%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET884+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:42:14 PM UTC 2026
% Result : Theorem 2.56s 1.32s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 11 unt; 1 def)
% Number of atoms : 151 ( 82 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 190 ( 76 ~; 68 |; 37 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 72 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X1
& X0 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X1
& X0 != X2 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X1
& X0 != X2 ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X1 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X1
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f21]) ).
fof(f25,plain,
( subset(singleton(sK4),unordered_pair(sK5,sK6))
& sK4 != sK5
& sK4 != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f15]) ).
fof(f29,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f42,plain,
sK4 != sK6,
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
subset(singleton(sK4),unordered_pair(sK5,sK6)),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f29]) ).
fof(f46,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f45]) ).
fof(f52,plain,
! [X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
fof(f53,definition,
! [X0,X1] :
( sQ7_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ7_eqProxy])],[equality_proxy_definition]) ).
fof(f61,plain,
! [X0,X1,X4] :
( sQ7_eqProxy(X1,X4)
| sQ7_eqProxy(X0,X4)
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_proxy_replacement,[],[f52,f53,f53]) ).
fof(f62,plain,
~ sQ7_eqProxy(sK4,sK5),
inference(equality_proxy_replacement,[],[f43,f53]) ).
fof(f63,plain,
~ sQ7_eqProxy(sK4,sK6),
inference(equality_proxy_replacement,[],[f42,f53]) ).
fof(f65,plain,
! [X0,X1] :
( sQ7_eqProxy(X1,X0)
| ~ sQ7_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f53]) ).
fof(f67,plain,
~ sQ7_eqProxy(sK5,sK4),
inference(resolution,[],[f65,f62]) ).
fof(f68,plain,
~ sQ7_eqProxy(sK6,sK4),
inference(resolution,[],[f65,f63]) ).
fof(f75,plain,
! [X0] :
( in(X0,unordered_pair(sK5,sK6))
| ~ in(X0,singleton(sK4)) ),
inference(resolution,[],[f38,f44]) ).
fof(f80,plain,
! [X0] :
( sQ7_eqProxy(X0,sK4)
| ~ in(sK4,unordered_pair(X0,sK6)) ),
inference(resolution,[],[f61,f68]) ).
fof(f121,plain,
~ in(sK4,unordered_pair(sK5,sK6)),
inference(resolution,[],[f80,f67]) ).
fof(f127,plain,
~ in(sK4,singleton(sK4)),
inference(resolution,[],[f121,f75]) ).
fof(f131,plain,
$false,
inference(resolution,[],[f127,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET884+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:08:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.56/1.32 % (1145414)Detected formulas, will run a generic FOF schedule.
% 2.56/1.32 % (1145496)dis-21_1_sil=8000:lcm=predicate:random_seed=842429161:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.56/1.32 % (1145496)First to succeed.
% 2.56/1.32 % (1145496)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1145414"
% 2.56/1.32 % (1145493)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2423434022:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.32 % (1145492)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2804337503:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.32 % (1145493)Also succeeded, but the first one will report.
% 2.56/1.32 % (1145491)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3232873187:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.32 % (1145490)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2422439966:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.32 % (1145494)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1418228875:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.32 % (1145495)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2428265983:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.32 % (1145495)Also succeeded, but the first one will report.
% 2.56/1.32 % (1145494)Also succeeded, but the first one will report.
% 2.56/1.32 % (1145496)Refutation found. Thanks to Tanya!
% 2.56/1.32 % SZS status Theorem for theBenchmark
% 2.56/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.32 % (1145496)------------------------------
% 2.56/1.32 % (1145496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.32 % (1145496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.32 % (1145496)CaDiCaL version: 2.1.3
% 2.56/1.32 % (1145496)Termination reason: Refutation
% 2.56/1.32 % (1145496)Time elapsed: 0.002 s
% 2.56/1.32 % (1145496)Peak memory usage: 88 MB
% 2.56/1.32 % (1145496)Instructions burned: 4 (million)
% 2.56/1.32 % (1145496)------------------------------
% 2.56/1.32 % (1145496)------------------------------
% 2.56/1.32 % (1145414)Success in time 0.267 s
% 2.56/1.32 % Vampire exiting
%------------------------------------------------------------------------------