%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU126+1 : 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 : n006.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 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 10 unt; 5 def)
% Number of atoms : 202 ( 23 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 222 ( 84 ~; 92 |; 33 &)
% ( 10 <=>; 3 =>; 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 : 80 ( 0 sgn 73 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f16,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f27,plain,
? [X0,X1] :
( set_union2(X0,X1) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f31,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f31]) ).
fof(f33,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,[],[f4]) ).
fof(f34,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,[],[f33]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK0(X0,X1,X2),X0)
& ~ in(sK0(X0,X1,X2),X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f35]) ).
fof(f37,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,[],[f24]) ).
fof(f38,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,[],[f37]) ).
fof(f39,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))],[f38]) ).
fof(f42,plain,
( sK5 != set_union2(sK4,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f48,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
sK5 != set_union2(sK4,sK5),
inference(cnf_transformation,[],[f42]) ).
fof(f73,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f49]) ).
fof(f74,plain,
! [X0,X1,X4] :
( ~ in(X4,set_union2(X0,X1))
| in(X4,X1)
| in(X4,X0) ),
inference(equality_resolution,[],[f48]) ).
fof(f75,definition,
! [X0,X1] :
( sQ6_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ6_eqProxy])],[equality_proxy_definition]) ).
fof(f77,plain,
! [X0,X1] :
( sQ6_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f47,f75]) ).
fof(f82,plain,
~ sQ6_eqProxy(sK5,set_union2(sK4,sK5)),
inference(equality_proxy_replacement,[],[f65,f75]) ).
fof(f113,plain,
! [X0] :
( ~ in(X0,sK4)
| in(X0,sK5) ),
inference(resolution,[],[f54,f64]) ).
fof(f117,plain,
( ~ subset(sK5,set_union2(sK4,sK5))
| ~ subset(set_union2(sK4,sK5),sK5) ),
inference(resolution,[],[f77,f82]) ).
fof(f120,definition,
( spl7_3
<=> subset(sK5,set_union2(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f121,plain,
( ~ subset(sK5,set_union2(sK4,sK5))
| spl7_3 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,definition,
( spl7_4
<=> subset(set_union2(sK4,sK5),sK5) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
fof(f124,plain,
( ~ subset(set_union2(sK4,sK5),sK5)
| spl7_4 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( ~ spl7_4
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f117,f120,f123]) ).
fof(f127,plain,
( ~ in(sK1(sK5,set_union2(sK4,sK5)),set_union2(sK4,sK5))
| spl7_3 ),
inference(resolution,[],[f121,f56]) ).
fof(f128,plain,
( in(sK1(sK5,set_union2(sK4,sK5)),sK5)
| spl7_3 ),
inference(resolution,[],[f121,f55]) ).
fof(f133,plain,
( ~ in(sK1(sK5,set_union2(sK4,sK5)),sK5)
| spl7_3 ),
inference(resolution,[],[f127,f73]) ).
fof(f135,plain,
( $false
| spl7_3 ),
inference(resolution,[],[f133,f128]) ).
fof(f136,plain,
spl7_3,
inference(avatar_contradiction_clause,[],[f135]) ).
fof(f137,plain,
( ~ in(sK1(set_union2(sK4,sK5),sK5),sK5)
| spl7_4 ),
inference(resolution,[],[f124,f56]) ).
fof(f138,plain,
( in(sK1(set_union2(sK4,sK5),sK5),set_union2(sK4,sK5))
| spl7_4 ),
inference(resolution,[],[f124,f55]) ).
fof(f143,plain,
( in(sK1(set_union2(sK4,sK5),sK5),sK5)
| in(sK1(set_union2(sK4,sK5),sK5),sK4)
| spl7_4 ),
inference(resolution,[],[f74,f138]) ).
fof(f145,definition,
( spl7_5
<=> in(sK1(set_union2(sK4,sK5),sK5),sK4) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f146,plain,
( in(sK1(set_union2(sK4,sK5),sK5),sK4)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,definition,
( spl7_6
<=> in(sK1(set_union2(sK4,sK5),sK5),sK5) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
fof(f149,plain,
( in(sK1(set_union2(sK4,sK5),sK5),sK5)
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f150,plain,
( spl7_5
| spl7_6
| spl7_4 ),
inference(avatar_split_clause,[],[f143,f123,f148,f145]) ).
fof(f151,plain,
( in(sK1(set_union2(sK4,sK5),sK5),sK5)
| ~ spl7_5 ),
inference(resolution,[],[f146,f113]) ).
fof(f154,plain,
( spl7_6
| ~ spl7_5 ),
inference(avatar_split_clause,[],[f151,f145,f148]) ).
fof(f155,plain,
( $false
| spl7_4
| ~ spl7_6 ),
inference(resolution,[],[f149,f137]) ).
fof(f158,plain,
( spl7_4
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f155]) ).
cnf(s4,plain,
( ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s5,plain,
spl7_3,
inference(sat_conversion,[],[f136]) ).
cnf(s6,plain,
( spl7_4
| spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f150]) ).
cnf(s7,plain,
( ~ spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s8,plain,
( spl7_4
| ~ spl7_6 ),
inference(sat_conversion,[],[f158]) ).
cnf(s9,plain,
~ spl7_4,
inference(rat,[],[s4,s5]) ).
cnf(s10,plain,
~ spl7_6,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
spl7_5,
inference(rat,[],[s6,s10,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s7,s10,s11]) ).
fof(f159,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU126+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:38:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.17/1.50 % (3553362)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (3553371)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2812719024:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (3553367)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=1233399987:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (3553369)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=2079687272:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (3553370)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2906267488:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (3553368)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=1989772900:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (3553370)Refutation not found, incomplete strategy
% 0.17/1.50 % (3553370)------------------------------
% 0.17/1.50 % (3553370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3553370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3553370)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3553370)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3553370)Time elapsed: 0.002 s
% 0.17/1.50 % (3553370)Peak memory usage: 88 MB
% 0.17/1.50 % (3553370)Instructions burned: 1 (million)
% 0.17/1.50 % (3553371)Instruction limit reached!
% 0.17/1.50 % (3553371)------------------------------
% 0.17/1.50 % (3553371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3553371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3553371)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3553371)Termination reason: Instruction limit
% 0.17/1.50 % (3553371)Termination phase: Saturation
% 0.17/1.50 % (3553371)Time elapsed: 0.037 s
% 0.17/1.50 % (3553371)Peak memory usage: 88 MB
% 0.17/1.50 % (3553371)Instructions burned: 121 (million)
% 0.17/1.50 % (3553372)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2840150696:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (3553373)dis-21_1_sil=8000:lcm=predicate:random_seed=2212401617: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)
% 0.17/1.50 % (3553373)First to succeed.
% 0.17/1.50 % (3553373)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3553362"
% 0.17/1.50 % (3553372)Also succeeded, but the first one will report.
% 0.17/1.50 % (3553379)lrs+10_1_sil=8000:sp=occurrence:random_seed=2099234988:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.17/1.50 % (3553379)Also succeeded, but the first one will report.
% 0.17/1.50 % (3553370)------------------------------
% 0.17/1.50 % (3553370)------------------------------
% 0.17/1.50 % (3553373)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3553373)------------------------------
% 0.17/1.50 % (3553373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3553373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3553373)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3553373)Termination reason: Refutation
% 0.17/1.50 % (3553373)Time elapsed: 0.004 s
% 0.17/1.50 % (3553373)Peak memory usage: 89 MB
% 0.17/1.50 % (3553373)Instructions burned: 4 (million)
% 0.17/1.50 % (3553373)------------------------------
% 0.17/1.50 % (3553373)------------------------------
% 0.17/1.50 % (3553362)Success in time 0.451 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------