%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT005-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:36:34 AM UTC 2026
% Result : Unsatisfiable 2.79s 1.18s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 11 unt; 2 def)
% Number of atoms : 47 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 16 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f20,axiom,
there_exists(compose(a,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ad_exists) ).
fof(f21,axiom,
! [X0] :
( compose(X0,d) = X0
| ~ there_exists(compose(X0,d)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xd_equals_x) ).
fof(f23,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
fof(f24,plain,
d != domain(a),
inference(reorient_equations,[],[f23]) ).
fof(f38,plain,
( d = codomain(d)
| ~ there_exists(compose(codomain(d),d)) ),
inference(superposition,[],[f11,f21]) ).
fof(f39,plain,
( ~ there_exists(d)
| d = codomain(d) ),
inference(forward_demodulation,[],[f38,f11]) ).
fof(f41,definition,
( spl0_1
<=> there_exists(d) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f43,plain,
( ~ there_exists(d)
| spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl0_2
<=> d = codomain(d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f47,plain,
( d = codomain(d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f49,plain,
( spl0_2
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f39,f41,f45]) ).
fof(f56,plain,
domain(a) = codomain(d),
inference(resolution,[],[f7,f20]) ).
fof(f79,plain,
( ~ there_exists(domain(a))
| there_exists(d) ),
inference(superposition,[],[f5,f56]) ).
fof(f80,plain,
( ~ there_exists(domain(a))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f79,f43]) ).
fof(f82,plain,
( ! [X0] : ~ there_exists(compose(a,X0))
| spl0_1 ),
inference(resolution,[],[f80,f6]) ).
fof(f88,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f82,f20]) ).
fof(f93,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f107,plain,
( d = domain(a)
| ~ spl0_2 ),
inference(superposition,[],[f47,f56]) ).
fof(f114,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f107,f24]) ).
fof(f115,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s2,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f93]) ).
cnf(s7,plain,
~ spl0_2,
inference(sat_conversion,[],[f115]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s7,s3]) ).
fof(f116,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:15:10 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.79/1.18 % (3794333)Input is clausal, will run a generic CNF schedule.
% 2.79/1.18 % (3794420)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3405492606:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.79/1.18 % (3794420)First to succeed.
% 2.79/1.18 % (3794420)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3794333"
% 2.79/1.18 % (3794419)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1043655171:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.79/1.18 % (3794413)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=1245931742:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.79/1.18 % (3794414)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3663485243:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.79/1.18 % (3794419)Also succeeded, but the first one will report.
% 2.79/1.18 % (3794417)lrs+10_1_sil=8000:sp=occurrence:random_seed=684309426:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.79/1.18 % (3794422)dis-21_1_sil=8000:lcm=predicate:random_seed=2564101492: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)
% 2.79/1.18 % (3794417)Also succeeded, but the first one will report.
% 2.79/1.18 % (3794416)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=81014166:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.79/1.18 % (3794422)Instruction limit reached!
% 2.79/1.18 % (3794422)------------------------------
% 2.79/1.18 % (3794422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.18 % (3794422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.18 % (3794422)CaDiCaL version: 2.1.3
% 2.79/1.18 % (3794422)Termination reason: Instruction limit
% 2.79/1.18 % (3794422)Termination phase: Saturation
% 2.79/1.18 % (3794422)Time elapsed: 0.064 s
% 2.79/1.18 % (3794422)Peak memory usage: 90 MB
% 2.79/1.18 % (3794422)Instructions burned: 120 (million)
% 2.79/1.18 % (3794420)Refutation found. Thanks to Tanya!
% 2.79/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.79/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/1.18 % (3794420)------------------------------
% 2.79/1.18 % (3794420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.18 % (3794420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.18 % (3794420)CaDiCaL version: 2.1.3
% 2.79/1.18 % (3794420)Termination reason: Refutation
% 2.79/1.18 % (3794420)Time elapsed: 0.003 s
% 2.79/1.18 % (3794420)Peak memory usage: 89 MB
% 2.79/1.18 % (3794420)Instructions burned: 4 (million)
% 2.79/1.18 % (3794420)------------------------------
% 2.79/1.18 % (3794420)------------------------------
% 2.79/1.18 % (3794333)Success in time 0.313 s
% 2.79/1.18 % Vampire exiting
%------------------------------------------------------------------------------