%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Unsatisfiable 2.81s 1.38s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 18 unt; 4 def)
% Number of atoms : 107 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 97 ( 45 ~; 48 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f125,axiom,
! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| member(X0,universal_class)
| member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f137,axiom,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f187,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
fof(f188,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
fof(f189,negated_conjecture,
w != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
fof(f190,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f191,plain,
unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))) = unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),
inference(definition_unfolding,[],[f187,f190,f190]) ).
fof(f206,plain,
! [X0,X1] :
( ~ member(X0,unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f239,plain,
( member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))))
| ~ member(unordered_pair(y,y),universal_class) ),
inference(superposition,[],[f9,f191]) ).
fof(f242,plain,
member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x)))),
inference(forward_subsumption_resolution,[],[f239,f11]) ).
fof(f308,definition,
( spl0_5
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f309,plain,
( member(y,universal_class)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f566,plain,
( unordered_pair(w,w) = unordered_pair(y,y)
| unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
inference(resolution,[],[f8,f242]) ).
fof(f607,definition,
( spl0_27
<=> unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f608,plain,
( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f610,definition,
( spl0_28
<=> unordered_pair(w,w) = unordered_pair(y,y) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f611,plain,
( unordered_pair(w,w) = unordered_pair(y,y)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f612,plain,
( spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f566,f610,f607]) ).
fof(f749,plain,
( member(w,unordered_pair(y,y))
| ~ member(w,universal_class)
| ~ spl0_27 ),
inference(superposition,[],[f9,f608]) ).
fof(f762,plain,
( member(w,unordered_pair(y,y))
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f749,f188]) ).
fof(f824,plain,
( w = y
| ~ spl0_27 ),
inference(resolution,[],[f762,f206]) ).
fof(f834,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f824,f189]) ).
fof(f835,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f834]) ).
fof(f849,plain,
( null_class = unordered_pair(w,w)
| member(y,universal_class)
| member(y,universal_class)
| ~ spl0_28 ),
inference(superposition,[],[f611,f125]) ).
fof(f859,plain,
( member(y,unordered_pair(w,w))
| ~ member(y,universal_class)
| ~ spl0_28 ),
inference(superposition,[],[f10,f611]) ).
fof(f881,plain,
( null_class = unordered_pair(w,w)
| member(y,universal_class)
| ~ spl0_28 ),
inference(duplicate_literal_removal,[],[f849]) ).
fof(f884,plain,
( member(y,unordered_pair(w,w))
| ~ spl0_5
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f859,f309]) ).
fof(f947,plain,
( w = y
| w = y
| ~ spl0_5
| ~ spl0_28 ),
inference(resolution,[],[f884,f8]) ).
fof(f953,plain,
( w = y
| ~ spl0_5
| ~ spl0_28 ),
inference(duplicate_literal_removal,[],[f947]) ).
fof(f954,plain,
( $false
| ~ spl0_5
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f953,f189]) ).
fof(f955,plain,
( ~ spl0_5
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f954]) ).
fof(f965,definition,
( spl0_32
<=> null_class = unordered_pair(w,w) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f966,plain,
( null_class = unordered_pair(w,w)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f979,plain,
( spl0_5
| spl0_32
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f881,f610,f965,f308]) ).
fof(f1133,plain,
( member(w,null_class)
| ~ member(w,universal_class)
| ~ spl0_32 ),
inference(superposition,[],[f9,f966]) ).
fof(f1176,plain,
( ~ member(w,universal_class)
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1133,f113]) ).
fof(f1179,plain,
( $false
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1176,f188]) ).
fof(f1180,plain,
~ spl0_32,
inference(avatar_contradiction_clause,[],[f1179]) ).
cnf(s18,plain,
( spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f612]) ).
cnf(s25,plain,
~ spl0_27,
inference(sat_conversion,[],[f835]) ).
cnf(s28,plain,
( ~ spl0_5
| ~ spl0_28 ),
inference(sat_conversion,[],[f955]) ).
cnf(s37,plain,
( spl0_5
| ~ spl0_28
| spl0_32 ),
inference(sat_conversion,[],[f979]) ).
cnf(s58,plain,
~ spl0_32,
inference(sat_conversion,[],[f1180]) ).
cnf(s59,plain,
( spl0_5
| ~ spl0_28 ),
inference(rat,[],[s37,s58]) ).
cnf(s63,plain,
spl0_28,
inference(rat,[],[s18,s25]) ).
cnf(s64,plain,
spl0_5,
inference(rat,[],[s59,s63]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s28,s63,s64]) ).
fof(f1181,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 00:08:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.81/1.38 % (3906064)Input is clausal, will run a generic CNF schedule.
% 2.81/1.38 % (3906073)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=92224490:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.81/1.38 % (3906073)First to succeed.
% 2.81/1.38 % (3906073)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3906064"
% 2.81/1.38 % (3906075)dis-21_1_sil=8000:lcm=predicate:random_seed=651190294:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.81/1.38 % (3906072)lrs+10_1_sil=8000:sp=occurrence:random_seed=1423344821:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.81/1.38 % (3906069)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=2528804179:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.81/1.38 % (3906070)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2314363478:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.81/1.38 % (3906074)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2343124304:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.81/1.38 % (3906071)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2939091935:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.81/1.38 % (3906072)Also succeeded, but the first one will report.
% 2.81/1.38 % (3906074)Also succeeded, but the first one will report.
% 2.81/1.38 % (3906075)Instruction limit reached!
% 2.81/1.38 % (3906075)------------------------------
% 2.81/1.38 % (3906075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.38 % (3906075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.38 % (3906075)CaDiCaL version: 2.1.3
% 2.81/1.38 % (3906075)Termination reason: Instruction limit
% 2.81/1.38 % (3906075)Termination phase: Saturation
% 2.81/1.38 % (3906075)Time elapsed: 0.076 s
% 2.81/1.38 % (3906075)Peak memory usage: 88 MB
% 2.81/1.38 % (3906075)Instructions burned: 118 (million)
% 2.81/1.38 % (3906073)Refutation found. Thanks to Tanya!
% 2.81/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.81/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.81/1.38 % (3906073)------------------------------
% 2.81/1.38 % (3906073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/1.38 % (3906073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/1.38 % (3906073)CaDiCaL version: 2.1.3
% 2.81/1.38 % (3906073)Termination reason: Refutation
% 2.81/1.38 % (3906073)Time elapsed: 0.013 s
% 2.81/1.38 % (3906073)Peak memory usage: 90 MB
% 2.81/1.38 % (3906073)Instructions burned: 35 (million)
% 2.81/1.38 % (3906073)------------------------------
% 2.81/1.38 % (3906073)------------------------------
% 2.81/1.38 % (3906064)Success in time 0.321 s
% 2.81/1.38 % Vampire exiting
%------------------------------------------------------------------------------