%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET017+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 12:39:34 PM UTC 2026
% Result : Theorem 2.49s 1.21s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 81 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 24 ~; 26 |; 20 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& unordered_pair(X0,X1) = unordered_pair(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& unordered_pair(X0,X1) = unordered_pair(X0,X2) )
=> X1 = X2 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1,X2] :
( X1 != X2
& member(X1,universal_class)
& member(X2,universal_class)
& unordered_pair(X0,X1) = unordered_pair(X0,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1,X2] :
( X1 != X2
& member(X1,universal_class)
& member(X2,universal_class)
& unordered_pair(X0,X1) = unordered_pair(X0,X2) ),
inference(flattening,[],[f60]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f67]) ).
fof(f104,plain,
( sK7 != sK8
& member(sK7,universal_class)
& member(sK8,universal_class)
& unordered_pair(sK6,sK7) = unordered_pair(sK6,sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f61]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| X0 != X2 ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f192,plain,
unordered_pair(sK6,sK7) = unordered_pair(sK6,sK8),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
member(sK8,universal_class),
inference(cnf_transformation,[],[f104]) ).
fof(f194,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f104]) ).
fof(f195,plain,
sK7 != sK8,
inference(cnf_transformation,[],[f104]) ).
fof(f199,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f114]) ).
fof(f214,plain,
( member(sK8,unordered_pair(sK6,sK7))
| ~ member(sK8,universal_class) ),
inference(superposition,[],[f199,f192]) ).
fof(f216,plain,
member(sK8,unordered_pair(sK6,sK7)),
inference(forward_subsumption_resolution,[],[f214,f193]) ).
fof(f423,plain,
( sK7 = sK8
| sK6 = sK8 ),
inference(resolution,[],[f112,f216]) ).
fof(f427,plain,
! [X0] :
( ~ member(X0,unordered_pair(sK6,sK7))
| sK8 = X0
| sK6 = X0 ),
inference(superposition,[],[f112,f192]) ).
fof(f430,plain,
sK6 = sK8,
inference(forward_subsumption_resolution,[],[f423,f195]) ).
fof(f432,plain,
unordered_pair(sK8,sK7) = unordered_pair(sK8,sK8),
inference(superposition,[],[f192,f430]) ).
fof(f433,plain,
unordered_pair(sK8,sK7) = singleton(sK8),
inference(forward_demodulation,[],[f432,f117]) ).
fof(f447,plain,
( member(sK7,singleton(sK8))
| ~ member(sK7,universal_class) ),
inference(superposition,[],[f199,f433]) ).
fof(f450,plain,
member(sK7,singleton(sK8)),
inference(forward_subsumption_resolution,[],[f447,f194]) ).
fof(f678,plain,
! [X0] :
( ~ member(X0,unordered_pair(sK8,sK7))
| sK8 = X0
| sK6 = X0 ),
inference(forward_demodulation,[],[f427,f430]) ).
fof(f679,plain,
! [X0] :
( ~ member(X0,singleton(sK8))
| sK8 = X0
| sK6 = X0 ),
inference(forward_demodulation,[],[f678,f433]) ).
fof(f680,plain,
! [X0] :
( sK8 = X0
| ~ member(X0,singleton(sK8))
| sK8 = X0 ),
inference(forward_demodulation,[],[f679,f430]) ).
fof(f681,plain,
! [X0] :
( ~ member(X0,singleton(sK8))
| sK8 = X0 ),
inference(duplicate_literal_removal,[],[f680]) ).
fof(f684,plain,
sK7 = sK8,
inference(resolution,[],[f681,f450]) ).
fof(f690,plain,
$false,
inference(forward_subsumption_resolution,[],[f684,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET017+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:08:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 2.49/1.21 % (683878)Detected formulas, will run a generic FOF schedule.
% 2.49/1.21 % (683994)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1747031087:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.49/1.21 % (683994)First to succeed.
% 2.49/1.21 % (683994)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-683878"
% 2.49/1.21 % (683992)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2133024958:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.49/1.21 % (683988)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=3086734696:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.49/1.21 % (683991)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4207546114:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.49/1.21 % (683989)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=1318236176:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.49/1.21 % (683990)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=1840361227:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.49/1.21 % (683992)Also succeeded, but the first one will report.
% 2.49/1.21 % (683991)Also succeeded, but the first one will report.
% 2.49/1.21 % (683996)dis-21_1_sil=8000:lcm=predicate:random_seed=3643211643: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)
% 2.49/1.21 % (683996)Instruction limit reached!
% 2.49/1.21 % (683996)------------------------------
% 2.49/1.21 % (683996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.21 % (683996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.21 % (683996)CaDiCaL version: 2.1.3
% 2.49/1.21 % (683996)Termination reason: Instruction limit
% 2.49/1.21 % (683996)Termination phase: Saturation
% 2.49/1.21 % (683996)Time elapsed: 0.077 s
% 2.49/1.21 % (683996)Peak memory usage: 89 MB
% 2.49/1.21 % (683996)Instructions burned: 130 (million)
% 2.49/1.21 % (683994)Refutation found. Thanks to Tanya!
% 2.49/1.21 % SZS status Theorem for theBenchmark
% 2.49/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.49/1.21 % (683994)------------------------------
% 2.49/1.21 % (683994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.21 % (683994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.21 % (683994)CaDiCaL version: 2.1.3
% 2.49/1.22 % (683994)Termination reason: Refutation
% 2.49/1.22 % (683994)Time elapsed: 0.010 s
% 2.49/1.22 % (683994)Peak memory usage: 89 MB
% 2.49/1.22 % (683994)Instructions burned: 21 (million)
% 2.49/1.22 % (683994)------------------------------
% 2.49/1.22 % (683994)------------------------------
% 2.49/1.22 % (683878)Success in time 0.279 s
% 2.49/1.22 % Vampire exiting
%------------------------------------------------------------------------------