%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET767+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 : n013.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 12:41:52 PM UTC 2026
% Result : Theorem 3.59s 16.50s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 3 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 43 ( 14 ~; 13 |; 9 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% 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(f15,axiom,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( equivalence(X1,X0)
=> subset(equivalence_class(X2,X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII03) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( equivalence(X1,X0)
=> subset(equivalence_class(X2,X0,X1),X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ~ subset(equivalence_class(X2,X0,X1),X0)
& equivalence(X1,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f26,plain,
( ~ subset(equivalence_class(sK2,sK0,sK1),sK0)
& equivalence(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f22]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f23]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) )
& ( ( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ member(X3,X1)
| ~ apply(X0,X2,X3) )
& ( ( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f28]) ).
fof(f31,plain,
~ subset(equivalence_class(sK2,sK0,sK1),sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f32,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f33,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,equivalence_class(X2,X1,X0))
| member(X3,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( member(sK3(equivalence_class(X0,X1,X2),X3),X1)
| subset(equivalence_class(X0,X1,X2),X3) ),
inference(resolution,[],[f38,f32]) ).
fof(f47,plain,
! [X2,X0,X1] :
( subset(equivalence_class(X0,X1,X2),X1)
| subset(equivalence_class(X0,X1,X2),X1) ),
inference(resolution,[],[f42,f33]) ).
fof(f50,plain,
! [X2,X0,X1] : subset(equivalence_class(X0,X1,X2),X1),
inference(duplicate_literal_removal,[],[f47]) ).
fof(f51,plain,
$false,
inference(resolution,[],[f50,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET767+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/15.40 % Computer : n013.cluster.edu
% 0.13/15.40 % Model : x86_64 x86_64
% 0.13/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.40 % Memory : 8046.5625MB
% 0.13/15.40 % OS : Linux 6.8.0-71-generic
% 0.13/15.40 % CPULimit : 300
% 0.13/15.40 % WCLimit : 300
% 0.13/15.40 % DateTime : Mon Sep 28 02:45:10 UTC 2026
% 0.13/15.40 % CPUTime :
% 0.13/15.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/15.43 Running first-order theorem proving
% 0.13/15.43 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
% 3.59/16.50 % (755679)Detected formulas, will run a generic FOF schedule.
% 3.59/16.50 % (755684)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=278696204:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/16.50 % (755685)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=3222474412:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/16.50 % (755686)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=2514717176:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/16.50 % (755688)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2117091995:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/16.50 % (755689)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2106153981:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/16.50 % (755687)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1164311702:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/16.50 % (755690)dis-21_1_sil=8000:lcm=predicate:random_seed=191067509: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)
% 3.59/16.50 % (755688)First to succeed.
% 3.59/16.50 % (755687)Refutation not found, incomplete strategy
% 3.59/16.50 % (755687)------------------------------
% 3.59/16.50 % (755687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/16.50 % (755687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/16.50 % (755687)CaDiCaL version: 2.1.3
% 3.59/16.50 % (755687)Termination reason: Refutation not found, incomplete strategy
% 3.59/16.50 % (755687)Time elapsed: 0.001 s
% 3.59/16.50 % (755687)Peak memory usage: 88 MB
% 3.59/16.50 % (755687)Instructions burned: 1 (million)
% 3.59/16.50 % (755690)Also succeeded, but the first one will report.
% 3.59/16.50 % (755688)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-755679"
% 3.59/16.50 % (755689)Also succeeded, but the first one will report.
% 3.59/16.50 % (755687)------------------------------
% 3.59/16.50 % (755687)------------------------------
% 3.59/16.50 % (755688)Refutation found. Thanks to Tanya!
% 3.59/16.50 % SZS status Theorem for theBenchmark
% 3.59/16.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/16.50 % (755688)------------------------------
% 3.59/16.50 % (755688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/16.50 % (755688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/16.50 % (755688)CaDiCaL version: 2.1.3
% 3.59/16.50 % (755688)Termination reason: Refutation
% 3.59/16.50 % (755688)Time elapsed: 0.002 s
% 3.59/16.50 % (755688)Peak memory usage: 88 MB
% 3.59/16.50 % (755688)Instructions burned: 1 (million)
% 3.59/16.50 % (755688)------------------------------
% 3.59/16.50 % (755688)------------------------------
% 3.59/16.50 % (755679)Success in time 0.429 s
% 3.59/16.50 % Vampire exiting
%------------------------------------------------------------------------------