%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM386+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 : n019.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 02:19:56 PM UTC 2026
% Result : Theorem 52.05s 8.11s
% Output : Proof 52.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 142 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 147 ( 51 ~; 64 |; 26 &)
% ( 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 : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 73 ( 5 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f5_nnf,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f4,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p81,plain,
set_union2(X0,singleton(X0)) = succ(X0),
inference(superposition,[status(thm)],[c7,c6]) ).
fof(f7,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7_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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_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_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c14,plain,
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p108,plain,
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(p286,plain,
( in(X0,singleton(X1))
| in(X0,X1)
| ~ in(X0,succ(X1)) ),
inference(superposition,[status(thm)],[p81,p108]) ).
fof(f27,conjecture,
! [A,B] :
( in(A,succ(B))
<=> ( A = B
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f27_neg,negated_conjecture,
~ ! [A,B] :
( in(A,succ(B))
<=> ( A = B
| in(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A,B] :
( ( ( A = B
| in(A,B) )
& ~ in(A,succ(B)) )
| ( A != B
& ~ in(A,B)
& in(A,succ(B)) ) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
( ( ( sk13 = sk14
| in(sk13,sk14) )
& ~ in(sk13,succ(sk14)) )
| ( sk13 != sk14
& ~ in(sk13,sk14)
& in(sk13,succ(sk14)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f27_nnf]) ).
cnf(c58,plain,
( sk13 = sk14
| in(sk13,sk14)
| in(sk13,succ(sk14)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p2947,plain,
( sk13 = sk14
| in(sk13,sk14)
| in(sk13,singleton(sk14))
| in(sk13,sk14) ),
inference(resolution,[status(thm)],[p286,c58]) ).
cnf(p3001,plain,
( sk13 = sk14
| in(sk13,singleton(sk14))
| in(sk13,sk14) ),
inference(factoring,[status(thm)],[p2947]) ).
fof(f6,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6_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)],[f6]) ).
fof(f6_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])],[f6_nnf]) ).
cnf(c8,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p83,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(p3004,plain,
( sk13 = sk14
| sk13 = sk14
| in(sk13,sk14) ),
inference(resolution,[status(thm)],[p3001,p83]) ).
cnf(p3011,plain,
( sk13 = sk14
| in(sk13,sk14) ),
inference(factoring,[status(thm)],[p3004]) ).
cnf(c15,plain,
( ~ in(X3,X0)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p113,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c15]) ).
cnf(p3016,plain,
( in(sk13,set_union2(sk14,X0))
| sk13 = sk14 ),
inference(resolution,[status(thm)],[p3011,p113]) ).
cnf(p3196,plain,
( in(sk13,succ(sk14))
| sk13 = sk14 ),
inference(superposition,[status(thm)],[p81,p3016]) ).
cnf(c59,plain,
( ~ in(sk13,succ(sk14))
| ~ in(sk13,sk14) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p3013,plain,
( ~ in(sk13,succ(sk14))
| sk13 = sk14 ),
inference(resolution,[status(thm)],[p3011,c59]) ).
cnf(p3212,plain,
( sk13 = sk14
| sk13 = sk14 ),
inference(resolution,[status(thm)],[p3196,p3013]) ).
cnf(p3213,plain,
sk13 = sk14,
inference(factoring,[status(thm)],[p3212]) ).
cnf(c9,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p85,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(p3300,plain,
in(sk13,singleton(sk14)),
inference(resolution,[status(thm)],[p3213,p85]) ).
cnf(p114,plain,
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(p3309,plain,
in(sk13,set_union2(X0,singleton(sk14))),
inference(resolution,[status(thm)],[p3300,p114]) ).
cnf(p3603,plain,
in(sk13,succ(sk14)),
inference(superposition,[status(thm)],[p81,p3309]) ).
cnf(c61,plain,
( ~ in(sk13,succ(sk14))
| sk13 != sk14 ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p3299,plain,
~ in(sk13,succ(sk14)),
inference(resolution,[status(thm)],[p3213,c61]) ).
cnf(p3619,plain,
$false,
inference(resolution,[status(thm)],[p3603,p3299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 03:49:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 52.05/8.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.05/8.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------