%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU126+2 : 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 : n016.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 12:47:19 PM UTC 2026
% Result : Theorem 3.32s 1.16s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 15 unt; 5 def)
% Number of atoms : 194 ( 22 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 212 ( 81 ~; 83 |; 34 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 85 ( 1 sgn 78 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f20,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f22,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f37,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f20]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f45,plain,
? [X0,X1] :
( set_union2(X0,X1) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f57,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f63]) ).
fof(f65,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,[],[f41]) ).
fof(f66,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,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f66]) ).
fof(f75,plain,
( sK7 != set_union2(sK6,sK7)
& subset(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f45]) ).
fof(f83,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f87,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f93,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f94,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f37]) ).
fof(f112,plain,
subset(sK6,sK7),
inference(cnf_transformation,[],[f75]) ).
fof(f113,plain,
sK7 != set_union2(sK6,sK7),
inference(cnf_transformation,[],[f75]) ).
fof(f127,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f132,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f87]) ).
fof(f137,definition,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ10_eqProxy])],[equality_proxy_definition]) ).
fof(f140,plain,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f83,f137]) ).
fof(f152,plain,
~ sQ10_eqProxy(sK7,set_union2(sK6,sK7)),
inference(equality_proxy_replacement,[],[f113,f137]) ).
fof(f223,plain,
( ~ subset(sK7,set_union2(sK6,sK7))
| ~ subset(set_union2(sK6,sK7),sK7) ),
inference(resolution,[],[f140,f152]) ).
fof(f227,definition,
( spl11_5
<=> subset(sK7,set_union2(sK6,sK7)) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f228,plain,
( ~ subset(sK7,set_union2(sK6,sK7))
| spl11_5 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,definition,
( spl11_6
<=> subset(set_union2(sK6,sK7),sK7) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f231,plain,
( ~ subset(set_union2(sK6,sK7),sK7)
| spl11_6 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,plain,
( ~ spl11_6
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f223,f227,f230]) ).
fof(f235,plain,
( ~ in(sK2(sK7,set_union2(sK6,sK7)),set_union2(sK6,sK7))
| spl11_5 ),
inference(resolution,[],[f228,f94]) ).
fof(f236,plain,
( in(sK2(sK7,set_union2(sK6,sK7)),sK7)
| spl11_5 ),
inference(resolution,[],[f228,f93]) ).
fof(f248,plain,
( ~ in(sK2(sK7,set_union2(sK6,sK7)),sK7)
| spl11_5 ),
inference(resolution,[],[f235,f132]) ).
fof(f255,plain,
( $false
| spl11_5 ),
inference(resolution,[],[f248,f236]) ).
fof(f256,plain,
spl11_5,
inference(avatar_contradiction_clause,[],[f255]) ).
fof(f488,plain,
( ~ subset(sK6,sK7)
| ~ subset(sK7,sK7)
| spl11_6 ),
inference(resolution,[],[f127,f231]) ).
fof(f509,definition,
( spl11_15
<=> subset(sK7,sK7) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
fof(f510,plain,
( ~ subset(sK7,sK7)
| spl11_15 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f512,definition,
( spl11_16
<=> subset(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
fof(f513,plain,
( ~ subset(sK6,sK7)
| spl11_16 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f514,plain,
( ~ spl11_15
| ~ spl11_16
| spl11_6 ),
inference(avatar_split_clause,[],[f488,f230,f512,f509]) ).
fof(f543,plain,
( $false
| spl11_15 ),
inference(resolution,[],[f510,f110]) ).
fof(f547,plain,
spl11_15,
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f548,plain,
( $false
| spl11_16 ),
inference(resolution,[],[f513,f112]) ).
fof(f552,plain,
spl11_16,
inference(avatar_contradiction_clause,[],[f548]) ).
cnf(s6,plain,
( ~ spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f233]) ).
cnf(s7,plain,
spl11_5,
inference(sat_conversion,[],[f256]) ).
cnf(s14,plain,
( spl11_6
| ~ spl11_15
| ~ spl11_16 ),
inference(sat_conversion,[],[f514]) ).
cnf(s19,plain,
spl11_15,
inference(sat_conversion,[],[f547]) ).
cnf(s20,plain,
spl11_16,
inference(sat_conversion,[],[f552]) ).
cnf(s21,plain,
spl11_6,
inference(rat,[],[s14,s20,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s6,s21,s7]) ).
fof(f553,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU126+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.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 03:43:18 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.32/1.16 % (3236651)Detected formulas, will run a generic FOF schedule.
% 3.32/1.16 % (3236656)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=3885486452:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.32/1.16 % (3236662)dis-21_1_sil=8000:lcm=predicate:random_seed=2182560340: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)
% 3.32/1.16 % (3236660)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1988114602:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.32/1.16 % (3236659)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3305896799:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.32/1.16 % (3236657)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=1667411404:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.32/1.16 % (3236658)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=2680149527:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.32/1.16 % (3236661)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1428645365:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.32/1.16 % (3236662)First to succeed.
% 3.32/1.16 % (3236662)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3236651"
% 3.32/1.16 % (3236661)Also succeeded, but the first one will report.
% 3.32/1.16 % (3236659)Also succeeded, but the first one will report.
% 3.32/1.16 % (3236660)Instruction limit reached!
% 3.32/1.16 % (3236660)------------------------------
% 3.32/1.16 % (3236660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.16 % (3236660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.16 % (3236660)CaDiCaL version: 2.1.3
% 3.32/1.16 % (3236660)Termination reason: Instruction limit
% 3.32/1.16 % (3236660)Termination phase: Saturation
% 3.32/1.16 % (3236660)Time elapsed: 0.072 s
% 3.32/1.16 % (3236660)Peak memory usage: 88 MB
% 3.32/1.16 % (3236660)Instructions burned: 119 (million)
% 3.32/1.16 % (3236670)lrs+10_1_sil=8000:sp=occurrence:random_seed=1494389726:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.32/1.16 % (3236662)Refutation found. Thanks to Tanya!
% 3.32/1.16 % SZS status Theorem for theBenchmark
% 3.32/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/1.16 % (3236662)------------------------------
% 3.32/1.16 % (3236662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.16 % (3236662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.16 % (3236662)CaDiCaL version: 2.1.3
% 3.32/1.16 % (3236662)Termination reason: Refutation
% 3.32/1.16 % (3236662)Time elapsed: 0.009 s
% 3.32/1.16 % (3236662)Peak memory usage: 89 MB
% 3.32/1.16 % (3236662)Instructions burned: 11 (million)
% 3.32/1.16 % (3236662)------------------------------
% 3.32/1.16 % (3236662)------------------------------
% 3.32/1.16 % (3236651)Success in time 0.43 s
% 3.32/1.16 % Vampire exiting
%------------------------------------------------------------------------------