%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET947+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:42:23 PM UTC 2026
% Result : Theorem 3.39s 1.37s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 83 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 95 ( 38 ~; 36 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 51 ( 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f8,conjecture,
! [X0] : subset(X0,powerset(union(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0] : subset(X0,powerset(union(X0))),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
? [X0] : ~ subset(X0,powerset(union(X0))),
inference(ennf_transformation,[],[f9]) ).
fof(f15,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK0(X0,X1),X0)
| ~ in(sK0(X0,X1),X1) )
& ( subset(sK0(X0,X1),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f23,plain,
~ subset(sK4,powerset(union(sK4))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f14]) ).
fof(f26,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
~ subset(sK4,powerset(union(sK4))),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f26]) ).
fof(f43,plain,
in(sK1(sK4,powerset(union(sK4))),sK4),
inference(resolution,[],[f30,f36]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,powerset(X1))
| ~ subset(sK1(X0,powerset(X1)),X1) ),
inference(resolution,[],[f31,f37]) ).
fof(f56,plain,
~ subset(sK1(sK4,powerset(union(sK4))),union(sK4)),
inference(resolution,[],[f45,f36]) ).
fof(f58,plain,
~ in(sK1(sK4,powerset(union(sK4))),sK4),
inference(resolution,[],[f56,f32]) ).
fof(f60,plain,
$false,
inference(forward_subsumption_resolution,[],[f58,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET947+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:11:20 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.39/1.37 % (3173553)Detected formulas, will run a generic FOF schedule.
% 3.39/1.37 % (3173560)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=822156684:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/1.37 % (3173561)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1360641214:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/1.37 % (3173558)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=3814299760:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/1.37 % (3173559)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=2516431511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/1.37 % (3173562)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2466148606:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/1.37 % (3173561)Refutation not found, incomplete strategy
% 3.39/1.37 % (3173561)------------------------------
% 3.39/1.37 % (3173561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3173561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3173561)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3173561)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.37 % (3173561)Time elapsed: 0.001 s
% 3.39/1.37 % (3173561)Peak memory usage: 87 MB
% 3.39/1.37 % (3173563)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3086250148:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/1.37 % (3173563)First to succeed.
% 3.39/1.37 % (3173563)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3173553"
% 3.39/1.37 % (3173564)dis-21_1_sil=8000:lcm=predicate:random_seed=2520669075: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)
% 3.39/1.37 % (3173564)Also succeeded, but the first one will report.
% 3.39/1.37 % (3173562)Instruction limit reached!
% 3.39/1.37 % (3173562)------------------------------
% 3.39/1.37 % (3173562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3173562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3173562)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3173562)Termination reason: Instruction limit
% 3.39/1.37 % (3173562)Termination phase: Saturation
% 3.39/1.37 % (3173562)Time elapsed: 0.047 s
% 3.39/1.37 % (3173562)Peak memory usage: 87 MB
% 3.39/1.37 % (3173562)Instructions burned: 123 (million)
% 3.39/1.37 % (3173572)lrs+10_1_sil=8000:sp=occurrence:random_seed=1985432359:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.39/1.37 % (3173572)Also succeeded, but the first one will report.
% 3.39/1.37 % (3173561)------------------------------
% 3.39/1.37 % (3173561)------------------------------
% 3.39/1.37 % (3173563)Refutation found. Thanks to Tanya!
% 3.39/1.37 % SZS status Theorem for theBenchmark
% 3.39/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.37 % (3173563)------------------------------
% 3.39/1.37 % (3173563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.37 % (3173563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.37 % (3173563)CaDiCaL version: 2.1.3
% 3.39/1.37 % (3173563)Termination reason: Refutation
% 3.39/1.37 % (3173563)Time elapsed: 0.003 s
% 3.39/1.37 % (3173563)Peak memory usage: 88 MB
% 3.39/1.37 % (3173563)Instructions burned: 2 (million)
% 3.39/1.37 % (3173563)------------------------------
% 3.39/1.37 % (3173563)------------------------------
% 3.39/1.37 % (3173553)Success in time 0.411 s
% 3.39/1.37 % Vampire exiting
%------------------------------------------------------------------------------