%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET017-6 : 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 : n006.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 12:42:38 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 17 unt; 4 def)
% Number of atoms : 85 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 32 ~; 34 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 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(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(f101,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
fof(f102,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
fof(f103,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
fof(f108,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(f114,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,f108]) ).
fof(f115,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,f108]) ).
fof(f152,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f102,f108]) ).
fof(f162,plain,
( member(z,unordered_pair(x,y))
| ~ member(z,universal_class) ),
inference(superposition,[],[f10,f101]) ).
fof(f164,definition,
( spl0_1
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f166,plain,
( ~ member(z,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f168,definition,
( spl0_2
<=> member(z,unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f170,plain,
( member(z,unordered_pair(x,y))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f171,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f162,f168,f164]) ).
fof(f221,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,y))
| x = X0
| z = X0 ),
inference(superposition,[],[f8,f101]) ).
fof(f223,plain,
( x = y
| y = z
| ~ member(y,universal_class) ),
inference(resolution,[],[f221,f10]) ).
fof(f238,plain,
( x = y
| ~ member(y,universal_class) ),
inference(forward_subsumption_resolution,[],[f223,f103]) ).
fof(f240,definition,
( spl0_6
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f242,plain,
( ~ member(y,universal_class)
| spl0_6 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f244,definition,
( spl0_7
<=> x = y ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f246,plain,
( x = y
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f247,plain,
( ~ spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f238,f244,f240]) ).
fof(f291,plain,
member(y,universal_class),
inference(resolution,[],[f114,f152]) ).
fof(f292,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f291,f242]) ).
fof(f293,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f295,plain,
member(z,universal_class),
inference(resolution,[],[f115,f152]) ).
fof(f296,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f295,f166]) ).
fof(f297,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f296]) ).
fof(f311,plain,
( member(z,unordered_pair(y,y))
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f170,f246]) ).
fof(f324,plain,
( y = z
| y = z
| ~ spl0_2
| ~ spl0_7 ),
inference(resolution,[],[f311,f8]) ).
fof(f326,plain,
( y = z
| ~ spl0_2
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f324]) ).
fof(f327,plain,
( $false
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f326,f103]) ).
fof(f328,plain,
( ~ spl0_2
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f327]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s3,plain,
( ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f247]) ).
cnf(s5,plain,
spl0_6,
inference(sat_conversion,[],[f293]) ).
cnf(s6,plain,
spl0_1,
inference(sat_conversion,[],[f297]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_7 ),
inference(sat_conversion,[],[f328]) ).
cnf(s10,plain,
spl0_7,
inference(rat,[],[s3,s5]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s9,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s11,s6]) ).
fof(f329,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET017-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:08:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.46 % (3471792)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (3471799)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=869695799:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (3471798)% WARNING: option uhcvi not known.
% 0.11/0.46 % (3471800)dis+10_1_sil=32000:sp=arity:random_seed=768592869:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (3471797)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3118390450_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (3471801)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4148164079:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (3471802)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2384631290:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (3471803)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4213816671:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (3471798)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3570502596:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (3471801) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3471792-3471801"...
% 0.11/0.46 % (3471800) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3471792-3471800"...
% 0.11/0.46 % (3471801)...printing done.
% 0.11/0.46 % (3471798) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3471792-3471798"...
% 0.11/0.46 % (3471800)...printing done.
% 0.11/0.46 % (3471801)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (3471801)------------------------------
% 0.11/0.46 % (3471801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (3471801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (3471801)CaDiCaL version: 2.1.3
% 0.11/0.46 % (3471801)Termination reason: Refutation
% 0.11/0.46 % (3471801)Time elapsed: 0.011 s
% 0.11/0.46 % (3471801)Peak memory usage: 12 MB
% 0.11/0.46 % (3471801)Instructions burned: 15 (million)
% 0.11/0.46 % (3471792)Success in time 0.054 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------