%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU787_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:50:59 PM UTC 2026
% Result : Theorem 2.64s 1.31s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 395 ( 23 equ)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 234 ( 71 ~; 79 |; 24 &)
% ( 4 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 206 ( 186 fml; 20 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 71 ( 0 sgn 59 !; 12 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_9,type,
sK5: $o ).
tff(pred_def_4,type,
sP6: $o > $o ).
tff(pred_def_5,type,
sP7: $o > $o ).
tff(f1,axiom,
( breln1unionE
= ( ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ( in(kpair(X3,X4),X1)
| in(kpair(X3,X4),X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionE) ).
tff(f2,conjecture,
( breln1unionE
=> ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ! [X5: $o] :
( ( in(kpair(X3,X4),X1)
=> (X5) )
=> ( ( in(kpair(X3,X4),X2)
=> (X5) )
=> (X5) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionEcases) ).
tff(f3,negated_conjecture,
~ ( breln1unionE
=> ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ! [X5: $o] :
( ( in(kpair(X3,X4),X1)
=> (X5) )
=> ( ( in(kpair(X3,X4),X2)
=> (X5) )
=> (X5) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( breln1unionE
<=> ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ( in(kpair(X3,X4),X1)
| in(kpair(X3,X4),X2) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
tff(f5,plain,
~ ( breln1unionE
=> ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ! [X5: $o] :
( ( in(kpair(X3,X4),X1)
=> (X5) )
=> ( ( in(kpair(X3,X4),X2)
=> (X5) )
=> (X5) ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f6,plain,
~ ( breln1unionE
=> ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ! [X5: $o] :
( ( in(kpair(X3,X4),X1)
=> ( $true = (X5) ) )
=> ( ( in(kpair(X3,X4),X2)
=> ( $true = (X5) ) )
=> ( $true = (X5) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( breln1unionE
=> ! [X0: $i,X1: $i] :
( breln1(X0,X1)
=> ! [X2: $i] :
( breln1(X0,X2)
=> ! [X3: $i] :
( in(X3,X0)
=> ! [X4: $i] :
( in(X4,X0)
=> ( in(kpair(X3,X4),binunion(X1,X2))
=> ( in(kpair(X3,X4),X1)
| in(kpair(X3,X4),X2) ) ) ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
tff(f8,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != (X5) )
& ( ( $true = (X5) )
| ~ in(kpair(X3,X4),X2) )
& ( ( $true = (X5) )
| ~ in(kpair(X3,X4),X1) ) )
& in(kpair(X3,X4),binunion(X1,X2))
& in(X4,X0) )
& in(X3,X0) )
& breln1(X0,X2) )
& breln1(X0,X1) )
& breln1unionE ),
inference(ennf_transformation,[],[f6]) ).
tff(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != (X5) )
& ( ( $true = (X5) )
| ~ in(kpair(X3,X4),X2) )
& ( ( $true = (X5) )
| ~ in(kpair(X3,X4),X1) ) )
& in(kpair(X3,X4),binunion(X1,X2))
& in(X4,X0) )
& in(X3,X0) )
& breln1(X0,X2) )
& breln1(X0,X1) )
& breln1unionE ),
inference(flattening,[],[f8]) ).
tff(f10,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( in(kpair(X3,X4),X1)
| in(kpair(X3,X4),X2)
| ~ in(kpair(X3,X4),binunion(X1,X2))
| ~ in(X4,X0) )
| ~ in(X3,X0) )
| ~ breln1(X0,X2) )
| ~ breln1(X0,X1) )
| ~ breln1unionE ),
inference(ennf_transformation,[],[f7]) ).
tff(f11,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( in(kpair(X3,X4),X1)
| in(kpair(X3,X4),X2)
| ~ in(kpair(X3,X4),binunion(X1,X2))
| ~ in(X4,X0) )
| ~ in(X3,X0) )
| ~ breln1(X0,X2) )
| ~ breln1(X0,X1) )
| ~ breln1unionE ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
( ( $true != sK5 )
& ( ( $true = sK5 )
| ~ in(kpair(sK3,sK4),sK2) )
& ( ( $true = sK5 )
| ~ in(kpair(sK3,sK4),sK1) )
& in(kpair(sK3,sK4),binunion(sK1,sK2))
& in(sK4,sK0)
& in(sK3,sK0)
& breln1(sK0,sK2)
& breln1(sK0,sK1)
& breln1unionE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f9]) ).
tff(f13,plain,
breln1unionE,
inference(cnf_transformation,[],[f12]) ).
tff(f14,plain,
breln1(sK0,sK1),
inference(cnf_transformation,[],[f12]) ).
tff(f15,plain,
breln1(sK0,sK2),
inference(cnf_transformation,[],[f12]) ).
tff(f16,plain,
in(sK3,sK0),
inference(cnf_transformation,[],[f12]) ).
tff(f17,plain,
in(sK4,sK0),
inference(cnf_transformation,[],[f12]) ).
tff(f18,plain,
in(kpair(sK3,sK4),binunion(sK1,sK2)),
inference(cnf_transformation,[],[f12]) ).
tff(f19,plain,
( ( $true = sK5 )
| ~ in(kpair(sK3,sK4),sK1) ),
inference(cnf_transformation,[],[f12]) ).
tff(f20,plain,
( ( $true = sK5 )
| ~ in(kpair(sK3,sK4),sK2) ),
inference(cnf_transformation,[],[f12]) ).
tff(f21,plain,
$true != sK5,
inference(cnf_transformation,[],[f12]) ).
tff(f22,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ~ in(kpair(X3,X4),binunion(X1,X2))
| in(kpair(X3,X4),X2)
| in(kpair(X3,X4),X1)
| ~ in(X4,X0)
| ~ in(X3,X0)
| ~ breln1(X0,X2)
| ~ breln1(X0,X1)
| ~ breln1unionE ),
inference(cnf_transformation,[],[f11]) ).
tff(f24,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f27,definition,
~ sP7($true),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
tff(f28,plain,
sP7(sK5),
inference(inequality_splitting,[],[f21,f27]) ).
tff(f30,definition,
( spl8_1
<=> in(kpair(sK3,sK4),sK1) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
tff(f32,plain,
( ~ in(kpair(sK3,sK4),sK1)
| spl8_1 ),
inference(avatar_component_clause,[],[f30]) ).
tff(f34,definition,
( spl8_2
<=> ( $true = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
tff(f36,plain,
( ( $true = sK5 )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f19,f34,f30]) ).
tff(f39,definition,
( spl8_3
<=> in(kpair(sK3,sK4),sK2) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
tff(f41,plain,
( ~ in(kpair(sK3,sK4),sK2)
| spl8_3 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
( ~ spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f20,f34,f39]) ).
tff(f44,plain,
( sP7($true)
| ( sK5 = $false ) ),
inference(superposition,[],[f28,f24]) ).
tff(f45,plain,
sK5 = $false,
inference(forward_subsumption_resolution,[],[f44,f27]) ).
tff(f49,plain,
! [X0: $i] :
( in(kpair(sK3,sK4),sK2)
| in(kpair(sK3,sK4),sK1)
| ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ breln1(X0,sK2)
| ~ breln1(X0,sK1)
| ~ breln1unionE ),
inference(resolution,[],[f18,f22]) ).
tff(f50,plain,
( ! [X0: $i] :
( in(kpair(sK3,sK4),sK1)
| ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ breln1(X0,sK2)
| ~ breln1(X0,sK1)
| ~ breln1unionE )
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f49,f41]) ).
tff(f51,plain,
( ! [X0: $i] :
( ~ in(sK4,X0)
| ~ in(sK3,X0)
| ~ breln1(X0,sK2)
| ~ breln1(X0,sK1)
| ~ breln1unionE )
| spl8_1
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f50,f32]) ).
tff(f52,plain,
( ! [X0: $i] :
( ~ breln1(X0,sK2)
| ~ in(sK3,X0)
| ~ in(sK4,X0)
| ~ breln1(X0,sK1) )
| spl8_1
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f51,f13]) ).
tff(f56,plain,
( ~ in(sK3,sK0)
| ~ in(sK4,sK0)
| ~ breln1(sK0,sK1)
| spl8_1
| spl8_3 ),
inference(resolution,[],[f52,f15]) ).
tff(f57,plain,
( ~ in(sK4,sK0)
| ~ breln1(sK0,sK1)
| spl8_1
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f56,f16]) ).
tff(f58,plain,
( ~ breln1(sK0,sK1)
| spl8_1
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f57,f17]) ).
tff(f59,plain,
( $false
| spl8_1
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f58,f14]) ).
tff(f60,plain,
( spl8_1
| spl8_3 ),
inference(avatar_contradiction_clause,[],[f59]) ).
tff(f61,plain,
( ( $true = $false )
| ~ spl8_2 ),
inference(forward_demodulation,[],[f36,f45]) ).
tff(f62,plain,
( $false
| ~ spl8_2 ),
inference(trivial_inequality_removal,[],[f61]) ).
tff(f63,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f62]) ).
cnf(s1,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
( spl8_2
| ~ spl8_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
~ spl8_2,
inference(sat_conversion,[],[f63]) ).
cnf(s5,plain,
~ spl8_3,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
spl8_1,
inference(rat,[],[s3,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s4,s6]) ).
tff(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU787_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 05:58:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.64/1.31 % (3581635)Detected formulas, will run a generic FOF schedule.
% 2.64/1.31 % (3581683)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2314847777:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.31 % (3581683)First to succeed.
% 2.64/1.31 % (3581683)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3581635"
% 2.64/1.31 % (3581682)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=3095789464:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.31 % (3581684)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=755306701:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.31 % (3581681)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=1107992787:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.31 % (3581684)Also succeeded, but the first one will report.
% 2.64/1.31 % (3581680)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=1598810922:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.31 % (3581686)dis-21_1_sil=8000:lcm=predicate:random_seed=1488197181: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)
% 2.64/1.31 % (3581685)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2292082993:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.31 % (3581685)Also succeeded, but the first one will report.
% 2.64/1.31 % (3581686)Also succeeded, but the first one will report.
% 2.64/1.31 % (3581683)Refutation found. Thanks to Tanya!
% 2.64/1.31 % SZS status Theorem for theBenchmark
% 2.64/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.31 % (3581683)------------------------------
% 2.64/1.31 % (3581683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.31 % (3581683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.31 % (3581683)CaDiCaL version: 2.1.3
% 2.64/1.31 % (3581683)Termination reason: Refutation
% 2.64/1.31 % (3581683)Time elapsed: 0.002 s
% 2.64/1.31 % (3581683)Peak memory usage: 90 MB
% 2.64/1.31 % (3581683)Instructions burned: 3 (million)
% 2.64/1.31 % (3581683)------------------------------
% 2.64/1.31 % (3581683)------------------------------
% 2.64/1.31 % (3581635)Success in time 0.283 s
% 2.64/1.31 % Vampire exiting
%------------------------------------------------------------------------------