%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET694+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:41:40 PM UTC 2026
% Result : Theorem 0.73s 0.97s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 12 unt; 2 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 60 ~; 61 |; 11 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 77 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X1)
| member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f12,conjecture,
! [X0,X1] : subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI22) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1] : ~ subset(union(power_set(X0),power_set(X1)),power_set(union(X0,X1))),
inference(ennf_transformation,[],[f13]) ).
fof(f17,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,[],[f14]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X0,union(X1,X2))
| ( ~ member(X0,X1)
& ~ member(X0,X2) ) )
& ( member(X0,X1)
| member(X0,X2)
| ~ member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f23]) ).
fof(f36,plain,
~ subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f16]) ).
fof(f37,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X0,X1] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f63,plain,
~ subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),
inference(cnf_transformation,[],[f36]) ).
fof(f73,plain,
! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ member(sK0(X0,union(X1,X2)),X2) ),
inference(resolution,[],[f46,f39]) ).
fof(f75,plain,
! [X2,X0,X1] :
( subset(X0,union(X1,X2))
| ~ member(sK0(X0,union(X1,X2)),X1) ),
inference(resolution,[],[f47,f39]) ).
fof(f81,plain,
! [X2,X0,X1] :
( subset(union(X0,X1),X2)
| member(sK0(union(X0,X1),X2),X0)
| member(sK0(union(X0,X1),X2),X1) ),
inference(resolution,[],[f45,f38]) ).
fof(f108,plain,
! [X2,X0,X1] :
( member(X0,power_set(union(X1,X2)))
| ~ member(sK0(X0,union(X1,X2)),X2) ),
inference(resolution,[],[f73,f41]) ).
fof(f121,plain,
! [X2,X0,X1] :
( member(X0,power_set(union(X1,X2)))
| ~ member(sK0(X0,union(X1,X2)),X1) ),
inference(resolution,[],[f75,f41]) ).
fof(f133,plain,
( member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK3))
| member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK4)) ),
inference(resolution,[],[f81,f63]) ).
fof(f137,definition,
( spl5_1
<=> member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f139,plain,
( member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl5_2
<=> member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f143,plain,
( member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(sK3))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f133,f141,f137]) ).
fof(f145,plain,
( subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),sK3)
| ~ spl5_2 ),
inference(resolution,[],[f143,f40]) ).
fof(f148,plain,
( ! [X0] :
( member(X0,sK3)
| ~ member(X0,sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4)))) )
| ~ spl5_2 ),
inference(resolution,[],[f145,f37]) ).
fof(f171,plain,
! [X2,X0,X1] :
( subset(X0,power_set(union(X1,X2)))
| ~ member(sK0(sK0(X0,power_set(union(X1,X2))),union(X1,X2)),X2) ),
inference(resolution,[],[f108,f39]) ).
fof(f173,plain,
! [X2,X0,X1] :
( subset(X0,power_set(union(X1,X2)))
| ~ member(sK0(sK0(X0,power_set(union(X1,X2))),union(X1,X2)),X1) ),
inference(resolution,[],[f121,f39]) ).
fof(f466,plain,
~ member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK3),
inference(resolution,[],[f173,f63]) ).
fof(f469,plain,
( ~ member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))))
| ~ spl5_2 ),
inference(resolution,[],[f466,f148]) ).
fof(f480,plain,
( subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f469,f38]) ).
fof(f484,plain,
( member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(union(sK3,sK4)))
| ~ spl5_2 ),
inference(resolution,[],[f480,f41]) ).
fof(f489,plain,
( subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4)))
| ~ spl5_2 ),
inference(resolution,[],[f484,f39]) ).
fof(f491,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f489,f63]) ).
fof(f492,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f491]) ).
fof(f493,plain,
( subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),sK4)
| ~ spl5_1 ),
inference(resolution,[],[f139,f40]) ).
fof(f494,plain,
( ! [X0] :
( ~ member(X0,sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))))
| member(X0,sK4) )
| ~ spl5_1 ),
inference(resolution,[],[f493,f37]) ).
fof(f496,plain,
( ! [X0] :
( subset(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),X0)
| member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),X0),sK4) )
| ~ spl5_1 ),
inference(resolution,[],[f494,f38]) ).
fof(f504,plain,
( ! [X0] :
( member(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),power_set(X0))
| member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),X0),sK4) )
| ~ spl5_1 ),
inference(resolution,[],[f496,f41]) ).
fof(f507,plain,
( member(sK0(sK0(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4))),union(sK3,sK4)),sK4)
| subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4)))
| ~ spl5_1 ),
inference(resolution,[],[f504,f39]) ).
fof(f509,plain,
( subset(union(power_set(sK3),power_set(sK4)),power_set(union(sK3,sK4)))
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f507,f171]) ).
fof(f510,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f509,f63]) ).
fof(f511,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f510]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f144]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f492]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f511]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f512,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET694+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 02:33:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.73/0.97 % (2965122)Detected formulas, will run a generic FOF schedule.
% 0.73/0.97 % (2965127)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=3615962373:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.73/0.97 % (2965129)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=1866763079:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.73/0.97 % (2965130)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3602761616:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.73/0.97 % (2965131)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1686218503:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.73/0.97 % (2965132)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3941223772:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.73/0.97 % (2965133)dis-21_1_sil=8000:lcm=predicate:random_seed=2748569930: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)
% 0.73/0.97 % (2965128)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=2654934340:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.73/0.97 % (2965130)Refutation not found, incomplete strategy
% 0.73/0.97 % (2965130)------------------------------
% 0.73/0.97 % (2965130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.97 % (2965130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.97 % (2965130)CaDiCaL version: 2.1.3
% 0.73/0.97 % (2965130)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.97 % (2965130)Time elapsed: 0.001 s
% 0.73/0.97 % (2965130)Peak memory usage: 87 MB
% 0.73/0.97 % (2965132)First to succeed.
% 0.73/0.97 % (2965132)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2965122"
% 0.73/0.97 % (2965131)Instruction limit reached!
% 0.73/0.97 % (2965131)------------------------------
% 0.73/0.97 % (2965131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.97 % (2965131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.97 % (2965131)CaDiCaL version: 2.1.3
% 0.73/0.97 % (2965131)Termination reason: Instruction limit
% 0.73/0.97 % (2965131)Termination phase: Saturation
% 0.73/0.97 % (2965131)Time elapsed: 0.070 s
% 0.73/0.97 % (2965131)Peak memory usage: 88 MB
% 0.73/0.97 % (2965131)Instructions burned: 120 (million)
% 0.73/0.97 % (2965133)Instruction limit reached!
% 0.73/0.97 % (2965133)------------------------------
% 0.73/0.97 % (2965133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.73/0.97 % (2965133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.97 % (2965133)CaDiCaL version: 2.1.3
% 0.73/0.97 % (2965133)Termination reason: Instruction limit
% 0.73/0.97 % (2965133)Termination phase: Saturation
% 0.73/0.97 % (2965133)Time elapsed: 0.079 s
% 0.73/0.97 % (2965133)Peak memory usage: 89 MB
% 0.73/0.97 % (2965133)Instructions burned: 130 (million)
% 0.73/0.97 % (2965141)lrs+10_1_sil=8000:sp=occurrence:random_seed=3118262126:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.73/0.97 % (2965142)lrs+10_1_sil=32000:urr=on:br=off:random_seed=665305544:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.73/0.97 % (2965142)Also succeeded, but the first one will report.
% 0.73/0.97 % (2965130)------------------------------
% 0.73/0.97 % (2965130)------------------------------
% 0.73/0.97 % (2965132)Refutation found. Thanks to Tanya!
% 0.73/0.97 % SZS status Theorem for theBenchmark
% 0.73/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.96/1.07 % (2965132)------------------------------
% 2.96/1.07 % (2965132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.07 % (2965132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.07 % (2965132)CaDiCaL version: 2.1.3
% 2.96/1.07 % (2965132)Termination reason: Refutation
% 2.96/1.07 % (2965132)Time elapsed: 0.029 s
% 2.96/1.07 % (2965132)Peak memory usage: 90 MB
% 2.96/1.07 % (2965132)Instructions burned: 41 (million)
% 2.96/1.07 % (2965132)------------------------------
% 2.96/1.07 % (2965132)------------------------------
% 2.96/1.07 % (2965122)Success in time 0.378 s
% 2.96/1.07 % Vampire exiting
%------------------------------------------------------------------------------