%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET072-6 : 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 : n011.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 : 13
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 15 unt; 2 def)
% Number of atoms : 66 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 28 |; 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 : 30 ( 0 sgn 30 !; 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(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
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(f101,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
fof(f102,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
fof(f103,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_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(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f102,f108]) ).
fof(f199,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(superposition,[],[f9,f101]) ).
fof(f201,definition,
( spl0_1
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f205,definition,
( spl0_2
<=> member(y,unordered_pair(x,z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f207,plain,
( member(y,unordered_pair(x,z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f199,f205,f201]) ).
fof(f293,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,z))
| y = X0
| z = X0 ),
inference(superposition,[],[f8,f101]) ).
fof(f337,plain,
member(x,universal_class),
inference(resolution,[],[f114,f152]) ).
fof(f339,plain,
member(y,universal_class),
inference(resolution,[],[f115,f152]) ).
fof(f343,plain,
spl0_1,
inference(avatar_split_clause,[],[f339,f201]) ).
fof(f372,plain,
( x = y
| z = y
| ~ spl0_2 ),
inference(resolution,[],[f207,f8]) ).
fof(f374,plain,
( z = y
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f372,f103]) ).
fof(f476,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(x,y))
| y = X0
| z = X0 )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f293,f374]) ).
fof(f477,plain,
( ! [X0] :
( y = X0
| ~ member(X0,unordered_pair(x,y))
| y = X0 )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f476,f374]) ).
fof(f478,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(x,y))
| y = X0 )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f477]) ).
fof(f490,plain,
( x = y
| ~ member(x,universal_class)
| ~ spl0_2 ),
inference(resolution,[],[f478,f9]) ).
fof(f525,plain,
( ~ member(x,universal_class)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f490,f103]) ).
fof(f531,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f525,f337]) ).
fof(f532,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f531]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f208]) ).
cnf(s8,plain,
spl0_1,
inference(sat_conversion,[],[f343]) ).
cnf(s24,plain,
~ spl0_2,
inference(sat_conversion,[],[f532]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s1,s24,s8]) ).
fof(f533,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n011.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 00:30:45 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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 % (2909880)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (2909886)% WARNING: option uhcvi not known.
% 0.17/0.48 % (2909886)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3436252421:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (2909888)dis+10_1_sil=32000:sp=arity:random_seed=142176427:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (2909885)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3746354148_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (2909887)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=699679967:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (2909889)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2461853162:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (2909890)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3308291098:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (2909891)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3399211598:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (2909886) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2909880-2909886"...
% 0.17/0.48 % (2909886)...printing done.
% 0.17/0.48 % (2909886)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 % (2909886)------------------------------
% 0.17/0.48 % (2909886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (2909886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (2909886)CaDiCaL version: 2.1.3
% 0.17/0.48 % (2909886)Termination reason: Refutation
% 0.17/0.48 % (2909886)Time elapsed: 0.010 s
% 0.17/0.48 % (2909886)Peak memory usage: 13 MB
% 0.17/0.48 % (2909886)Instructions burned: 23 (million)
% 0.17/0.48 % (2909880)Success in time 0.041 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------