%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET018+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 12:39:35 PM UTC 2026
% Result : Theorem 3.44s 1.36s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 12 unt; 0 def)
% Number of atoms : 139 ( 66 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 39 ~; 62 |; 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 : 85 ( 81 !; 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)))
=> X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50b) ).
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)))
=> X1 = X3 ),
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] :
( X1 != X3
& 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,
( sK1 != sK3
& 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,
sK1 != sK3,
inference(cnf_transformation,[],[f19]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
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(f44,plain,
! [X2,X3,X0,X1] :
( ~ equal_set(unordered_pair(X1,X3),X2)
| ~ member(X0,X2)
| X0 = X3
| X0 = X1 ),
inference(resolution,[],[f42,f25]) ).
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(f47,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| unordered_pair(sK0,sK1) = singleton(sK2) ),
inference(resolution,[],[f45,f35]) ).
fof(f49,plain,
! [X0] :
( ~ member(X0,unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)))
| unordered_pair(sK0,sK1) = X0
| singleton(sK0) = X0 ),
inference(resolution,[],[f44,f23]) ).
fof(f56,plain,
( singleton(sK0) = singleton(sK2)
| member(sK2,singleton(sK0)) ),
inference(superposition,[],[f34,f46]) ).
fof(f58,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
| singleton(sK0) = unordered_pair(sK2,sK3) ),
inference(resolution,[],[f49,f35]) ).
fof(f85,plain,
! [X0] :
( ~ member(X0,unordered_pair(sK0,sK1))
| sK3 = X0
| sK2 = X0
| unordered_pair(sK0,sK1) = singleton(sK2) ),
inference(superposition,[],[f29,f47]) ).
fof(f102,plain,
( member(sK3,unordered_pair(sK0,sK1))
| singleton(sK0) = unordered_pair(sK2,sK3) ),
inference(superposition,[],[f35,f58]) ).
fof(f111,plain,
( member(sK2,singleton(sK0))
| member(sK2,singleton(sK0)) ),
inference(superposition,[],[f33,f56]) ).
fof(f112,plain,
member(sK2,singleton(sK0)),
inference(duplicate_literal_removal,[],[f111]) ).
fof(f116,plain,
sK0 = sK2,
inference(resolution,[],[f112,f27]) ).
fof(f131,plain,
( singleton(sK0) = unordered_pair(sK0,sK3)
| member(sK3,unordered_pair(sK0,sK1)) ),
inference(forward_demodulation,[],[f102,f116]) ).
fof(f163,plain,
( member(sK3,unordered_pair(sK0,sK1))
| member(sK3,singleton(sK0)) ),
inference(superposition,[],[f35,f131]) ).
fof(f184,plain,
( member(sK3,singleton(sK0))
| sK1 = sK3
| sK0 = sK3 ),
inference(resolution,[],[f163,f29]) ).
fof(f190,plain,
( sK1 = sK3
| sK0 = sK3 ),
inference(forward_subsumption_resolution,[],[f184,f27]) ).
fof(f191,plain,
sK0 = sK3,
inference(forward_subsumption_resolution,[],[f190,f24]) ).
fof(f196,plain,
sK0 != sK1,
inference(superposition,[],[f24,f191]) ).
fof(f223,plain,
! [X0] :
( sK0 = X0
| ~ member(X0,unordered_pair(sK0,sK1))
| sK2 = X0
| unordered_pair(sK0,sK1) = singleton(sK2) ),
inference(forward_demodulation,[],[f85,f191]) ).
fof(f224,plain,
! [X0] :
( sK0 = X0
| sK0 = X0
| ~ member(X0,unordered_pair(sK0,sK1))
| unordered_pair(sK0,sK1) = singleton(sK2) ),
inference(forward_demodulation,[],[f223,f116]) ).
fof(f225,plain,
! [X0] :
( sK0 = X0
| ~ member(X0,unordered_pair(sK0,sK1))
| unordered_pair(sK0,sK1) = singleton(sK2) ),
inference(duplicate_literal_removal,[],[f224]) ).
fof(f226,plain,
! [X0] :
( singleton(sK0) = unordered_pair(sK0,sK1)
| sK0 = X0
| ~ member(X0,unordered_pair(sK0,sK1)) ),
inference(forward_demodulation,[],[f225,f116]) ).
fof(f283,plain,
! [X0] :
( ~ member(X0,unordered_pair(sK0,sK1))
| sK0 = X0
| member(sK1,singleton(sK0)) ),
inference(superposition,[],[f35,f226]) ).
fof(f320,plain,
( sK0 = sK1
| member(sK1,singleton(sK0)) ),
inference(resolution,[],[f283,f35]) ).
fof(f330,plain,
member(sK1,singleton(sK0)),
inference(forward_subsumption_resolution,[],[f320,f196]) ).
fof(f331,plain,
sK0 = sK1,
inference(resolution,[],[f330,f27]) ).
fof(f332,plain,
$false,
inference(forward_subsumption_resolution,[],[f331,f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 00:08:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.44/1.36 % (682628)Detected formulas, will run a generic FOF schedule.
% 3.44/1.36 % (682639)dis-21_1_sil=8000:lcm=predicate:random_seed=458270124: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)
% 3.44/1.36 % (682633)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=3582939106:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.36 % (682635)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=4183558620:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.36 % (682634)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=3131888265:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.36 % (682636)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1681855340:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.36 % (682637)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2143314867:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.36 % (682639)Instruction limit reached!
% 3.44/1.36 % (682639)------------------------------
% 3.44/1.36 % (682639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.36 % (682639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.36 % (682639)CaDiCaL version: 2.1.3
% 3.44/1.36 % (682639)Termination reason: Instruction limit
% 3.44/1.36 % (682639)Termination phase: Saturation
% 3.44/1.36 % (682639)Time elapsed: 0.045 s
% 3.44/1.36 % (682639)Peak memory usage: 90 MB
% 3.44/1.36 % (682639)Instructions burned: 130 (million)
% 3.44/1.36 % (682636)Refutation not found, incomplete strategy
% 3.44/1.36 % (682636)------------------------------
% 3.44/1.36 % (682636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.36 % (682636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.36 % (682636)CaDiCaL version: 2.1.3
% 3.44/1.36 % (682636)Termination reason: Refutation not found, incomplete strategy
% 3.44/1.36 % (682636)Time elapsed: 0.001 s
% 3.44/1.36 % (682636)Peak memory usage: 88 MB
% 3.44/1.36 % (682637)First to succeed.
% 3.44/1.36 % (682637)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-682628"
% 3.44/1.36 % (682638)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3426125143:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.36 % (682638)Also succeeded, but the first one will report.
% 3.44/1.36 % (682646)lrs+10_1_sil=8000:sp=occurrence:random_seed=1786473707:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.44/1.36 % (682646)Also succeeded, but the first one will report.
% 3.44/1.36 % (682636)------------------------------
% 3.44/1.36 % (682636)------------------------------
% 3.44/1.36 % (682637)Refutation found. Thanks to Tanya!
% 3.44/1.36 % SZS status Theorem for theBenchmark
% 3.44/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.36 % (682637)------------------------------
% 3.44/1.36 % (682637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.36 % (682637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.36 % (682637)CaDiCaL version: 2.1.3
% 3.44/1.36 % (682637)Termination reason: Refutation
% 3.44/1.36 % (682637)Time elapsed: 0.008 s
% 3.44/1.36 % (682637)Peak memory usage: 88 MB
% 3.44/1.36 % (682637)Instructions burned: 13 (million)
% 3.44/1.36 % (682637)------------------------------
% 3.44/1.36 % (682637)------------------------------
% 3.44/1.36 % (682628)Success in time 0.419 s
% 3.44/1.36 % Vampire exiting
%------------------------------------------------------------------------------