%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU506_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 : n002.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 12:49:22 PM UTC 2026
% Result : Theorem 3.47s 1.46s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 193 ( 30 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 144 ( 51 ~; 41 |; 17 &)
% ( 7 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 57 ( 49 fml; 8 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 63 ( 0 sgn 55 !; 8 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
tff(f2,axiom,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> ( ! [X2: $i] :
( in(X2,X1)
=> in(X2,X0) )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
tff(f3,conjecture,
( emptysetE
=> ( setext
=> ! [X0: $i] :
( ! [X1: $i] : ~ in(X1,X0)
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
tff(f4,negated_conjecture,
~ ( emptysetE
=> ( setext
=> ! [X0: $i] :
( ! [X1: $i] : ~ in(X1,X0)
=> ( X0 = emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,plain,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
inference(rectify,[],[f1]) ).
tff(f6,plain,
( emptysetE
<=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f5]) ).
tff(f7,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> ( ! [X3: $i] :
( in(X3,X1)
=> in(X3,X0) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f2]) ).
tff(f8,plain,
( setext
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> ( ! [X3: $i] :
( in(X3,X1)
=> in(X3,X0) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
tff(f9,plain,
( setext
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> ( ! [X3: $i] :
( in(X3,X1)
=> in(X3,X0) )
=> ( X0 = X1 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
tff(f10,plain,
( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
tff(f11,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = (X1) )
| ~ in(X0,emptyset) )
| ~ emptysetE ),
inference(ennf_transformation,[],[f10]) ).
tff(f12,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ? [X3: $i] :
( ~ in(X3,X0)
& in(X3,X1) )
| ? [X2: $i] :
( ~ in(X2,X1)
& in(X2,X0) ) )
| ~ setext ),
inference(ennf_transformation,[],[f9]) ).
tff(f13,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ? [X3: $i] :
( ~ in(X3,X0)
& in(X3,X1) )
| ? [X2: $i] :
( ~ in(X2,X1)
& in(X2,X0) ) )
| ~ setext ),
inference(flattening,[],[f12]) ).
tff(f14,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] : ~ in(X1,X0) )
& setext
& emptysetE ),
inference(ennf_transformation,[],[f4]) ).
tff(f15,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] : ~ in(X1,X0) )
& setext
& emptysetE ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ? [X2: $i] :
( ~ in(X2,X0)
& in(X2,X1) )
| ? [X3: $i] :
( ~ in(X3,X1)
& in(X3,X0) ) )
| ~ setext ),
inference(rectify,[],[f13]) ).
tff(f17,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ~ in(sK0(X0,X1),X0)
& in(sK0(X0,X1),X1) )
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
| ~ setext ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f16]) ).
tff(f18,plain,
( ( emptyset != sK2 )
& ! [X1: $i] : ~ in(X1,sK2)
& setext
& emptysetE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f15]) ).
tff(f19,plain,
! [X0: $i,X1: $o] :
( ( $true = (X1) )
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(cnf_transformation,[],[f11]) ).
tff(f20,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| in(sK0(X0,X1),X1)
| in(sK1(X0,X1),X0)
| ~ setext ),
inference(cnf_transformation,[],[f17]) ).
tff(f24,plain,
emptysetE,
inference(cnf_transformation,[],[f18]) ).
tff(f25,plain,
setext,
inference(cnf_transformation,[],[f18]) ).
tff(f26,plain,
! [X1: $i] : ~ in(X1,sK2),
inference(cnf_transformation,[],[f18]) ).
tff(f27,plain,
emptyset != sK2,
inference(cnf_transformation,[],[f18]) ).
tff(f28,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f31,definition,
( spl3_1
<=> setext ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f35,definition,
( spl3_2
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| in(sK1(X0,X1),X0)
| in(sK0(X0,X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f36,plain,
( ! [X0: $i,X1: $i] :
( in(sK1(X0,X1),X0)
| ( X0 = X1 )
| in(sK0(X0,X1),X1) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f37,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f20,f35,f31]) ).
tff(f51,definition,
( spl3_6
<=> emptysetE ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f55,definition,
( spl3_7
<=> ! [X0: $i] : ~ in(X0,emptyset) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
tff(f56,plain,
( ! [X0: $i] : ~ in(X0,emptyset)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f58,definition,
( spl3_8
<=> ! [X1: $o] : ( $true = (X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
tff(f59,plain,
( ! [X1: $o] : ( $true = (X1) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f58]) ).
tff(f60,plain,
( ~ spl3_6
| spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f19,f58,f55,f51]) ).
tff(f61,plain,
spl3_6,
inference(avatar_split_clause,[],[f24,f51]) ).
tff(f62,plain,
spl3_1,
inference(avatar_split_clause,[],[f25,f31]) ).
tff(f63,plain,
( ! [X0: $i] :
( in(sK0(sK2,X0),X0)
| ( sK2 = X0 ) )
| ~ spl3_2 ),
inference(resolution,[],[f36,f26]) ).
tff(f66,plain,
( ( emptyset = sK2 )
| ~ spl3_2
| ~ spl3_7 ),
inference(resolution,[],[f63,f56]) ).
tff(f67,plain,
( $false
| ~ spl3_2
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f66,f27]) ).
tff(f68,plain,
( ~ spl3_2
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f67]) ).
tff(f73,plain,
( $false
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f28,f59]) ).
tff(f74,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f73]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s5,plain,
( ~ spl3_6
| spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f60]) ).
cnf(s6,plain,
spl3_6,
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
spl3_1,
inference(sat_conversion,[],[f62]) ).
cnf(s8,plain,
( ~ spl3_2
| ~ spl3_7 ),
inference(sat_conversion,[],[f68]) ).
cnf(s9,plain,
~ spl3_8,
inference(sat_conversion,[],[f74]) ).
cnf(s10,plain,
spl3_7,
inference(rat,[],[s5,s9,s6]) ).
cnf(s11,plain,
~ spl3_2,
inference(rat,[],[s8,s10]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s11,s7]) ).
tff(f75,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU506_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 05:43:59 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.47/1.46 % (65471)Detected formulas, will run a generic FOF schedule.
% 3.47/1.46 % (65479)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2860753287:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.46 % (65479)Refutation not found, incomplete strategy
% 3.47/1.46 % (65479)------------------------------
% 3.47/1.46 % (65479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.46 % (65479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.46 % (65479)CaDiCaL version: 2.1.3
% 3.47/1.46 % (65479)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.46 % (65479)Time elapsed: 0.001 s
% 3.47/1.46 % (65479)Peak memory usage: 88 MB
% 3.47/1.46 % (65478)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=1146186028:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.46 % (65480)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1798451390:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.46 % (65480)Refutation not found, incomplete strategy
% 3.47/1.46 % (65480)------------------------------
% 3.47/1.46 % (65480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.46 % (65480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.46 % (65480)CaDiCaL version: 2.1.3
% 3.47/1.46 % (65480)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.46 % (65480)Time elapsed: 0.001 s
% 3.47/1.46 % (65480)Peak memory usage: 88 MB
% 3.47/1.46 % (65476)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=3314454336:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.46 % (65477)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=20758218:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.46 % (65481)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2257440111:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.46 % (65481)First to succeed.
% 3.47/1.46 % (65481)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-65471"
% 3.47/1.46 % (65482)dis-21_1_sil=8000:lcm=predicate:random_seed=3744663127: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)
% 3.47/1.46 % (65482)Also succeeded, but the first one will report.
% 3.47/1.46 % (65479)------------------------------
% 3.47/1.46 % (65479)------------------------------
% 3.47/1.46 % (65490)lrs+10_1_sil=8000:sp=occurrence:random_seed=2304210900:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.47/1.46 % (65490)Also succeeded, but the first one will report.
% 3.47/1.46 % (65480)------------------------------
% 3.47/1.46 % (65480)------------------------------
% 3.47/1.46 % (65481)Refutation found. Thanks to Tanya!
% 3.47/1.46 % SZS status Theorem for theBenchmark
% 3.47/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.46 % (65481)------------------------------
% 3.47/1.46 % (65481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.46 % (65481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.46 % (65481)CaDiCaL version: 2.1.3
% 3.47/1.46 % (65481)Termination reason: Refutation
% 3.47/1.46 % (65481)Time elapsed: 0.004 s
% 3.47/1.46 % (65481)Peak memory usage: 90 MB
% 3.47/1.46 % (65481)Instructions burned: 2 (million)
% 3.47/1.46 % (65481)------------------------------
% 3.47/1.46 % (65481)------------------------------
% 3.47/1.46 % (65471)Success in time 0.408 s
% 3.47/1.46 % Vampire exiting
%------------------------------------------------------------------------------