%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU146+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 : n014.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 2.87s 1.32s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 10 unt; 3 def)
% Number of atoms : 185 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 190 ( 75 ~; 91 |; 13 &)
% ( 8 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 1 sgn 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f14,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f15,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f16,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f17,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2)))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1,X2] :
( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2)))
| ~ subset(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( X0 = empty_set
| X0 = singleton(X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f27,plain,
? [X0,X1] :
( ( ( empty_set != X0
& singleton(X1) != X0 )
| ~ subset(X0,singleton(X1)) )
& ( X0 = empty_set
| X0 = singleton(X1)
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
( ( ( empty_set != sK0
& sK0 != singleton(sK1) )
| ~ subset(sK0,singleton(sK1)) )
& ( empty_set = sK0
| sK0 = singleton(sK1)
| subset(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
( empty_set = sK0
| sK0 = singleton(sK1)
| subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f53,definition,
( spl4_1
<=> subset(sK0,singleton(sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f54,plain,
( ~ subset(sK0,singleton(sK1))
| spl4_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( subset(sK0,singleton(sK1))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl4_2
<=> sK0 = singleton(sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f58,plain,
( sK0 != singleton(sK1)
| spl4_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( sK0 = singleton(sK1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl4_3
<=> empty_set = sK0 ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f62,plain,
( empty_set != sK0
| spl4_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( empty_set = sK0
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f40,f61,f57,f53]) ).
fof(f65,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f41,f57,f53]) ).
fof(f66,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f42,f61,f53]) ).
fof(f67,plain,
( ~ subset(sK0,sK0)
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f54,f59]) ).
fof(f68,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f45,f67]) ).
fof(f69,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f70,plain,
( ~ subset(empty_set,singleton(sK1))
| spl4_1
| ~ spl4_3 ),
inference(superposition,[],[f54,f63]) ).
fof(f72,plain,
( $false
| spl4_1
| ~ spl4_3 ),
inference(resolution,[],[f46,f70]) ).
fof(f73,plain,
( spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f83,plain,
( sK0 = singleton(sK1)
| ~ subset(singleton(sK1),sK0)
| ~ spl4_1 ),
inference(resolution,[],[f35,f55]) ).
fof(f85,plain,
( ~ subset(singleton(sK1),sK0)
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f83,f58]) ).
fof(f88,plain,
! [X2,X0,X1] :
( subset(X0,empty_set)
| in(X2,X0)
| ~ subset(X0,X1)
| ~ subset(X1,singleton(X2)) ),
inference(superposition,[],[f39,f48]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ~ subset(X2,singleton(X0))
| ~ subset(X1,X2)
| in(X0,X1)
| empty_set = X1 ),
inference(resolution,[],[f88,f49]) ).
fof(f93,plain,
( ! [X0] :
( ~ subset(X0,sK0)
| in(sK1,X0)
| empty_set = X0 )
| ~ spl4_1 ),
inference(resolution,[],[f89,f55]) ).
fof(f100,plain,
( in(sK1,sK0)
| empty_set = sK0
| ~ spl4_1 ),
inference(resolution,[],[f93,f45]) ).
fof(f102,plain,
( in(sK1,sK0)
| ~ spl4_1
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f100,f62]) ).
fof(f107,plain,
( subset(singleton(sK1),sK0)
| ~ spl4_1
| spl4_3 ),
inference(resolution,[],[f102,f38]) ).
fof(f109,plain,
( $false
| ~ spl4_1
| spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f107,f85]) ).
fof(f110,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( ~ spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f110]) ).
cnf(s7,plain,
spl4_1,
inference(rat,[],[s1,s4,s5]) ).
cnf(s8,plain,
~ spl4_3,
inference(rat,[],[s3,s7]) ).
cnf(s9,plain,
~ spl4_2,
inference(rat,[],[s2,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s8,s7,s9]) ).
fof(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n014.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 03:43:46 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 2.87/1.32 % (1412905)Detected formulas, will run a generic FOF schedule.
% 2.87/1.32 % (1412911)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=3203505031:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.87/1.32 % (1412916)dis-21_1_sil=8000:lcm=predicate:random_seed=4132939618: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)
% 2.87/1.32 % (1412910)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=1868832088:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.87/1.32 % (1412914)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1186160230:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.87/1.32 % (1412912)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=2511828378:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.87/1.32 % (1412913)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2332797205:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.87/1.32 % (1412914)Refutation not found, incomplete strategy
% 2.87/1.32 % (1412914)------------------------------
% 2.87/1.32 % (1412914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.32 % (1412914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.32 % (1412914)CaDiCaL version: 2.1.3
% 2.87/1.32 % (1412914)Termination reason: Refutation not found, incomplete strategy
% 2.87/1.32 % (1412914)Time elapsed: 0.002 s
% 2.87/1.32 % (1412914)Peak memory usage: 87 MB
% 2.87/1.32 % (1412914)Instructions burned: 1 (million)
% 2.87/1.32 % (1412913)Refutation not found, incomplete strategy
% 2.87/1.32 % (1412913)------------------------------
% 2.87/1.32 % (1412913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.32 % (1412913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.32 % (1412913)CaDiCaL version: 2.1.3
% 2.87/1.32 % (1412913)Termination reason: Refutation not found, incomplete strategy
% 2.87/1.32 % (1412913)Time elapsed: 0.002 s
% 2.87/1.32 % (1412913)Peak memory usage: 88 MB
% 2.87/1.32 % (1412915)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1100760859:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.87/1.32 % (1412915)First to succeed.
% 2.87/1.32 % (1412915)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1412905"
% 2.87/1.32 % (1412916)Instruction limit reached!
% 2.87/1.32 % (1412916)------------------------------
% 2.87/1.32 % (1412916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.32 % (1412916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.32 % (1412916)CaDiCaL version: 2.1.3
% 2.87/1.32 % (1412916)Termination reason: Instruction limit
% 2.87/1.32 % (1412916)Termination phase: Saturation
% 2.87/1.32 % (1412916)Time elapsed: 0.070 s
% 2.87/1.32 % (1412916)Peak memory usage: 88 MB
% 2.87/1.32 % (1412916)Instructions burned: 130 (million)
% 2.87/1.32 % (1412924)lrs+10_1_sil=8000:sp=occurrence:random_seed=1490575869:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.87/1.32 % (1412924)Also succeeded, but the first one will report.
% 2.87/1.32 % (1412913)------------------------------
% 2.87/1.32 % (1412913)------------------------------
% 2.87/1.32 % (1412914)------------------------------
% 2.87/1.32 % (1412914)------------------------------
% 2.87/1.32 % (1412915)Refutation found. Thanks to Tanya!
% 2.87/1.32 % SZS status Theorem for theBenchmark
% 2.87/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (1412915)------------------------------
% 0.18/1.51 % (1412915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1412915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1412915)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1412915)Termination reason: Refutation
% 0.18/1.51 % (1412915)Time elapsed: 0.005 s
% 0.18/1.51 % (1412915)Peak memory usage: 89 MB
% 0.18/1.51 % (1412915)Instructions burned: 4 (million)
% 0.18/1.51 % (1412915)------------------------------
% 0.18/1.51 % (1412915)------------------------------
% 0.18/1.51 % (1412905)Success in time 0.434 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------