%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:45:07 PM UTC 2026
% Result : Theorem 0.06s 0.37s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 2 def)
% Number of atoms : 38 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 9 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
( cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2))
& cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2))
& cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1))) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,axiom,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f15,plain,
? [X0,X1,X2] :
( cartesian_product2(unordered_pair(X0,X1),X2) != set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2))
| cartesian_product2(X2,unordered_pair(X0,X1)) != set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1))) ),
inference(ennf_transformation,[],[f10]) ).
fof(f23,plain,
! [X2,X0,X1] : cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f24,plain,
! [X2,X0,X1] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f25,plain,
( cartesian_product2(sK4,unordered_pair(sK2,sK3)) != set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3)))
| cartesian_product2(unordered_pair(sK2,sK3),sK4) != set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f28,plain,
( set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) != cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3)))
| set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) != cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4) ),
inference(definition_unfolding,[],[f25,f26,f26]) ).
fof(f30,definition,
( spl5_1
<=> set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) = cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f32,plain,
( set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) != cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f34,definition,
( spl5_2
<=> set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) = cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3))) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f36,plain,
( set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) != cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3)))
| spl5_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f28,f34,f30]) ).
fof(f38,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f32,f24]) ).
fof(f39,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f40,plain,
( $false
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f36,f23]) ).
fof(f41,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f40]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
spl5_2,
inference(sat_conversion,[],[f41]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f42,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 03:18:19 UTC 2026
% 0.03/0.32 % CPUTime :
% 0.03/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.33 Running first-order model finding
% 0.06/0.33 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
% 0.06/0.37 % (2985332)Will run a generic schedule for satisfiability detection.
% 0.06/0.37 % (2985338)% WARNING: option uhcvi not known.
% 0.06/0.37 % (2985337)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1135117048_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.37 % (2985338)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2208698060:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.37 % (2985339)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=680381017:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.37 % (2985341)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3646524179:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.37 % (2985340)dis+10_1_sil=32000:sp=arity:random_seed=1985757001:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.37 % (2985342)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2992919890:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.37 % (2985343)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=552932851:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.37 % (2985341) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2985332-2985341"...
% 0.06/0.37 % (2985342) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2985332-2985342"...
% 0.06/0.37 % TRYING [1]
% 0.06/0.37 % TRYING [2]
% 0.06/0.37 % (2985338) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2985332-2985338"...
% 0.06/0.37 % (2985343) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2985332-2985343"...
% 0.06/0.37 % (2985340) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2985332-2985340"...
% 0.06/0.37 % (2985341)...printing done.
% 0.06/0.37 % (2985342)...printing done.
% 0.06/0.37 % (2985339) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2985332-2985339"...
% 0.06/0.37 % TRYING [3]
% 0.06/0.37 % (2985338)...printing done.
% 0.06/0.37 % (2985343)...printing done.
% 0.06/0.37 % (2985341)Refutation found. Thanks to Tanya!
% 0.06/0.37 % SZS status Theorem for theBenchmark
% 0.06/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.37 % (2985341)------------------------------
% 0.06/0.37 % (2985341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.37 % (2985341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.37 % (2985341)CaDiCaL version: 2.1.3
% 0.06/0.37 % (2985341)Termination reason: Refutation
% 0.06/0.37 % (2985341)Time elapsed: 0.001 s
% 0.06/0.37 % (2985341)Peak memory usage: 12 MB
% 0.06/0.37 % (2985341)Instructions burned: 1 (million)
% 0.06/0.37 % (2985332)Success in time 0.027 s
% 0.06/0.37 % Vampire exiting
%------------------------------------------------------------------------------