%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 12:42:58 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 18 unt; 2 def)
% Number of atoms : 73 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 29 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 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(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
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(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f127,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
fof(f128,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
fof(f129,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_right_cancellation_3) ).
fof(f134,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(f140,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f134]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f134]) ).
fof(f187,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f128,f134]) ).
fof(f203,plain,
unordered_pair(x,z) = unordered_pair(z,y),
inference(superposition,[],[f120,f127]) ).
fof(f238,definition,
( spl0_3
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f239,plain,
( member(y,universal_class)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f242,definition,
( spl0_4
<=> member(y,unordered_pair(x,z)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f244,plain,
( member(y,unordered_pair(x,z))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f249,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(superposition,[],[f10,f203]) ).
fof(f440,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,z))
| y = X0
| z = X0 ),
inference(superposition,[],[f8,f127]) ).
fof(f817,plain,
member(x,universal_class),
inference(resolution,[],[f140,f187]) ).
fof(f860,plain,
member(y,universal_class),
inference(resolution,[],[f141,f187]) ).
fof(f923,plain,
spl0_3,
inference(avatar_split_clause,[],[f860,f238]) ).
fof(f977,plain,
( member(y,unordered_pair(x,z))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f249,f239]) ).
fof(f978,plain,
( spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f977,f238,f242]) ).
fof(f992,plain,
( x = y
| z = y
| ~ spl0_4 ),
inference(resolution,[],[f244,f8]) ).
fof(f994,plain,
( z = y
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f992,f129]) ).
fof(f1013,plain,
( x != z
| ~ spl0_4 ),
inference(superposition,[],[f129,f994]) ).
fof(f1408,plain,
( ! [X0] :
( z = X0
| ~ member(X0,unordered_pair(x,z))
| z = X0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f440,f994]) ).
fof(f1409,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(x,z))
| z = X0 )
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f1408]) ).
fof(f1410,plain,
( x = z
| ~ member(x,universal_class)
| ~ spl0_4 ),
inference(resolution,[],[f1409,f9]) ).
fof(f1442,plain,
( ~ member(x,universal_class)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1410,f1013]) ).
fof(f1457,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f1442,f817]) ).
fof(f1458,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f1457]) ).
cnf(s13,plain,
spl0_3,
inference(sat_conversion,[],[f923]) ).
cnf(s17,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f978]) ).
cnf(s46,plain,
~ spl0_4,
inference(sat_conversion,[],[f1458]) ).
cnf(s47,plain,
~ spl0_3,
inference(rat,[],[s17,s46]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s13,s47]) ).
fof(f1459,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 00:34:01 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 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
% 0.17/0.50 % (2160715)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (2160723)dis+10_1_sil=32000:sp=arity:random_seed=3469685909:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (2160721)% WARNING: option uhcvi not known.
% 0.17/0.50 % (2160720)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3183731680_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % (2160721)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1421931423:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (2160722)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4209858935:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (2160726)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2166126287:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % (2160724)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2072046832:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (2160725)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1181639627:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (2160723) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2160715-2160723"...
% 0.17/0.50 % (2160723)...printing done.
% 0.17/0.50 % (2160723)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (2160723)------------------------------
% 0.17/0.50 % (2160723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (2160723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (2160723)CaDiCaL version: 2.1.3
% 0.17/0.50 % (2160723)Termination reason: Refutation
% 0.17/0.50 % (2160723)Time elapsed: 0.023 s
% 0.17/0.50 % (2160723)Peak memory usage: 13 MB
% 0.17/0.50 % (2160723)Instructions burned: 65 (million)
% 0.17/0.50 % (2160715)Success in time 0.056 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------