%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU155+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:47:27 PM UTC 2026
% Result : Theorem 3.60s 1.49s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 97 ( 8 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 118 ( 45 ~; 42 |; 24 &)
% ( 4 <=>; 3 =>; 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 : 60 ( 49 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f14,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(f40,conjecture,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f91,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f101,plain,
? [X0,X1] :
( ~ subset(X0,union(X1))
& in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f147,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,[],[f91]) ).
fof(f148,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,[],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f148]) ).
fof(f154,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,[],[f14]) ).
fof(f155,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,[],[f154]) ).
fof(f156,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK7(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK7(X0,X1),X1) )
& ( ( in(sK7(X0,X1),sK8(X0,X1))
& in(sK8(X0,X1),X0) )
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK9(X0,X5))
& in(sK9(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f155]) ).
fof(f166,plain,
( ~ subset(sK11,union(sK12))
& in(sK11,sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f101]) ).
fof(f206,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f207,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f216,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X5,X6)
| ~ in(X6,X0)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f156]) ).
fof(f247,plain,
in(sK11,sK12),
inference(cnf_transformation,[],[f166]) ).
fof(f248,plain,
~ subset(sK11,union(sK12)),
inference(cnf_transformation,[],[f166]) ).
fof(f349,plain,
! [X0,X6,X5] :
( in(X5,union(X0))
| ~ in(X5,X6)
| ~ in(X6,X0) ),
inference(equality_resolution,[],[f216]) ).
fof(f477,plain,
in(sK5(sK11,union(sK12)),sK11),
inference(resolution,[],[f206,f248]) ).
fof(f483,plain,
~ in(sK5(sK11,union(sK12)),union(sK12)),
inference(resolution,[],[f207,f248]) ).
fof(f647,plain,
! [X0] :
( ~ in(sK5(sK11,union(sK12)),X0)
| ~ in(X0,sK12) ),
inference(resolution,[],[f349,f483]) ).
fof(f795,plain,
~ in(sK11,sK12),
inference(resolution,[],[f647,f477]) ).
fof(f813,plain,
$false,
inference(resolution,[],[f795,f247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU155+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:46:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.60/1.49 % (4127975)Detected formulas, will run a generic FOF schedule.
% 3.60/1.49 % (4127985)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1456997367:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.49 % (4127985)Instruction limit reached!
% 3.60/1.49 % (4127985)------------------------------
% 3.60/1.49 % (4127985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (4127985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (4127985)CaDiCaL version: 2.1.3
% 3.60/1.49 % (4127985)Termination reason: Instruction limit
% 3.60/1.49 % (4127985)Termination phase: Saturation
% 3.60/1.49 % (4127985)Time elapsed: 0.043 s
% 3.60/1.49 % (4127985)Peak memory usage: 89 MB
% 3.60/1.49 % (4127985)Instructions burned: 122 (million)
% 3.60/1.49 % (4127984)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=377260091:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.49 % (4127982)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=3673641602:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.49 % (4127983)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=4059800586:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.49 % (4127981)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=303537894:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.49 % (4127987)dis-21_1_sil=8000:lcm=predicate:random_seed=513492580: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)
% 3.60/1.49 % (4127987)First to succeed.
% 3.60/1.49 % (4127987)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4127975"
% 3.60/1.49 % (4127986)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3961061271:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.49 % (4127984)Instruction limit reached!
% 3.60/1.49 % (4127984)------------------------------
% 3.60/1.49 % (4127984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (4127984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (4127984)CaDiCaL version: 2.1.3
% 3.60/1.49 % (4127984)Termination reason: Instruction limit
% 3.60/1.49 % (4127984)Termination phase: Saturation
% 3.60/1.49 % (4127984)Time elapsed: 0.071 s
% 3.60/1.49 % (4127984)Peak memory usage: 89 MB
% 3.60/1.49 % (4127984)Instructions burned: 110 (million)
% 3.60/1.49 % (4127993)lrs+10_1_sil=8000:sp=occurrence:random_seed=3351273777:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.60/1.49 % (4127993)Also succeeded, but the first one will report.
% 3.60/1.49 % (4127986)Instruction limit reached!
% 3.60/1.49 % (4127986)------------------------------
% 3.60/1.49 % (4127986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (4127986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (4127986)CaDiCaL version: 2.1.3
% 3.60/1.49 % (4127986)Termination reason: Instruction limit
% 3.60/1.49 % (4127986)Termination phase: Saturation
% 3.60/1.49 % (4127986)Time elapsed: 0.099 s
% 3.60/1.49 % (4127986)Peak memory usage: 90 MB
% 3.60/1.49 % (4127986)Instructions burned: 139 (million)
% 3.60/1.49 % (4127996)lrs+10_1_sil=32000:urr=on:br=off:random_seed=948278324:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.60/1.49 % (4127996)Also succeeded, but the first one will report.
% 3.60/1.49 % (4127998)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2303580306:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.60/1.49 % (4127987)Refutation found. Thanks to Tanya!
% 3.60/1.49 % SZS status Theorem for theBenchmark
% 3.60/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.49 % (4127987)------------------------------
% 3.60/1.49 % (4127987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.49 % (4127987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.49 % (4127987)CaDiCaL version: 2.1.3
% 3.60/1.49 % (4127987)Termination reason: Refutation
% 3.60/1.49 % (4127987)Time elapsed: 0.011 s
% 3.60/1.49 % (4127987)Peak memory usage: 89 MB
% 3.60/1.49 % (4127987)Instructions burned: 15 (million)
% 3.60/1.49 % (4127987)------------------------------
% 3.60/1.49 % (4127987)------------------------------
% 3.60/1.49 % (4127975)Success in time 0.429 s
% 3.60/1.49 % Vampire exiting
%------------------------------------------------------------------------------