf(c20,plain,
( ~ subset(unordered_pair(sk4,sk5),sk6)
| ~ in(sk5,sk6)
| ~ in(sk4,sk6) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p80,plain,
( ~ subset(unordered_pair(sk4,sk5),sk6)
| ~ in(sk5,sk6) ),
inference(resolution,[status(thm)],[p77,c20]) ).
cnf(p87,plain,
~ subset(unordered_pair(sk4,sk5),sk6),
inference(resolution,[status(thm)],[p85,p80]) ).
cnf(p3110,plain,
$false,
inference(resolution,[status(thm)],[p3010,p87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU159+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 12:59:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.55/3.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.55/3.86 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------