%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET632+3 : 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 : n006.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 12:41:28 PM UTC 2026
% Result : Theorem 3.57s 1.39s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 127 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 51 ~; 44 |; 31 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 66 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) )
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th114) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) )
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ~ intersect(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1,X2] :
( empty_set != X0
& subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
? [X0,X1,X2] :
( empty_set != X0
& subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) ),
inference(flattening,[],[f15]) ).
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,[],[f12]) ).
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] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK1(X0,X1),X0)
& member(sK1(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( empty_set != sK2
& subset(sK2,sK3)
& subset(sK2,sK4)
& disjoint(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f16]) ).
fof(f26,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| intersect(X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
disjoint(sK3,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
subset(sK2,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(resolution,[],[f36,f27]) ).
fof(f76,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f48,f32]) ).
fof(f89,plain,
! [X0] :
( member(sK0(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f76,f27]) ).
fof(f132,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(sK0(X0,empty_set),X1)
| empty_set = X0 ),
inference(resolution,[],[f89,f26]) ).
fof(f212,plain,
( member(sK0(sK2,empty_set),sK4)
| empty_set = sK2 ),
inference(resolution,[],[f132,f40]) ).
fof(f213,plain,
( member(sK0(sK2,empty_set),sK3)
| empty_set = sK2 ),
inference(resolution,[],[f132,f41]) ).
fof(f216,plain,
member(sK0(sK2,empty_set),sK3),
inference(forward_subsumption_resolution,[],[f213,f42]) ).
fof(f217,plain,
member(sK0(sK2,empty_set),sK4),
inference(forward_subsumption_resolution,[],[f212,f42]) ).
fof(f224,plain,
! [X0] :
( intersect(sK3,X0)
| ~ member(sK0(sK2,empty_set),X0) ),
inference(resolution,[],[f216,f31]) ).
fof(f343,plain,
! [X0] :
( ~ disjoint(sK3,X0)
| ~ member(sK0(sK2,empty_set),X0) ),
inference(resolution,[],[f224,f33]) ).
fof(f554,plain,
~ member(sK0(sK2,empty_set),sK4),
inference(resolution,[],[f343,f39]) ).
fof(f555,plain,
$false,
inference(forward_subsumption_resolution,[],[f554,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:22:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.57/1.39 % (3529412)Detected formulas, will run a generic FOF schedule.
% 3.57/1.39 % (3529417)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=3123429763:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.39 % (3529419)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=3234567298:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.39 % (3529423)dis-21_1_sil=8000:lcm=predicate:random_seed=1421484547: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)
% 3.57/1.39 % (3529420)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=839862277:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.39 % (3529418)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=4036643827:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.39 % (3529422)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4097845109:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.39 % (3529421)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3849258714:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.39 % (3529420)Refutation not found, incomplete strategy
% 3.57/1.39 % (3529420)------------------------------
% 3.57/1.39 % (3529420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (3529420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (3529420)CaDiCaL version: 2.1.3
% 3.57/1.39 % (3529420)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.39 % (3529420)Time elapsed: 0.001 s
% 3.57/1.39 % (3529420)Peak memory usage: 88 MB
% 3.57/1.39 % (3529422)First to succeed.
% 3.57/1.39 % (3529422)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3529412"
% 3.57/1.39 % (3529421)Also succeeded, but the first one will report.
% 3.57/1.39 % (3529423)Instruction limit reached!
% 3.57/1.39 % (3529423)------------------------------
% 3.57/1.39 % (3529423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (3529423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (3529423)CaDiCaL version: 2.1.3
% 3.57/1.39 % (3529423)Termination reason: Instruction limit
% 3.57/1.39 % (3529423)Termination phase: Saturation
% 3.57/1.39 % (3529423)Time elapsed: 0.054 s
% 3.57/1.39 % (3529423)Peak memory usage: 88 MB
% 3.57/1.39 % (3529423)Instructions burned: 132 (million)
% 3.57/1.39 % (3529431)lrs+10_1_sil=8000:sp=occurrence:random_seed=369036222:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.57/1.39 % (3529431)Also succeeded, but the first one will report.
% 3.57/1.39 % (3529420)------------------------------
% 3.57/1.39 % (3529420)------------------------------
% 3.57/1.39 % (3529422)Refutation found. Thanks to Tanya!
% 3.57/1.39 % SZS status Theorem for theBenchmark
% 3.57/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.39 % (3529422)------------------------------
% 3.57/1.39 % (3529422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (3529422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (3529422)CaDiCaL version: 2.1.3
% 3.57/1.39 % (3529422)Termination reason: Refutation
% 3.57/1.39 % (3529422)Time elapsed: 0.015 s
% 3.57/1.39 % (3529422)Peak memory usage: 89 MB
% 3.57/1.39 % (3529422)Instructions burned: 18 (million)
% 3.57/1.39 % (3529422)------------------------------
% 3.57/1.39 % (3529422)------------------------------
% 3.57/1.39 % (3529412)Success in time 0.438 s
% 3.57/1.39 % Vampire exiting
%------------------------------------------------------------------------------