%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:47:24 PM UTC 2026
% Result : Theorem 3.63s 1.48s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 5 unt; 2 def)
% Number of atoms : 145 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 154 ( 59 ~; 68 |; 17 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,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,[],[f2]) ).
fof(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,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,[],[f10]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f19,plain,
( ( ~ in(sK2,sK3)
| ~ subset(singleton(sK2),sK3) )
& ( in(sK2,sK3)
| subset(singleton(sK2),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f18]) ).
fof(f21,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
( in(sK2,sK3)
| subset(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
( ~ in(sK2,sK3)
| ~ subset(singleton(sK2),sK3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f22]) ).
fof(f32,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f31]) ).
fof(f33,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f21]) ).
fof(f35,definition,
( spl4_1
<=> subset(singleton(sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f36,plain,
( ~ subset(singleton(sK2),sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f37,plain,
( subset(singleton(sK2),sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f39,definition,
( spl4_2
<=> in(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f40,plain,
( ~ in(sK2,sK3)
| spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( in(sK2,sK3)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f28,f39,f35]) ).
fof(f43,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f29,f39,f35]) ).
fof(f48,plain,
( in(sK1(singleton(sK2),sK3),singleton(sK2))
| spl4_1 ),
inference(resolution,[],[f26,f36]) ).
fof(f49,plain,
( sK2 = sK1(singleton(sK2),sK3)
| spl4_1 ),
inference(resolution,[],[f48,f33]) ).
fof(f52,plain,
( ~ in(sK2,sK3)
| subset(singleton(sK2),sK3)
| spl4_1 ),
inference(superposition,[],[f27,f49]) ).
fof(f53,plain,
( subset(singleton(sK2),sK3)
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f52,f41]) ).
fof(f54,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f53,f36]) ).
fof(f55,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ subset(singleton(X0),X1)
| in(X0,X1) ),
inference(resolution,[],[f25,f32]) ).
fof(f60,plain,
( in(sK2,sK3)
| ~ spl4_1 ),
inference(resolution,[],[f56,f37]) ).
fof(f63,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f60,f40]) ).
fof(f64,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f63]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f65,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:43:30 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.48 % (2997882)Detected formulas, will run a generic FOF schedule.
% 3.63/1.48 % (2997891)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=337735058:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.48 % (2997891)Instruction limit reached!
% 3.63/1.48 % (2997891)------------------------------
% 3.63/1.48 % (2997891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2997891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2997891)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2997891)Termination reason: Instruction limit
% 3.63/1.48 % (2997891)Termination phase: Saturation
% 3.63/1.48 % (2997891)Time elapsed: 0.029 s
% 3.63/1.48 % (2997891)Peak memory usage: 88 MB
% 3.63/1.48 % (2997891)Instructions burned: 120 (million)
% 3.63/1.48 % (2997888)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=3188145802:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.48 % (2997890)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3640024896:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.48 % (2997889)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=931469546:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.48 % (2997887)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=1181399545:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.48 % (2997890)Refutation not found, incomplete strategy
% 3.63/1.48 % (2997890)------------------------------
% 3.63/1.48 % (2997890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2997890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2997890)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2997890)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.48 % (2997890)Time elapsed: 0.001 s
% 3.63/1.48 % (2997890)Peak memory usage: 88 MB
% 3.63/1.48 % (2997893)dis-21_1_sil=8000:lcm=predicate:random_seed=2512792118: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)
% 3.63/1.48 % (2997892)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4253490379:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.48 % (2997892)First to succeed.
% 3.63/1.48 % (2997892)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2997882"
% 3.63/1.48 % (2997893)Instruction limit reached!
% 3.63/1.48 % (2997893)------------------------------
% 3.63/1.48 % (2997893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2997893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2997893)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2997893)Termination reason: Instruction limit
% 3.63/1.48 % (2997893)Termination phase: Saturation
% 3.63/1.48 % (2997893)Time elapsed: 0.078 s
% 3.63/1.48 % (2997893)Peak memory usage: 89 MB
% 3.63/1.48 % (2997893)Instructions burned: 130 (million)
% 3.63/1.48 % (2997895)lrs+10_1_sil=8000:sp=occurrence:random_seed=1837098500:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.63/1.48 % (2997895)Also succeeded, but the first one will report.
% 3.63/1.48 % (2997890)------------------------------
% 3.63/1.48 % (2997890)------------------------------
% 3.63/1.48 % (2997902)lrs+10_1_sil=32000:urr=on:br=off:random_seed=749014738:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.63/1.48 % (2997892)Refutation found. Thanks to Tanya!
% 3.63/1.48 % SZS status Theorem for theBenchmark
% 3.63/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.48 % (2997892)------------------------------
% 3.63/1.48 % (2997892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (2997892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (2997892)CaDiCaL version: 2.1.3
% 3.63/1.48 % (2997892)Termination reason: Refutation
% 3.63/1.48 % (2997892)Time elapsed: 0.004 s
% 3.63/1.48 % (2997892)Peak memory usage: 90 MB
% 3.63/1.48 % (2997892)Instructions burned: 2 (million)
% 3.63/1.48 % (2997892)------------------------------
% 3.63/1.48 % (2997892)------------------------------
% 3.63/1.48 % (2997882)Success in time 0.429 s
% 3.63/1.48 % Vampire exiting
%------------------------------------------------------------------------------