%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET689+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 : n018.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 12:41:39 PM UTC 2026
% Result : Theorem 3.44s 1.42s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 10 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 34 ~; 23 |; 21 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 40 !; 8 ?)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2)
& subset(X2,X0) )
=> equal_set(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI05) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2)
& subset(X2,X0) )
=> equal_set(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f16]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ~ equal_set(X0,X2)
& subset(X0,X1)
& subset(X1,X2)
& subset(X2,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ~ equal_set(X0,X2)
& subset(X0,X1)
& subset(X1,X2)
& subset(X2,X0) ),
inference(flattening,[],[f19]) ).
fof(f21,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(f22,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,[],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f40,plain,
( ~ equal_set(sK3,sK5)
& subset(sK3,sK4)
& subset(sK4,sK5)
& subset(sK5,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f20]) ).
fof(f41,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f68,plain,
subset(sK5,sK3),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f70,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f71,plain,
~ equal_set(sK3,sK5),
inference(cnf_transformation,[],[f40]) ).
fof(f82,plain,
( ~ subset(sK3,sK5)
| ~ subset(sK5,sK3) ),
inference(resolution,[],[f44,f71]) ).
fof(f83,plain,
~ subset(sK3,sK5),
inference(forward_subsumption_resolution,[],[f82,f68]) ).
fof(f84,plain,
~ member(sK0(sK3,sK5),sK5),
inference(resolution,[],[f83,f43]) ).
fof(f85,plain,
member(sK0(sK3,sK5),sK3),
inference(resolution,[],[f83,f42]) ).
fof(f87,plain,
! [X0] :
( ~ subset(X0,sK5)
| ~ member(sK0(sK3,sK5),X0) ),
inference(resolution,[],[f84,f41]) ).
fof(f91,plain,
~ member(sK0(sK3,sK5),sK4),
inference(resolution,[],[f87,f69]) ).
fof(f92,plain,
! [X0] :
( ~ subset(X0,sK4)
| ~ member(sK0(sK3,sK5),X0) ),
inference(resolution,[],[f91,f41]) ).
fof(f96,plain,
~ member(sK0(sK3,sK5),sK3),
inference(resolution,[],[f92,f70]) ).
fof(f97,plain,
$false,
inference(forward_subsumption_resolution,[],[f96,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET689+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 02:36:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.44/1.42 % (2939601)Detected formulas, will run a generic FOF schedule.
% 3.44/1.42 % (2939610)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=3163431965:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.42 % (2939615)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2503370102:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.42 % (2939615)First to succeed.
% 3.44/1.42 % (2939615)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2939601"
% 3.44/1.42 % (2939612)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=2531957062:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.42 % (2939613)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3279612347:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.42 % (2939611)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=4253574363:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.42 % (2939614)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2191194920:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.42 % (2939613)Refutation not found, incomplete strategy
% 3.44/1.42 % (2939613)------------------------------
% 3.44/1.42 % (2939613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (2939613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (2939613)CaDiCaL version: 2.1.3
% 3.44/1.42 % (2939613)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.42 % (2939613)Time elapsed: 0.001 s
% 3.44/1.42 % (2939613)Peak memory usage: 88 MB
% 3.44/1.42 % (2939614)Also succeeded, but the first one will report.
% 3.44/1.42 % (2939616)dis-21_1_sil=8000:lcm=predicate:random_seed=3464401155: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)
% 3.44/1.42 % (2939616)Also succeeded, but the first one will report.
% 3.44/1.42 % (2939613)------------------------------
% 3.44/1.42 % (2939613)------------------------------
% 3.44/1.42 % (2939615)Refutation found. Thanks to Tanya!
% 3.44/1.42 % SZS status Theorem for theBenchmark
% 3.44/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.42 % (2939615)------------------------------
% 3.44/1.42 % (2939615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (2939615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (2939615)CaDiCaL version: 2.1.3
% 3.44/1.42 % (2939615)Termination reason: Refutation
% 3.44/1.42 % (2939615)Time elapsed: 0.004 s
% 3.44/1.42 % (2939615)Peak memory usage: 89 MB
% 3.44/1.42 % (2939615)Instructions burned: 3 (million)
% 3.44/1.42 % (2939615)------------------------------
% 3.44/1.42 % (2939615)------------------------------
% 3.44/1.42 % (2939601)Success in time 0.397 s
% 3.44/1.42 % Vampire exiting
%------------------------------------------------------------------------------