%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n016.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 12:42:27 PM UTC 2026
% Result : Theorem 2.40s 1.23s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 12 unt; 3 def)
% Number of atoms : 52 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 14 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 29 !; 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(f18,plain,
( cartesian_product2(unordered_pair(sK2,sK3),sK4) != set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4))
| cartesian_product2(sK4,unordered_pair(sK2,sK3)) != set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f15]) ).
fof(f26,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(f27,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(f28,plain,
( cartesian_product2(unordered_pair(sK2,sK3),sK4) != set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4))
| cartesian_product2(sK4,unordered_pair(sK2,sK3)) != set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
( set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)) != cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4)
| set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))) != cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3))) ),
inference(definition_unfolding,[],[f28,f29,f29]) ).
fof(f32,definition,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ5_eqProxy])],[equality_proxy_definition]) ).
fof(f36,plain,
! [X2,X0,X1] : sQ5_eqProxy(cartesian_product2(set_union2(X0,X1),X2),set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))),
inference(equality_proxy_replacement,[],[f27,f32]) ).
fof(f37,plain,
! [X2,X0,X1] : sQ5_eqProxy(cartesian_product2(X2,set_union2(X0,X1)),set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1))),
inference(equality_proxy_replacement,[],[f26,f32]) ).
fof(f38,plain,
( ~ sQ5_eqProxy(set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)),cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4))
| ~ sQ5_eqProxy(set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))),cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3)))) ),
inference(equality_proxy_replacement,[],[f31,f32,f32]) ).
fof(f40,plain,
! [X0,X1] :
( sQ5_eqProxy(X1,X0)
| ~ sQ5_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f32]) ).
fof(f42,definition,
( spl6_1
<=> sQ5_eqProxy(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,[spl6_1])],[avatar_definition]) ).
fof(f43,plain,
( ~ sQ5_eqProxy(set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))),cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3))))
| spl6_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,definition,
( spl6_2
<=> sQ5_eqProxy(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,[spl6_2])],[avatar_definition]) ).
fof(f46,plain,
( ~ sQ5_eqProxy(set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)),cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4))
| spl6_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f38,f45,f42]) ).
fof(f48,plain,
( ~ sQ5_eqProxy(cartesian_product2(sK4,set_union2(singleton(sK2),singleton(sK3))),set_union2(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK4,singleton(sK3))))
| spl6_1 ),
inference(resolution,[],[f40,f43]) ).
fof(f50,plain,
( $false
| spl6_1 ),
inference(resolution,[],[f37,f48]) ).
fof(f51,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f52,plain,
( ~ sQ5_eqProxy(cartesian_product2(set_union2(singleton(sK2),singleton(sK3)),sK4),set_union2(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK4)))
| spl6_2 ),
inference(resolution,[],[f46,f40]) ).
fof(f53,plain,
( $false
| spl6_2 ),
inference(resolution,[],[f52,f36]) ).
fof(f55,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
spl6_1,
inference(sat_conversion,[],[f51]) ).
cnf(s3,plain,
spl6_2,
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET979+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n016.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:23:33 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.40/1.23 % (3228488)Detected formulas, will run a generic FOF schedule.
% 2.40/1.23 % (3228499)dis-21_1_sil=8000:lcm=predicate:random_seed=841971408:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.40/1.23 % (3228499)First to succeed.
% 2.40/1.23 % (3228499)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3228488"
% 2.40/1.23 % (3228495)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2357882643:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.40/1.23 % (3228494)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3933722058:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.40/1.23 % (3228497)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3972287430:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.40/1.23 % (3228493)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3795884134:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.40/1.23 % (3228496)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1680919985:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.40/1.23 % (3228498)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1986718763:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.40/1.23 % (3228496)Also succeeded, but the first one will report.
% 2.40/1.23 % (3228497)Also succeeded, but the first one will report.
% 2.40/1.23 % (3228498)Also succeeded, but the first one will report.
% 2.40/1.23 % (3228499)Refutation found. Thanks to Tanya!
% 2.40/1.23 % SZS status Theorem for theBenchmark
% 2.40/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/1.23 % (3228499)------------------------------
% 2.40/1.23 % (3228499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/1.23 % (3228499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/1.23 % (3228499)CaDiCaL version: 2.1.3
% 2.40/1.23 % (3228499)Termination reason: Refutation
% 2.40/1.23 % (3228499)Time elapsed: 0.002 s
% 2.40/1.23 % (3228499)Peak memory usage: 89 MB
% 2.40/1.23 % (3228499)Instructions burned: 2 (million)
% 2.40/1.23 % (3228499)------------------------------
% 2.40/1.23 % (3228499)------------------------------
% 2.40/1.23 % (3228488)Success in time 0.27 s
% 2.40/1.23 % Vampire exiting
%------------------------------------------------------------------------------