%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET016+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 : n016.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 12:39:34 PM UTC 2026
% Result : Theorem 2.59s 1.32s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 102 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 29 ~; 38 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 68 !; 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f9,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( X0 = X1
| X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f12,conjecture,
! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
=> X0 = X2 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( equal_set(X0,X1)
=> ( subset(X0,X1)
& subset(X1,X0) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f19,plain,
( sK0 != sK2
& equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X1
& X0 != X2 ) )
& ( X0 = X1
| X0 = X2
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X1
& X0 != X2 ) )
& ( X0 = X1
| X0 = X2
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
inference(cnf_transformation,[],[f19]) ).
fof(f24,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f28]) ).
fof(f34,plain,
! [X2,X1] : member(X1,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f31]) ).
fof(f35,plain,
! [X2,X1] : member(X2,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f30]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,unordered_pair(X2,X1))
| X0 = X2
| ~ member(X0,X3)
| X0 = X1 ),
inference(resolution,[],[f29,f32]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ equal_set(X2,unordered_pair(X1,X3))
| ~ member(X0,X2)
| X0 = X3
| X0 = X1 ),
inference(resolution,[],[f42,f26]) ).
fof(f45,plain,
! [X0] :
( ~ member(X0,unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))
| unordered_pair(sK2,sK3) = X0
| singleton(sK2) = X0 ),
inference(resolution,[],[f43,f23]) ).
fof(f46,plain,
( singleton(sK0) = unordered_pair(sK2,sK3)
| singleton(sK0) = singleton(sK2) ),
inference(resolution,[],[f45,f34]) ).
fof(f55,plain,
( singleton(sK0) = singleton(sK2)
| member(sK3,singleton(sK0)) ),
inference(superposition,[],[f35,f46]) ).
fof(f56,plain,
( member(sK2,singleton(sK0))
| singleton(sK0) = singleton(sK2) ),
inference(superposition,[],[f34,f46]) ).
fof(f67,plain,
( member(sK3,singleton(sK0))
| member(sK2,singleton(sK0)) ),
inference(superposition,[],[f33,f55]) ).
fof(f68,plain,
( member(sK2,singleton(sK0))
| sK0 = sK3 ),
inference(resolution,[],[f67,f27]) ).
fof(f77,plain,
( sK0 = sK3
| sK0 = sK2 ),
inference(resolution,[],[f68,f27]) ).
fof(f78,plain,
sK0 = sK3,
inference(forward_subsumption_resolution,[],[f77,f24]) ).
fof(f93,plain,
( member(sK2,singleton(sK3))
| singleton(sK0) = singleton(sK2) ),
inference(forward_demodulation,[],[f56,f78]) ).
fof(f94,plain,
( singleton(sK2) = singleton(sK3)
| member(sK2,singleton(sK3)) ),
inference(forward_demodulation,[],[f93,f78]) ).
fof(f127,plain,
( member(sK2,singleton(sK3))
| member(sK2,singleton(sK3)) ),
inference(superposition,[],[f33,f94]) ).
fof(f128,plain,
member(sK2,singleton(sK3)),
inference(duplicate_literal_removal,[],[f127]) ).
fof(f133,plain,
sK2 = sK3,
inference(resolution,[],[f128,f27]) ).
fof(f137,plain,
sK0 != sK3,
inference(superposition,[],[f24,f133]) ).
fof(f148,plain,
$false,
inference(forward_subsumption_resolution,[],[f137,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 00:12:18 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.42 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
% 2.59/1.32 % (3141311)Detected formulas, will run a generic FOF schedule.
% 2.59/1.32 % (3141320)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2720646649:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.59/1.32 % (3141320)First to succeed.
% 2.59/1.32 % (3141320)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3141311"
% 2.59/1.32 % (3141318)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=3884013535:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.59/1.32 % (3141319)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=855921568:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.59/1.32 % (3141316)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=3688061031:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.59/1.32 % (3141317)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=1091267833:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.59/1.32 % (3141319)Refutation not found, incomplete strategy
% 2.59/1.32 % (3141319)------------------------------
% 2.59/1.32 % (3141319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.32 % (3141319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.32 % (3141319)CaDiCaL version: 2.1.3
% 2.59/1.32 % (3141319)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.32 % (3141319)Time elapsed: 0.001 s
% 2.59/1.32 % (3141319)Peak memory usage: 88 MB
% 2.59/1.32 % (3141321)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2278178235:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.59/1.32 % (3141321)Also succeeded, but the first one will report.
% 2.59/1.32 % (3141322)dis-21_1_sil=8000:lcm=predicate:random_seed=1354764770: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)
% 2.59/1.32 % (3141322)Instruction limit reached!
% 2.59/1.32 % (3141322)------------------------------
% 2.59/1.32 % (3141322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.32 % (3141322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.32 % (3141322)CaDiCaL version: 2.1.3
% 2.59/1.32 % (3141322)Termination reason: Instruction limit
% 2.59/1.32 % (3141322)Termination phase: Saturation
% 2.59/1.32 % (3141322)Time elapsed: 0.081 s
% 2.59/1.32 % (3141322)Peak memory usage: 90 MB
% 2.59/1.32 % (3141322)Instructions burned: 129 (million)
% 2.59/1.32 % (3141320)Refutation found. Thanks to Tanya!
% 2.59/1.32 % SZS status Theorem for theBenchmark
% 2.59/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/1.32 % (3141320)------------------------------
% 2.59/1.32 % (3141320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.59/1.32 % (3141320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/1.32 % (3141320)CaDiCaL version: 2.1.3
% 2.59/1.32 % (3141320)Termination reason: Refutation
% 2.59/1.32 % (3141320)Time elapsed: 0.003 s
% 2.59/1.32 % (3141320)Peak memory usage: 88 MB
% 2.59/1.32 % (3141320)Instructions burned: 6 (million)
% 2.59/1.32 % (3141320)------------------------------
% 2.59/1.32 % (3141320)------------------------------
% 2.59/1.32 % (3141311)Success in time 0.276 s
% 2.59/1.32 % Vampire exiting
%------------------------------------------------------------------------------