%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:40:09 PM UTC 2026
% Result : Unsatisfiable 2.65s 1.34s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 20 ( 13 unt; 1 def)
% Number of atoms : 27 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f124,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f138,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f166,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_1) ).
fof(f167,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_2) ).
fof(f168,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_3) ).
fof(f169,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(f170,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f166,f12,f169]) ).
fof(f177,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X1)
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f124,f12]) ).
fof(f197,plain,
! [X0] :
( unordered_pair(X0,X0) = null_class
| member(X0,universal_class) ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f200,definition,
~ sP0(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f201,plain,
sP0(unordered_pair(null_class,unordered_pair(null_class,null_class))),
inference(inequality_splitting,[],[f170,f200]) ).
fof(f239,plain,
( ~ sP0(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)))
| member(y,universal_class) ),
inference(superposition,[],[f200,f197]) ).
fof(f248,plain,
~ sP0(unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class))),
inference(forward_subsumption_resolution,[],[f239,f168]) ).
fof(f250,plain,
( ~ sP0(unordered_pair(null_class,unordered_pair(x,null_class)))
| member(x,universal_class) ),
inference(superposition,[],[f248,f197]) ).
fof(f256,plain,
~ sP0(unordered_pair(null_class,unordered_pair(x,null_class))),
inference(forward_subsumption_resolution,[],[f250,f167]) ).
fof(f309,plain,
( ~ sP0(unordered_pair(null_class,unordered_pair(null_class,null_class)))
| member(x,universal_class) ),
inference(superposition,[],[f256,f177]) ).
fof(f333,plain,
member(x,universal_class),
inference(forward_subsumption_resolution,[],[f309,f201]) ).
fof(f334,plain,
$false,
inference(forward_subsumption_resolution,[],[f333,f167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:45:19 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.65/1.34 % (3925977)Input is clausal, will run a generic CNF schedule.
% 2.65/1.34 % (3925986)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2523288473:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.34 % (3925986)First to succeed.
% 2.65/1.34 % (3925986)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3925977"
% 2.65/1.34 % (3925982)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=98791705:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.34 % (3925983)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1404093128:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.34 % (3925985)lrs+10_1_sil=8000:sp=occurrence:random_seed=3704231651:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.34 % (3925984)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=660327297:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.34 % (3925985)Also succeeded, but the first one will report.
% 2.65/1.34 % (3925987)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=205873310:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.34 % (3925988)dis-21_1_sil=8000:lcm=predicate:random_seed=3665242419: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)
% 2.65/1.34 % (3925988)Instruction limit reached!
% 2.65/1.34 % (3925988)------------------------------
% 2.65/1.34 % (3925988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (3925988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (3925988)CaDiCaL version: 2.1.3
% 2.65/1.34 % (3925988)Termination reason: Instruction limit
% 2.65/1.34 % (3925988)Termination phase: Saturation
% 2.65/1.34 % (3925988)Time elapsed: 0.074 s
% 2.65/1.34 % (3925988)Peak memory usage: 89 MB
% 2.65/1.34 % (3925988)Instructions burned: 118 (million)
% 2.65/1.34 % (3925986)Refutation found. Thanks to Tanya!
% 2.65/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.34 % (3925986)------------------------------
% 2.65/1.34 % (3925986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.34 % (3925986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.34 % (3925986)CaDiCaL version: 2.1.3
% 2.65/1.34 % (3925986)Termination reason: Refutation
% 2.65/1.34 % (3925986)Time elapsed: 0.004 s
% 2.65/1.34 % (3925986)Peak memory usage: 89 MB
% 2.65/1.34 % (3925986)Instructions burned: 7 (million)
% 2.65/1.34 % (3925986)------------------------------
% 2.65/1.34 % (3925986)------------------------------
% 2.65/1.34 % (3925977)Success in time 0.291 s
% 2.65/1.34 % Vampire exiting
%------------------------------------------------------------------------------