%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n001.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 12:42:37 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 18 unt; 3 def)
% Number of atoms : 95 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 38 ~; 39 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',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/Axioms/SET004-0.ax',ordered_pair) ).
fof(f128,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f132,axiom,
! [X0] : member(singleton(X0),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletons_are_sets) ).
fof(f137,axiom,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f138,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f148,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member_of(singleton(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_singleton_is_unique) ).
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(f194,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(f250,plain,
! [X0] : member(unordered_pair(X0,X0),universal_class),
inference(definition_unfolding,[],[f132,f12]) ).
fof(f255,plain,
! [X0,X1] :
( ~ member(X0,unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f256,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f263,plain,
! [X0] :
( ~ member(X0,universal_class)
| member_of(unordered_pair(X0,X0)) = X0 ),
inference(definition_unfolding,[],[f148,f12]) ).
fof(f292,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,f194,f194]) ).
fof(f316,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,f292]) ).
fof(f319,plain,
member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x)))),
inference(forward_subsumption_resolution,[],[f316,f250]) ).
fof(f337,plain,
! [X0] : null_class != unordered_pair(w,X0),
inference(resolution,[],[f128,f188]) ).
fof(f580,plain,
w = member_of(unordered_pair(w,w)),
inference(resolution,[],[f263,f188]) ).
fof(f682,plain,
( unordered_pair(w,w) = unordered_pair(y,y)
| unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
inference(resolution,[],[f8,f319]) ).
fof(f713,definition,
( spl0_15
<=> unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f715,plain,
( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f717,definition,
( spl0_16
<=> unordered_pair(w,w) = unordered_pair(y,y) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f719,plain,
( unordered_pair(w,w) = unordered_pair(y,y)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f720,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f682,f717,f713]) ).
fof(f748,plain,
( member(w,unordered_pair(y,y))
| ~ member(w,universal_class)
| ~ spl0_15 ),
inference(superposition,[],[f9,f715]) ).
fof(f754,plain,
( member(w,unordered_pair(y,y))
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f748,f188]) ).
fof(f782,plain,
( w = y
| ~ spl0_15 ),
inference(resolution,[],[f754,f255]) ).
fof(f787,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f782,f189]) ).
fof(f788,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f787]) ).
fof(f853,definition,
( spl0_21
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f854,plain,
( member(y,universal_class)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f855,plain,
( ~ member(y,universal_class)
| spl0_21 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f878,plain,
( null_class = unordered_pair(y,y)
| spl0_21 ),
inference(resolution,[],[f855,f256]) ).
fof(f895,plain,
( null_class = unordered_pair(w,w)
| ~ spl0_16
| spl0_21 ),
inference(superposition,[],[f719,f878]) ).
fof(f913,plain,
( $false
| ~ spl0_16
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f895,f337]) ).
fof(f914,plain,
( ~ spl0_16
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f913]) ).
fof(f933,plain,
( y = member_of(unordered_pair(y,y))
| ~ spl0_21 ),
inference(resolution,[],[f854,f263]) ).
fof(f937,plain,
( y = member_of(unordered_pair(w,w))
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f933,f719]) ).
fof(f938,plain,
( w = y
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f937,f580]) ).
fof(f939,plain,
( $false
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f938,f189]) ).
fof(f940,plain,
( ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f939]) ).
cnf(s16,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f720]) ).
cnf(s19,plain,
~ spl0_15,
inference(sat_conversion,[],[f788]) ).
cnf(s24,plain,
( ~ spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f914]) ).
cnf(s26,plain,
( ~ spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f940]) ).
cnf(s27,plain,
spl0_16,
inference(rat,[],[s16,s19]) ).
cnf(s28,plain,
~ spl0_21,
inference(rat,[],[s26,s27]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s24,s28,s27]) ).
fof(f941,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:13:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.46 % (4103457)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (4103466)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2913719539:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (4103463)% WARNING: option uhcvi not known.
% 0.16/0.46 % (4103463)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3378999720:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (4103462)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=659047129_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (4103464)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1492150976:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (4103465)dis+10_1_sil=32000:sp=arity:random_seed=528651134:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (4103467)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2567425402:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (4103468)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4069760699:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (4103466) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4103457-4103466"...
% 0.16/0.46 % (4103466)...printing done.
% 0.16/0.46 % (4103466)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (4103466)------------------------------
% 0.16/0.46 % (4103466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (4103466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (4103466)CaDiCaL version: 2.1.3
% 0.16/0.46 % (4103466)Termination reason: Refutation
% 0.16/0.46 % (4103466)Time elapsed: 0.015 s
% 0.16/0.46 % (4103466)Peak memory usage: 13 MB
% 0.16/0.46 % (4103466)Instructions burned: 43 (million)
% 0.16/0.46 % (4103457)Success in time 0.051 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------