%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n015.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 12:42:23 PM UTC 2026
% Result : Theorem 3.62s 1.45s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 111 ( 9 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 129 ( 48 ~; 48 |; 24 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 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 : 71 ( 60 !; 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] :
( ~ in(X3,X0)
| in(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
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,union(X0))
| in(X5,sK3(X0,X5)) ),
inference(equality_resolution,[],[f27]) ).
fof(f39,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK3(X0,X5),X0) ),
inference(equality_resolution,[],[f26]) ).
fof(f41,plain,
in(sK0(union(sK6),sK7),union(sK6)),
inference(resolution,[],[f24,f36]) ).
fof(f46,plain,
in(sK0(union(sK6),sK7),sK3(sK6,sK0(union(sK6),sK7))),
inference(resolution,[],[f38,f41]) ).
fof(f47,plain,
! [X0] :
( ~ subset(sK3(sK6,sK0(union(sK6),sK7)),X0)
| in(sK0(union(sK6),sK7),X0) ),
inference(resolution,[],[f46,f23]) ).
fof(f49,plain,
in(sK3(sK6,sK0(union(sK6),sK7)),sK6),
inference(resolution,[],[f39,f41]) ).
fof(f50,plain,
subset(sK3(sK6,sK0(union(sK6),sK7)),sK7),
inference(resolution,[],[f49,f35]) ).
fof(f235,plain,
in(sK0(union(sK6),sK7),sK7),
inference(resolution,[],[f47,f50]) ).
fof(f238,plain,
subset(union(sK6),sK7),
inference(resolution,[],[f235,f25]) ).
fof(f242,plain,
$false,
inference(forward_subsumption_resolution,[],[f238,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET941+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:19:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.62/1.45 % (2226253)Detected formulas, will run a generic FOF schedule.
% 3.62/1.45 % (2226262)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4022804985:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.45 % (2226262)Instruction limit reached!
% 3.62/1.45 % (2226262)------------------------------
% 3.62/1.45 % (2226262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.45 % (2226262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.45 % (2226262)CaDiCaL version: 2.1.3
% 3.62/1.45 % (2226262)Termination reason: Instruction limit
% 3.62/1.45 % (2226262)Termination phase: Saturation
% 3.62/1.45 % (2226262)Time elapsed: 0.029 s
% 3.62/1.45 % (2226262)Peak memory usage: 87 MB
% 3.62/1.45 % (2226262)Instructions burned: 122 (million)
% 3.62/1.45 % (2226258)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=1959469291:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.45 % (2226261)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=650577492:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.45 % (2226259)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=818558388:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.45 % (2226260)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=2176967649:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.45 % (2226261)Refutation not found, incomplete strategy
% 3.62/1.45 % (2226261)------------------------------
% 3.62/1.45 % (2226261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.45 % (2226261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.45 % (2226261)CaDiCaL version: 2.1.3
% 3.62/1.45 % (2226261)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.45 % (2226261)Time elapsed: 0.001 s
% 3.62/1.45 % (2226261)Peak memory usage: 88 MB
% 3.62/1.45 % (2226263)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2272428338:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.45 % (2226264)dis-21_1_sil=8000:lcm=predicate:random_seed=3197593339: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)
% 3.62/1.45 % (2226263)First to succeed.
% 3.62/1.45 % (2226263)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2226253"
% 3.62/1.45 % (2226264)Instruction limit reached!
% 3.62/1.45 % (2226264)------------------------------
% 3.62/1.45 % (2226264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.45 % (2226264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.45 % (2226264)CaDiCaL version: 2.1.3
% 3.62/1.45 % (2226264)Termination reason: Instruction limit
% 3.62/1.45 % (2226264)Termination phase: Saturation
% 3.62/1.45 % (2226264)Time elapsed: 0.076 s
% 3.62/1.45 % (2226264)Peak memory usage: 89 MB
% 3.62/1.45 % (2226264)Instructions burned: 129 (million)
% 3.62/1.45 % (2226266)lrs+10_1_sil=8000:sp=occurrence:random_seed=741477554:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.62/1.45 % (2226266)Also succeeded, but the first one will report.
% 3.62/1.45 % (2226261)------------------------------
% 3.62/1.45 % (2226261)------------------------------
% 3.62/1.45 % (2226273)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2891755421:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.62/1.45 % (2226263)Refutation found. Thanks to Tanya!
% 3.62/1.45 % SZS status Theorem for theBenchmark
% 3.62/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.45 % (2226263)------------------------------
% 3.62/1.45 % (2226263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.45 % (2226263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.45 % (2226263)CaDiCaL version: 2.1.3
% 3.62/1.45 % (2226263)Termination reason: Refutation
% 3.62/1.45 % (2226263)Time elapsed: 0.010 s
% 3.62/1.45 % (2226263)Peak memory usage: 89 MB
% 3.62/1.45 % (2226263)Instructions burned: 12 (million)
% 3.62/1.45 % (2226263)------------------------------
% 3.62/1.45 % (2226263)------------------------------
% 3.62/1.45 % (2226253)Success in time 0.432 s
% 3.62/1.45 % Vampire exiting
%------------------------------------------------------------------------------