%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT011-2 : 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 : 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 09:36:36 AM UTC 2026
% Result : Unsatisfiable 2.06s 0.66s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 5 ( 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : codomain(domain(X0)) = domain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_of_domain_is_domain) ).
fof(f2,plain,
! [X0] : domain(X0) = codomain(domain(X0)),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X0] : domain(codomain(X0)) = codomain(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
fof(f4,plain,
! [X0] : codomain(X0) = domain(codomain(X0)),
inference(reorient_equations,[],[f3]) ).
fof(f11,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
fof(f12,plain,
domain(a) != domain(domain(a)),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(superposition,[],[f4,f2]) ).
fof(f21,plain,
domain(a) != domain(a),
inference(superposition,[],[f12,f13]) ).
fof(f25,plain,
$false,
inference(trivial_inequality_removal,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CAT011-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 21:12:49 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 2.06/0.66 % (3774226)Input is clausal, will run a generic CNF schedule.
% 2.06/0.66 % (3774235)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3588758425:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.06/0.66 % (3774233)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1039746830:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.06/0.66 % (3774236)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2625180397:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.06/0.66 % (3774232)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3715688157:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.06/0.66 % (3774231)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=3009835338:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.06/0.66 % (3774237)dis-21_1_sil=8000:lcm=predicate:random_seed=3425226240: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)
% 2.06/0.66 % (3774234)lrs+10_1_sil=8000:sp=occurrence:random_seed=3337645546:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.06/0.66 % (3774237)Refutation not found, incomplete strategy
% 2.06/0.66 % (3774237)------------------------------
% 2.06/0.66 % (3774237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/0.66 % (3774237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.66 % (3774237)CaDiCaL version: 2.1.3
% 2.06/0.66 % (3774237)Termination reason: Refutation not found, incomplete strategy
% 2.06/0.66 % (3774237)Time elapsed: 0.0000 s
% 2.06/0.66 % (3774237)Peak memory usage: 88 MB
% 2.06/0.66 % (3774234)Also succeeded, but the first one will report.
% 2.06/0.66 % (3774235)Also succeeded, but the first one will report.
% 2.06/0.66 % (3774236)First to succeed.
% 2.06/0.66 % (3774236)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3774226"
% 2.06/0.66 % (3774237)------------------------------
% 2.06/0.66 % (3774237)------------------------------
% 2.06/0.66 % (3774236)Refutation found. Thanks to Tanya!
% 2.06/0.66 % SZS status Unsatisfiable for theBenchmark
% 2.06/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 2.06/0.66 % (3774236)------------------------------
% 2.06/0.66 % (3774236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.06/0.66 % (3774236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.06/0.66 % (3774236)CaDiCaL version: 2.1.3
% 2.06/0.66 % (3774236)Termination reason: Refutation
% 2.06/0.66 % (3774236)Time elapsed: 0.001 s
% 2.06/0.66 % (3774236)Peak memory usage: 88 MB
% 2.06/0.66 % (3774236)Instructions burned: 1 (million)
% 2.06/0.66 % (3774236)------------------------------
% 2.06/0.66 % (3774236)------------------------------
% 2.06/0.66 % (3774226)Success in time 0.263 s
% 2.06/0.67 % Vampire exiting
%------------------------------------------------------------------------------