%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET017-7 : 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 : n018.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 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 23 unt; 3 def)
% Number of atoms : 100 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 35 ~; 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; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f10,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f126,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
fof(f127,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
fof(f128,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
fof(f133,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(f139,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,f133]) ).
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(X1,X3) ),
inference(definition_unfolding,[],[f15,f133]) ).
fof(f185,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f127,f133]) ).
fof(f425,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,y))
| x = X0
| z = X0 ),
inference(superposition,[],[f8,f126]) ).
fof(f430,plain,
( x = regular(unordered_pair(x,y))
| z = regular(unordered_pair(x,y))
| null_class = unordered_pair(x,y) ),
inference(resolution,[],[f425,f68]) ).
fof(f432,definition,
( spl0_12
<=> null_class = unordered_pair(x,y) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f434,plain,
( null_class = unordered_pair(x,y)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f436,definition,
( spl0_13
<=> z = regular(unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f437,plain,
( z != regular(unordered_pair(x,y))
| spl0_13 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f438,plain,
( z = regular(unordered_pair(x,y))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f440,definition,
( spl0_14
<=> x = regular(unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f442,plain,
( x = regular(unordered_pair(x,y))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f443,plain,
( spl0_12
| spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f430,f440,f436,f432]) ).
fof(f774,plain,
member(y,universal_class),
inference(resolution,[],[f139,f185]) ).
fof(f791,plain,
! [X0] : member(y,unordered_pair(X0,y)),
inference(resolution,[],[f774,f10]) ).
fof(f795,plain,
member(z,universal_class),
inference(resolution,[],[f140,f185]) ).
fof(f812,plain,
! [X0] : member(z,unordered_pair(X0,z)),
inference(resolution,[],[f795,f10]) ).
fof(f836,plain,
( x = y
| y = z ),
inference(resolution,[],[f791,f425]) ).
fof(f841,plain,
( member(y,null_class)
| ~ spl0_12 ),
inference(superposition,[],[f791,f434]) ).
fof(f848,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f841,f113]) ).
fof(f849,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f848]) ).
fof(f850,plain,
x = y,
inference(forward_subsumption_resolution,[],[f836,f128]) ).
fof(f852,plain,
( z = regular(unordered_pair(x,x))
| ~ spl0_13 ),
inference(forward_demodulation,[],[f438,f850]) ).
fof(f952,plain,
member(z,unordered_pair(x,y)),
inference(superposition,[],[f812,f126]) ).
fof(f953,plain,
member(z,unordered_pair(x,x)),
inference(forward_demodulation,[],[f952,f850]) ).
fof(f1072,plain,
( y != regular(unordered_pair(x,x))
| ~ spl0_13 ),
inference(superposition,[],[f128,f852]) ).
fof(f1080,plain,
( x != regular(unordered_pair(x,x))
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1072,f850]) ).
fof(f1211,plain,
( z != regular(unordered_pair(x,x))
| spl0_13 ),
inference(forward_demodulation,[],[f437,f850]) ).
fof(f1212,plain,
( x = regular(unordered_pair(x,x))
| ~ spl0_14 ),
inference(forward_demodulation,[],[f442,f850]) ).
fof(f1290,plain,
( x != z
| spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1211,f1212]) ).
fof(f1341,plain,
( x = z
| x = z ),
inference(resolution,[],[f953,f8]) ).
fof(f1345,plain,
x = z,
inference(duplicate_literal_removal,[],[f1341]) ).
fof(f1346,plain,
( $false
| spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1345,f1290]) ).
fof(f1347,plain,
( spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f1346]) ).
fof(f1348,plain,
( z = regular(unordered_pair(x,x))
| ~ spl0_13 ),
inference(forward_demodulation,[],[f438,f850]) ).
fof(f1356,plain,
( x = regular(unordered_pair(x,x))
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1348,f1345]) ).
fof(f1359,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1356,f1080]) ).
fof(f1360,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f1359]) ).
cnf(s11,plain,
( spl0_12
| spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f443]) ).
cnf(s16,plain,
~ spl0_12,
inference(sat_conversion,[],[f849]) ).
cnf(s37,plain,
( spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f1347]) ).
cnf(s40,plain,
~ spl0_13,
inference(sat_conversion,[],[f1360]) ).
cnf(s41,plain,
~ spl0_14,
inference(rat,[],[s37,s40]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s11,s41,s40,s16]) ).
fof(f1361,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 00:11:09 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 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
% 0.11/0.45 % (2871613)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2871623)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1638899390:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (2871619)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2871620)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3230642319:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (2871618)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1302056639_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (2871624)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=890229118:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (2871621)dis+10_1_sil=32000:sp=arity:random_seed=3476685792:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (2871622)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3812779843:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2871619)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1843653598:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (2871623) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2871613-2871623"...
% 0.11/0.45 % (2871623)...printing done.
% 0.11/0.45 % (2871623)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2871623)------------------------------
% 0.11/0.45 % (2871623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2871623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2871623)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2871623)Termination reason: Refutation
% 0.11/0.45 % (2871623)Time elapsed: 0.019 s
% 0.11/0.45 % (2871623)Peak memory usage: 13 MB
% 0.11/0.45 % (2871623)Instructions burned: 53 (million)
% 0.11/0.45 % (2871613)Success in time 0.052 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------