%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET095+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 : n001.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 12:40:04 PM UTC 2026
% Result : Theorem 0.24s 1.91s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 43 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 36 ( 13 ~; 11 |; 5 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 3 ?)
% 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(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
fof(f12,conjecture,
! [X0,X1] :
( member(X1,X0)
=> subset(singleton(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI44) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(singleton(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f15,plain,
? [X0,X1] :
( ~ subset(singleton(X1),X0)
& member(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
( ~ subset(singleton(sK1),sK0)
& member(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f20,plain,
member(sK1,sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f21,plain,
~ subset(singleton(sK1),sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f22,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f23,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f24,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X0,X1] :
( sK2(singleton(X0),X1) = X0
| subset(singleton(X0),X1) ),
inference(resolution,[],[f22,f24]) ).
fof(f31,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subset(singleton(X0),X1)
| subset(singleton(X0),X1) ),
inference(superposition,[],[f23,f28]) ).
fof(f34,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(duplicate_literal_removal,[],[f31]) ).
fof(f35,plain,
~ member(sK1,sK0),
inference(resolution,[],[f34,f21]) ).
fof(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET095+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.42 % Computer : n001.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Mon Sep 28 00:45:16 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 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
% 0.24/1.91 % (4115912)Detected formulas, will run a generic FOF schedule.
% 0.24/1.91 % (4115921)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=2161275895:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.24/1.91 % (4115927)dis-21_1_sil=8000:lcm=predicate:random_seed=849275956: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)
% 0.24/1.91 % (4115923)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=256459612:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.24/1.91 % (4115922)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=552581049:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.24/1.91 % (4115924)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1962588730:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.24/1.91 % (4115925)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2404497108:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.24/1.91 % (4115924)Refutation not found, incomplete strategy
% 0.24/1.91 % (4115924)------------------------------
% 0.24/1.91 % (4115924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.91 % (4115924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.91 % (4115924)CaDiCaL version: 2.1.3
% 0.24/1.91 % (4115924)Termination reason: Refutation not found, incomplete strategy
% 0.24/1.91 % (4115924)Time elapsed: 0.002 s
% 0.24/1.91 % (4115924)Peak memory usage: 88 MB
% 0.24/1.91 % (4115925)First to succeed.
% 0.24/1.91 % (4115925)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4115912"
% 0.24/1.91 % (4115926)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2075828876:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.24/1.91 % (4115926)Also succeeded, but the first one will report.
% 0.24/1.91 % (4115927)Instruction limit reached!
% 0.24/1.91 % (4115927)------------------------------
% 0.24/1.91 % (4115927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.91 % (4115927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.91 % (4115927)CaDiCaL version: 2.1.3
% 0.24/1.91 % (4115927)Termination reason: Instruction limit
% 0.24/1.91 % (4115927)Termination phase: Saturation
% 0.24/1.91 % (4115927)Time elapsed: 0.110 s
% 0.24/1.91 % (4115927)Peak memory usage: 89 MB
% 0.24/1.91 % (4115927)Instructions burned: 129 (million)
% 0.24/1.91 % (4115935)lrs+10_1_sil=8000:sp=occurrence:random_seed=246702944:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 0.24/1.91 % (4115935)Also succeeded, but the first one will report.
% 0.24/1.91 % (4115924)------------------------------
% 0.24/1.91 % (4115924)------------------------------
% 0.24/1.91 % (4115925)Refutation found. Thanks to Tanya!
% 0.24/1.91 % SZS status Theorem for theBenchmark
% 0.24/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/1.91 % (4115925)------------------------------
% 0.24/1.91 % (4115925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.91 % (4115925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.91 % (4115925)CaDiCaL version: 2.1.3
% 0.24/1.91 % (4115925)Termination reason: Refutation
% 0.24/1.91 % (4115925)Time elapsed: 0.003 s
% 0.24/1.91 % (4115925)Peak memory usage: 88 MB
% 0.24/1.91 % (4115925)Instructions burned: 1 (million)
% 0.24/1.91 % (4115925)------------------------------
% 0.24/1.91 % (4115925)------------------------------
% 0.24/1.91 % (4115912)Success in time 0.647 s
% 0.24/1.91 % Vampire exiting
%------------------------------------------------------------------------------