%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET702+4 : TPTP v9.3.1. Released v2.2.0.
% 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 12:41:41 PM UTC 2026
% Result : Theorem 2.79s 1.27s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 16 unt; 2 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 155 ( 65 ~; 62 |; 18 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 93 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f11,axiom,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
fof(f12,conjecture,
! [X0,X1] : subset(intersection(product(X0),product(X1)),product(intersection(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI36) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : subset(intersection(product(X0),product(X1)),product(intersection(X0,X1))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1] : ~ subset(intersection(product(X0),product(X1)),product(intersection(X0,X1))),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
~ subset(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) )
| ~ member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(rectify,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ( ~ member(X0,sK3(X0,X1))
& member(sK3(X0,X1),X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f25]) ).
fof(f27,plain,
~ subset(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X3,X0,X1] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
! [X0,X1] :
( member(sK3(X0,X1),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X0,X1] :
( ~ member(X0,sK3(X0,X1))
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
~ member(intersection(product(sK0),product(sK1)),power_set(product(intersection(sK0,sK1)))),
inference(resolution,[],[f28,f27]) ).
fof(f41,plain,
member(sK2(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),intersection(product(sK0),product(sK1))),
inference(resolution,[],[f31,f27]) ).
fof(f42,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f31,f29]) ).
fof(f43,plain,
~ member(sK2(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),product(intersection(sK0,sK1))),
inference(resolution,[],[f32,f27]) ).
fof(f46,plain,
member(sK2(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),product(sK0)),
inference(resolution,[],[f34,f41]) ).
fof(f47,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,X1)
| ~ member(sK2(X1,X2),X2) ),
inference(resolution,[],[f30,f32]) ).
fof(f49,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,X1)
| ~ member(X1,power_set(X2)) ),
inference(resolution,[],[f30,f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( member(sK3(X0,intersection(X1,X2)),X1)
| member(X0,product(intersection(X1,X2))) ),
inference(resolution,[],[f37,f34]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,X1),X2)
| ~ member(X0,product(X2))
| member(X0,product(X1)) ),
inference(resolution,[],[f36,f38]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X0)
| member(intersection(X0,X1),power_set(X2)) ),
inference(resolution,[],[f42,f34]) ).
fof(f78,plain,
! [X0] :
( ~ member(sK2(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),X0)
| ~ member(X0,power_set(product(intersection(sK0,sK1)))) ),
inference(resolution,[],[f49,f43]) ).
fof(f91,plain,
! [X0] :
( ~ member(sK2(intersection(product(sK0),product(sK1)),product(intersection(sK0,sK1))),X0)
| ~ member(sK2(X0,product(intersection(sK0,sK1))),product(intersection(sK0,sK1))) ),
inference(resolution,[],[f47,f43]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ member(X0,product(X1))
| member(X0,product(intersection(X1,X2)))
| member(X0,product(intersection(X1,X2))) ),
inference(resolution,[],[f56,f50]) ).
fof(f173,plain,
! [X2,X0,X1] :
( member(X0,product(intersection(X1,X2)))
| ~ member(X0,product(X1)) ),
inference(duplicate_literal_removal,[],[f164]) ).
fof(f248,plain,
~ member(product(sK0),power_set(product(intersection(sK0,sK1)))),
inference(resolution,[],[f78,f46]) ).
fof(f519,plain,
( member(intersection(product(sK0),product(sK1)),power_set(product(intersection(sK0,sK1))))
| ~ member(sK2(product(sK0),product(intersection(sK0,sK1))),product(intersection(sK0,sK1))) ),
inference(resolution,[],[f63,f91]) ).
fof(f532,definition,
( spl4_1
<=> member(sK2(product(sK0),product(intersection(sK0,sK1))),product(intersection(sK0,sK1))) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f533,plain,
( ~ member(sK2(product(sK0),product(intersection(sK0,sK1))),product(intersection(sK0,sK1)))
| spl4_1 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f535,definition,
( spl4_2
<=> member(intersection(product(sK0),product(sK1)),power_set(product(intersection(sK0,sK1)))) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f536,plain,
( member(intersection(product(sK0),product(sK1)),power_set(product(intersection(sK0,sK1))))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f537,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f519,f535,f532]) ).
fof(f538,plain,
( ~ member(sK2(product(sK0),product(intersection(sK0,sK1))),product(sK0))
| spl4_1 ),
inference(resolution,[],[f533,f173]) ).
fof(f548,plain,
( member(product(sK0),power_set(product(intersection(sK0,sK1))))
| spl4_1 ),
inference(resolution,[],[f538,f42]) ).
fof(f563,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f548,f248]) ).
fof(f565,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f563]) ).
fof(f573,plain,
( $false
| ~ spl4_2 ),
inference(resolution,[],[f536,f39]) ).
fof(f575,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f573]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f537]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f565]) ).
cnf(s4,plain,
~ spl4_2,
inference(sat_conversion,[],[f575]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f580,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET702+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 02:39:02 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 2.79/1.27 % (3202770)Detected formulas, will run a generic FOF schedule.
% 2.79/1.27 % (3202779)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=772385035:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.79/1.27 % (3202779)Instruction limit reached!
% 2.79/1.27 % (3202779)------------------------------
% 2.79/1.27 % (3202779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.27 % (3202779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.27 % (3202779)CaDiCaL version: 2.1.3
% 2.79/1.27 % (3202779)Termination reason: Instruction limit
% 2.79/1.27 % (3202779)Termination phase: Saturation
% 2.79/1.27 % (3202779)Time elapsed: 0.039 s
% 2.79/1.27 % (3202779)Peak memory usage: 89 MB
% 2.79/1.27 % (3202779)Instructions burned: 119 (million)
% 2.79/1.27 % (3202781)dis-21_1_sil=8000:lcm=predicate:random_seed=2285792178: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)
% 2.79/1.27 % (3202776)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=3564148248:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.79/1.27 % (3202777)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=3524534642:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.79/1.27 % (3202775)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=3025360795:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.79/1.27 % (3202778)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3056382156:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.79/1.27 % (3202780)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2061389793:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.79/1.27 % (3202778)Refutation not found, incomplete strategy
% 2.79/1.27 % (3202778)------------------------------
% 2.79/1.27 % (3202778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.27 % (3202778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.27 % (3202778)CaDiCaL version: 2.1.3
% 2.79/1.27 % (3202778)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.27 % (3202778)Time elapsed: 0.001 s
% 2.79/1.27 % (3202778)Peak memory usage: 88 MB
% 2.79/1.27 % (3202781)First to succeed.
% 2.79/1.27 % (3202780)Also succeeded, but the first one will report.
% 2.79/1.27 % (3202781)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3202770"
% 2.79/1.27 % (3202789)lrs+10_1_sil=8000:sp=occurrence:random_seed=4272926798:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.79/1.27 % (3202789)Also succeeded, but the first one will report.
% 2.79/1.27 % (3202778)------------------------------
% 2.79/1.27 % (3202778)------------------------------
% 2.79/1.27 % (3202781)Refutation found. Thanks to Tanya!
% 2.79/1.27 % SZS status Theorem for theBenchmark
% 2.79/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.48 % (3202781)------------------------------
% 3.68/1.48 % (3202781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.48 % (3202781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.48 % (3202781)CaDiCaL version: 2.1.3
% 3.68/1.48 % (3202781)Termination reason: Refutation
% 3.68/1.48 % (3202781)Time elapsed: 0.011 s
% 3.68/1.48 % (3202781)Peak memory usage: 89 MB
% 3.68/1.48 % (3202781)Instructions burned: 14 (million)
% 3.68/1.48 % (3202781)------------------------------
% 3.68/1.48 % (3202781)------------------------------
% 3.68/1.48 % (3202770)Success in time 0.437 s
% 3.68/1.48 % Vampire exiting
%------------------------------------------------------------------------------