%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 : Tue Sep 29 12:45:03 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 3 unt; 0 def)
% Number of atoms : 118 ( 9 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 141 ( 53 ~; 55 |; 24 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 65 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f7,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> subset(X2,X1) )
=> subset(union(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> subset(X2,X1) )
=> subset(union(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
? [X0,X1] :
( ~ subset(union(X0),X1)
& ! [X2] :
( subset(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK1(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK1(X0,X1),sK2(X0,X1))
& in(sK2(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK3(X0,X5))
& in(sK3(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f17]) ).
fof(f21,plain,
( ~ subset(union(sK6),sK7)
& ! [X2] :
( subset(X2,sK7)
| ~ in(X2,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f12]) ).
fof(f23,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1,X5] :
( in(X5,sK3(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2] :
( ~ in(X2,sK6)
| subset(X2,sK7) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
~ subset(union(sK6),sK7),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X5] :
( in(X5,sK3(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f27]) ).
fof(f39,plain,
! [X0,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f26]) ).
fof(f51,plain,
! [X0] :
( subset(sK3(sK6,X0),sK7)
| ~ in(X0,union(sK6)) ),
inference(resolution,[],[f39,f35]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(X1,sK3(sK6,X0))
| ~ in(X0,union(sK6))
| in(X1,sK7) ),
inference(resolution,[],[f51,f23]) ).
fof(f60,plain,
! [X0] :
( ~ in(X0,union(sK6))
| in(X0,sK7)
| ~ in(X0,union(sK6)) ),
inference(resolution,[],[f54,f38]) ).
fof(f62,plain,
! [X0] :
( ~ in(X0,union(sK6))
| in(X0,sK7) ),
inference(duplicate_literal_removal,[],[f60]) ).
fof(f72,plain,
! [X0] :
( in(sK0(union(sK6),X0),sK7)
| subset(union(sK6),X0) ),
inference(resolution,[],[f62,f24]) ).
fof(f78,plain,
( subset(union(sK6),sK7)
| subset(union(sK6),sK7) ),
inference(resolution,[],[f72,f25]) ).
fof(f81,plain,
subset(union(sK6),sK7),
inference(duplicate_literal_removal,[],[f78]) ).
fof(f82,plain,
$false,
inference(forward_subsumption_resolution,[],[f81,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n006.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 03:15:25 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (3546829)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3546837)dis+10_1_sil=32000:sp=arity:random_seed=4132094988:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3546837) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3546829-3546837"...
% 0.17/0.47 % (3546837)...printing done.
% 0.17/0.47 % (3546835)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3546837)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3546837)------------------------------
% 0.17/0.47 % (3546837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3546837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3546837)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3546837)Termination reason: Refutation
% 0.17/0.47 % (3546837)Time elapsed: 0.002 s
% 0.17/0.47 % (3546837)Peak memory usage: 11 MB
% 0.17/0.47 % (3546837)Instructions burned: 3 (million)
% 0.17/0.47 % (3546829)Success in time 0.025 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------