%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO057-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:51:23 AM UTC 2026
% Result : Unsatisfiable 3.46s 1.48s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 1 def)
% Number of atoms : 13 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-4 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
fof(f29,axiom,
! [X2,X0,X1] : X0 = extension(X1,X0,X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
fof(f30,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(reorient_equations,[],[f29]) ).
fof(f35,negated_conjecture,
u != reflection(u,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_extension_by_reflection) ).
fof(f38,plain,
u != extension(u,u,u,u),
inference(definition_unfolding,[],[f35,f19]) ).
fof(f40,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f41,plain,
! [X2,X0,X1] : sQ0_eqProxy(extension(X1,X0,X2,X2),X0),
inference(equality_proxy_replacement,[],[f30,f40]) ).
fof(f42,plain,
~ sQ0_eqProxy(u,extension(u,u,u,u)),
inference(equality_proxy_replacement,[],[f38,f40]) ).
fof(f48,plain,
! [X0,X1] :
( sQ0_eqProxy(X1,X0)
| ~ sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f40]) ).
fof(f49,plain,
~ sQ0_eqProxy(extension(u,u,u,u),u),
inference(resolution,[],[f48,f42]) ).
fof(f50,plain,
$false,
inference(resolution,[],[f49,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO057-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n015.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 06:49:30 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 3.46/1.48 % (1297191)Input is clausal, will run a generic CNF schedule.
% 3.46/1.48 % (1297197)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3659355538:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.46/1.48 % (1297199)lrs+10_1_sil=8000:sp=occurrence:random_seed=671022971:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.46/1.48 % (1297198)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2063392029:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.46/1.48 % (1297200)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3504666767:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.46/1.48 % (1297202)dis-21_1_sil=8000:lcm=predicate:random_seed=3121767680: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)
% 3.46/1.48 % (1297196)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=1803208879:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.46/1.48 % (1297201)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1917464156:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.46/1.48 % (1297199)Also succeeded, but the first one will report.
% 3.46/1.48 % (1297200)Also succeeded, but the first one will report.
% 3.46/1.48 % (1297202)First to succeed.
% 3.46/1.48 % (1297202)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1297191"
% 3.46/1.48 % (1297201)Also succeeded, but the first one will report.
% 3.46/1.48 % (1297202)Refutation found. Thanks to Tanya!
% 3.46/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.46/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.48 % (1297202)------------------------------
% 3.46/1.48 % (1297202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.48 % (1297202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.48 % (1297202)CaDiCaL version: 2.1.3
% 3.46/1.48 % (1297202)Termination reason: Refutation
% 3.46/1.48 % (1297202)Time elapsed: 0.002 s
% 3.46/1.48 % (1297202)Peak memory usage: 88 MB
% 3.46/1.48 % (1297202)Instructions burned: 1 (million)
% 3.46/1.48 % (1297202)------------------------------
% 3.46/1.48 % (1297202)------------------------------
% 3.46/1.48 % (1297191)Success in time 0.408 s
% 3.46/1.48 % Vampire exiting
%------------------------------------------------------------------------------