%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET071-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:42:57 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 22 unt; 4 def)
% Number of atoms : 101 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 33 ~; 40 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
inference(reorient_equations,[],[f67]) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f123,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X1,X0) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f125,negated_conjecture,
unordered_pair(x,y) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_unordered_pair_1) ).
fof(f126,plain,
null_class != unordered_pair(x,y),
inference(reorient_equations,[],[f125]) ).
fof(f127,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_unordered_pair_2) ).
fof(f128,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_unordered_pair_3) ).
fof(f183,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X1,X0) = unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f188,plain,
! [X2,X0,X1] :
( member(X2,X0)
| subclass(X0,X1)
| ~ member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f191,plain,
! [X0] : ~ subclass(X0,universal_class),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f195,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f238,plain,
! [X0] :
( ~ member(regular(X0),X0)
| null_class = X0 ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f267,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X1,X0) = unordered_pair(X1,X1) ),
inference(consistent_polarity_flipping,[],[f183]) ).
fof(f269,plain,
member(x,universal_class),
inference(consistent_polarity_flipping,[],[f127]) ).
fof(f270,plain,
member(y,universal_class),
inference(consistent_polarity_flipping,[],[f128]) ).
fof(f957,plain,
! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x),
inference(resolution,[],[f267,f269]) ).
fof(f958,plain,
! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,y),
inference(resolution,[],[f267,f270]) ).
fof(f1000,plain,
! [X0] : unordered_pair(X0,X0) = unordered_pair(y,X0),
inference(superposition,[],[f120,f958]) ).
fof(f1007,plain,
null_class != unordered_pair(x,x),
inference(superposition,[],[f126,f958]) ).
fof(f2025,plain,
! [X0,X1] :
( member(X1,unordered_pair(X0,x))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f195,f957]) ).
fof(f2038,plain,
! [X0,X1] :
( member(X1,unordered_pair(X0,x))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f2025]) ).
fof(f2061,plain,
! [X0] :
( member(X0,unordered_pair(x,x))
| y = X0 ),
inference(superposition,[],[f2038,f1000]) ).
fof(f2276,plain,
( y = regular(unordered_pair(x,x))
| null_class = unordered_pair(x,x) ),
inference(resolution,[],[f2061,f238]) ).
fof(f2278,definition,
( spl0_58
<=> null_class = unordered_pair(x,x) ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f2280,plain,
( null_class = unordered_pair(x,x)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f2282,definition,
( spl0_59
<=> y = regular(unordered_pair(x,x)) ),
introduced(definition,[new_symbols(definition,[spl0_59])],[avatar_definition]) ).
fof(f2284,plain,
( y = regular(unordered_pair(x,x))
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f2282]) ).
fof(f2285,plain,
( spl0_58
| spl0_59 ),
inference(avatar_split_clause,[],[f2276,f2282,f2278]) ).
fof(f2310,plain,
( null_class != null_class
| ~ spl0_58 ),
inference(superposition,[],[f1007,f2280]) ).
fof(f2357,plain,
( $false
| ~ spl0_58 ),
inference(trivial_inequality_removal,[],[f2310]) ).
fof(f2358,plain,
~ spl0_58,
inference(avatar_contradiction_clause,[],[f2357]) ).
fof(f2362,plain,
( ~ member(y,unordered_pair(x,x))
| null_class = unordered_pair(x,x)
| ~ spl0_59 ),
inference(superposition,[],[f238,f2284]) ).
fof(f2364,definition,
( spl0_65
<=> member(y,unordered_pair(x,x)) ),
introduced(definition,[new_symbols(definition,[spl0_65])],[avatar_definition]) ).
fof(f2366,plain,
( ~ member(y,unordered_pair(x,x))
| spl0_65 ),
inference(avatar_component_clause,[],[f2364]) ).
fof(f2367,plain,
( spl0_58
| ~ spl0_65
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f2362,f2282,f2364,f2278]) ).
fof(f2378,plain,
( ! [X0] :
( ~ member(y,X0)
| subclass(unordered_pair(x,x),X0) )
| spl0_65 ),
inference(resolution,[],[f2366,f188]) ).
fof(f2636,plain,
( subclass(unordered_pair(x,x),universal_class)
| spl0_65 ),
inference(resolution,[],[f2378,f270]) ).
fof(f2667,definition,
( spl0_70
<=> subclass(unordered_pair(x,x),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_70])],[avatar_definition]) ).
fof(f2669,plain,
( subclass(unordered_pair(x,x),universal_class)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f2667]) ).
fof(f2679,plain,
( spl0_70
| spl0_65 ),
inference(avatar_split_clause,[],[f2636,f2364,f2667]) ).
fof(f2697,plain,
( $false
| ~ spl0_70 ),
inference(resolution,[],[f2669,f191]) ).
fof(f2698,plain,
~ spl0_70,
inference(avatar_contradiction_clause,[],[f2697]) ).
cnf(s60,plain,
( spl0_58
| spl0_59 ),
inference(sat_conversion,[],[f2285]) ).
cnf(s67,plain,
~ spl0_58,
inference(sat_conversion,[],[f2358]) ).
cnf(s68,plain,
( spl0_58
| ~ spl0_59
| ~ spl0_65 ),
inference(sat_conversion,[],[f2367]) ).
cnf(s74,plain,
( spl0_65
| spl0_70 ),
inference(sat_conversion,[],[f2679]) ).
cnf(s75,plain,
~ spl0_70,
inference(sat_conversion,[],[f2698]) ).
cnf(s76,plain,
spl0_65,
inference(rat,[],[s74,s75]) ).
cnf(s77,plain,
( spl0_58
| ~ spl0_59 ),
inference(rat,[],[s68,s76]) ).
cnf(s78,plain,
~ spl0_59,
inference(rat,[],[s77,s67]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s60,s78,s67]) ).
fof(f2699,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:30:16 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (1316195)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1316206)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3427489193:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (1316201)% WARNING: option uhcvi not known.
% 0.17/0.48 % (1316200)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3708260511_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (1316204)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2635812906:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (1316202)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2677263117:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (1316201)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1196178731:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (1316203)dis+10_1_sil=32000:sp=arity:random_seed=2950638953:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (1316205)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=566469455:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (1316206) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1316195-1316206"...
% 0.17/0.48 % (1316206)...printing done.
% 0.17/0.48 % (1316206)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1316206)------------------------------
% 0.17/0.48 % (1316206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1316206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1316206)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1316206)Termination reason: Refutation
% 0.17/0.48 % (1316206)Time elapsed: 0.024 s
% 0.17/0.48 % (1316206)Peak memory usage: 13 MB
% 0.17/0.48 % (1316206)Instructions burned: 65 (million)
% 0.17/0.48 % (1316195)Success in time 0.049 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------