%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET053-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:39:48 PM UTC 2026
% Result : Unsatisfiable 2.47s 1.21s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 19 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',ordered_pair) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f101,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_cartesian_product_1) ).
fof(f102,negated_conjecture,
~ member(v,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_cartesian_product_2) ).
fof(f107,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(f111,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(x,y)),
inference(definition_unfolding,[],[f101,f107]) ).
fof(f118,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,f107]) ).
fof(f173,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f180,plain,
! [X0] : ~ member(v,X0),
inference(resolution,[],[f173,f102]) ).
fof(f208,plain,
member(v,y),
inference(resolution,[],[f118,f111]) ).
fof(f213,plain,
$false,
inference(resolution,[],[f208,f180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET053-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:22:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 2.47/1.21 % (320684)Input is clausal, will run a generic CNF schedule.
% 2.47/1.21 % (320695)dis-21_1_sil=8000:lcm=predicate:random_seed=2010319352:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.47/1.21 % (320695)First to succeed.
% 2.47/1.21 % (320695)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-320684"
% 2.47/1.21 % (320690)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=131893629:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.47/1.21 % (320692)lrs+10_1_sil=8000:sp=occurrence:random_seed=1557059471:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.47/1.21 % (320689)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=3956736894:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.47/1.21 % (320691)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=509523449:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.47/1.21 % (320694)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4147925000:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.47/1.21 % (320692)Refutation not found, incomplete strategy
% 2.47/1.21 % (320692)------------------------------
% 2.47/1.21 % (320692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.21 % (320692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.21 % (320692)CaDiCaL version: 2.1.3
% 2.47/1.21 % (320692)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.21 % (320692)Time elapsed: 0.001 s
% 2.47/1.21 % (320692)Peak memory usage: 87 MB
% 2.47/1.21 % (320693)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=47647014:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.47/1.21 % (320693)Also succeeded, but the first one will report.
% 2.47/1.21 % (320694)Also succeeded, but the first one will report.
% 2.47/1.21 % (320695)Refutation found. Thanks to Tanya!
% 2.47/1.21 % SZS status Unsatisfiable for theBenchmark
% 2.47/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.47/1.21 % (320695)------------------------------
% 2.47/1.21 % (320695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.21 % (320695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.21 % (320695)CaDiCaL version: 2.1.3
% 2.47/1.21 % (320695)Termination reason: Refutation
% 2.47/1.21 % (320695)Time elapsed: 0.003 s
% 2.47/1.21 % (320695)Peak memory usage: 88 MB
% 2.47/1.21 % (320695)Instructions burned: 7 (million)
% 2.47/1.21 % (320695)------------------------------
% 2.47/1.21 % (320695)------------------------------
% 2.47/1.21 % (320684)Success in time 0.278 s
% 2.47/1.21 % Vampire exiting
%------------------------------------------------------------------------------