%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU610_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 : 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 12:49:51 PM UTC 2026
% Result : Theorem 2.91s 1.28s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 24 unt; 0 typ; 8 def)
% Number of atoms : 291 ( 19 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 208 ( 77 ~; 74 |; 17 &)
% ( 11 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 97 ( 86 fml; 11 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 81 ( 0 sgn 76 !; 5 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
tff(f3,axiom,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> subset(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
tff(f4,axiom,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,setminus(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
tff(f5,conjecture,
( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [X0: $i,X1: $i] :
( ( setminus(X0,X1) = emptyset )
=> subset(X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
tff(f6,negated_conjecture,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [X0: $i,X1: $i] :
( ( setminus(X0,X1) = emptyset )
=> subset(X0,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f7,plain,
( emptysetE
= ( ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : (X1) ) ) ),
inference(rectify,[],[f1]) ).
tff(f8,plain,
( emptysetE
<=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(fool_elimination,[],[f7]) ).
tff(f10,plain,
( subsetI2
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> subset(X0,X1) ) ),
inference(fool_elimination,[],[f3]) ).
tff(f11,plain,
( setminusI
<=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,setminus(X0,X1)) ) ) ),
inference(fool_elimination,[],[f4]) ).
tff(f12,plain,
( setminusI
=> ! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,setminus(X0,X1)) ) ) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
tff(f13,plain,
( subsetI2
=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( in(X2,X0)
=> in(X2,X1) )
=> subset(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
tff(f15,plain,
( emptysetE
=> ! [X0: $i] :
( in(X0,emptyset)
=> ! [X1: $o] : ( $true = (X1) ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
tff(f16,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = (X1) )
| ~ in(X0,emptyset) )
| ~ emptysetE ),
inference(ennf_transformation,[],[f15]) ).
tff(f18,plain,
( ! [X0: $i,X1: $i] :
( subset(X0,X1)
| ? [X2: $i] :
( ~ in(X2,X1)
& in(X2,X0) ) )
| ~ subsetI2 ),
inference(ennf_transformation,[],[f13]) ).
tff(f19,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setminus(X0,X1))
| in(X2,X1)
| ~ in(X2,X0) )
| ~ setminusI ),
inference(ennf_transformation,[],[f12]) ).
tff(f20,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( in(X2,setminus(X0,X1))
| in(X2,X1)
| ~ in(X2,X0) )
| ~ setminusI ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( ? [X0: $i,X1: $i] :
( ~ subset(X0,X1)
& ( setminus(X0,X1) = emptyset ) )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(ennf_transformation,[],[f6]) ).
tff(f22,plain,
( ? [X0: $i,X1: $i] :
( ~ subset(X0,X1)
& ( setminus(X0,X1) = emptyset ) )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(flattening,[],[f21]) ).
tff(f24,plain,
( ! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
| ~ subsetI2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
tff(f25,plain,
( ~ subset(sK1,sK2)
& ( emptyset = setminus(sK1,sK2) )
& setminusI
& subsetI2
& in__Cong
& emptysetE ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f22]) ).
tff(f26,plain,
! [X0: $i,X1: $o] :
( ( $true = (X1) )
| ~ in(X0,emptyset)
| ~ emptysetE ),
inference(cnf_transformation,[],[f16]) ).
tff(f29,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0)
| ~ subsetI2 ),
inference(cnf_transformation,[],[f24]) ).
tff(f30,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1)
| ~ subsetI2 ),
inference(cnf_transformation,[],[f24]) ).
tff(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(X2,setminus(X0,X1))
| in(X2,X1)
| ~ in(X2,X0)
| ~ setminusI ),
inference(cnf_transformation,[],[f20]) ).
tff(f32,plain,
emptysetE,
inference(cnf_transformation,[],[f25]) ).
tff(f34,plain,
subsetI2,
inference(cnf_transformation,[],[f25]) ).
tff(f35,plain,
setminusI,
inference(cnf_transformation,[],[f25]) ).
tff(f36,plain,
emptyset = setminus(sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
tff(f37,plain,
~ subset(sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
tff(f38,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f45,definition,
( spl3_1
<=> setminusI ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f49,definition,
( spl3_2
<=> ! [X2: $i,X0: $i,X1: $i] :
( in(X2,setminus(X0,X1))
| ~ in(X2,X0)
| in(X2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f50,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ~ in(X2,X0)
| in(X2,setminus(X0,X1))
| in(X2,X1) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f51,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f31,f49,f45]) ).
tff(f53,definition,
( spl3_3
<=> subsetI2 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f57,definition,
( spl3_4
<=> ! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f58,plain,
( ! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f57]) ).
tff(f59,plain,
( ~ spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f29,f57,f53]) ).
tff(f61,definition,
( spl3_5
<=> ! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f62,plain,
( ! [X0: $i,X1: $i] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f63,plain,
( ~ spl3_3
| spl3_5 ),
inference(avatar_split_clause,[],[f30,f61,f53]) ).
tff(f65,definition,
( spl3_6
<=> emptysetE ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f69,definition,
( spl3_7
<=> ! [X0: $i] : ~ in(X0,emptyset) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
tff(f70,plain,
( ! [X0: $i] : ~ in(X0,emptyset)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f69]) ).
tff(f72,definition,
( spl3_8
<=> ! [X1: $o] : ( $true = (X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
tff(f73,plain,
( ! [X1: $o] : ( $true = (X1) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f72]) ).
tff(f74,plain,
( ~ spl3_6
| spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f26,f72,f69,f65]) ).
tff(f75,plain,
spl3_6,
inference(avatar_split_clause,[],[f32,f65]) ).
tff(f76,plain,
spl3_3,
inference(avatar_split_clause,[],[f34,f53]) ).
tff(f77,plain,
spl3_1,
inference(avatar_split_clause,[],[f35,f45]) ).
tff(f81,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X2)
| in(sK0(X0,X1),setminus(X0,X2)) )
| ~ spl3_2
| ~ spl3_4 ),
inference(resolution,[],[f50,f58]) ).
tff(f84,plain,
( ! [X0: $i] :
( in(sK0(sK1,sK2),setminus(sK1,X0))
| in(sK0(sK1,sK2),X0) )
| ~ spl3_2
| ~ spl3_4 ),
inference(resolution,[],[f81,f37]) ).
tff(f86,plain,
( in(sK0(sK1,sK2),emptyset)
| in(sK0(sK1,sK2),sK2)
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[],[f84,f36]) ).
tff(f87,plain,
( in(sK0(sK1,sK2),sK2)
| ~ spl3_2
| ~ spl3_4
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f86,f70]) ).
tff(f88,plain,
( subset(sK1,sK2)
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5
| ~ spl3_7 ),
inference(resolution,[],[f87,f62]) ).
tff(f90,plain,
( $false
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f88,f37]) ).
tff(f91,plain,
( ~ spl3_2
| ~ spl3_4
| ~ spl3_5
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f90]) ).
tff(f102,plain,
( ! [X0: $o,X1: $o] : ( (X0) = (X1) )
| ~ spl3_8 ),
inference(superposition,[],[f73,f73]) ).
tff(f106,plain,
( ! [X0: $o] : ( $false != (X0) )
| ~ spl3_8 ),
inference(superposition,[],[f38,f102]) ).
tff(f113,plain,
( $false
| ~ spl3_8 ),
inference(forward_subsumption_resolution,[],[f106,f102]) ).
tff(f114,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s3,plain,
( ~ spl3_3
| spl3_5 ),
inference(sat_conversion,[],[f63]) ).
cnf(s4,plain,
( ~ spl3_6
| spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f74]) ).
cnf(s5,plain,
spl3_6,
inference(sat_conversion,[],[f75]) ).
cnf(s6,plain,
spl3_3,
inference(sat_conversion,[],[f76]) ).
cnf(s7,plain,
spl3_1,
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl3_2
| ~ spl3_4
| ~ spl3_5
| ~ spl3_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s11,plain,
~ spl3_8,
inference(sat_conversion,[],[f114]) ).
cnf(s12,plain,
spl3_7,
inference(rat,[],[s4,s11,s5]) ).
cnf(s13,plain,
spl3_5,
inference(rat,[],[s3,s6]) ).
cnf(s14,plain,
spl3_4,
inference(rat,[],[s2,s6]) ).
cnf(s15,plain,
~ spl3_2,
inference(rat,[],[s8,s12,s13,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s15,s7]) ).
tff(f115,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU610_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % 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 05:45:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 2.91/1.27 % (3682192)Detected formulas, will run a generic FOF schedule.
% 2.91/1.27 % (3682198)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=863370143:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/1.27 % (3682199)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=2076887185:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/1.27 % (3682203)dis-21_1_sil=8000:lcm=predicate:random_seed=1563538687: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)
% 2.91/1.27 % (3682197)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=593725085:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/1.27 % (3682201)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1744153561:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/1.27 % (3682200)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1689362214:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/1.27 % (3682202)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1007621525:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/1.27 % (3682200)Refutation not found, incomplete strategy
% 2.91/1.27 % (3682200)------------------------------
% 2.91/1.27 % (3682200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.27 % (3682200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.27 % (3682200)CaDiCaL version: 2.1.3
% 2.91/1.27 % (3682200)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.27 % (3682200)Time elapsed: 0.001 s
% 2.91/1.27 % (3682200)Peak memory usage: 88 MB
% 2.91/1.27 % (3682201)Refutation not found, incomplete strategy
% 2.91/1.27 % (3682201)------------------------------
% 2.91/1.27 % (3682201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.27 % (3682201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.28 % (3682201)CaDiCaL version: 2.1.3
% 2.91/1.28 % (3682201)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.28 % (3682201)Time elapsed: 0.002 s
% 2.91/1.28 % (3682201)Peak memory usage: 88 MB
% 2.91/1.28 % (3682201)Instructions burned: 1 (million)
% 2.91/1.28 % (3682203)Refutation not found, incomplete strategy
% 2.91/1.28 % (3682203)------------------------------
% 2.91/1.28 % (3682203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.28 % (3682203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.28 % (3682203)CaDiCaL version: 2.1.3
% 2.91/1.28 % (3682203)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.28 % (3682203)Time elapsed: 0.002 s
% 2.91/1.28 % (3682203)Peak memory usage: 88 MB
% 2.91/1.28 % (3682203)Instructions burned: 1 (million)
% 2.91/1.28 % (3682202)First to succeed.
% 2.91/1.28 % (3682202)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3682192"
% 2.91/1.28 % (3682203)------------------------------
% 2.91/1.28 % (3682203)------------------------------
% 2.91/1.28 % (3682201)------------------------------
% 2.91/1.28 % (3682201)------------------------------
% 2.91/1.28 % (3682200)------------------------------
% 2.91/1.28 % (3682200)------------------------------
% 2.91/1.28 % (3682202)Refutation found. Thanks to Tanya!
% 2.91/1.28 % SZS status Theorem for theBenchmark
% 2.91/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.47 % (3682202)------------------------------
% 3.58/1.47 % (3682202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.47 % (3682202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.47 % (3682202)CaDiCaL version: 2.1.3
% 3.58/1.47 % (3682202)Termination reason: Refutation
% 3.58/1.47 % (3682202)Time elapsed: 0.004 s
% 3.58/1.47 % (3682202)Peak memory usage: 90 MB
% 3.58/1.47 % (3682202)Instructions burned: 4 (million)
% 3.58/1.47 % (3682202)------------------------------
% 3.58/1.47 % (3682202)------------------------------
% 3.58/1.47 % (3682192)Success in time 0.424 s
% 3.58/1.47 % Vampire exiting
%------------------------------------------------------------------------------