%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT006-3 : 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 : 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 09:36:35 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.23s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 14 unt; 1 def)
% Number of atoms : 32 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 8 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 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/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f7,axiom,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
fof(f14,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(codomain(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_codomain) ).
fof(f20,axiom,
there_exists(compose(d,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',da_exists) ).
fof(f22,axiom,
! [X0] :
( compose(d,X0) = X0
| ~ there_exists(compose(d,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dx_equals_x) ).
fof(f23,negated_conjecture,
codomain(a) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_is_d) ).
fof(f24,plain,
d != codomain(a),
inference(reorient_equations,[],[f23]) ).
fof(f28,plain,
there_exists(codomain(d)),
inference(resolution,[],[f14,f20]) ).
fof(f44,definition,
( spl0_3
<=> there_exists(d) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f45,plain,
( ~ there_exists(d)
| spl0_3 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( d = domain(d)
| ~ there_exists(d) ),
inference(superposition,[],[f22,f10]) ).
fof(f65,plain,
! [X0] :
( ~ there_exists(compose(X0,a))
| domain(X0) != d ),
inference(superposition,[],[f24,f7]) ).
fof(f69,plain,
d != domain(d),
inference(resolution,[],[f65,f20]) ).
fof(f90,plain,
there_exists(d),
inference(resolution,[],[f28,f5]) ).
fof(f92,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f90,f45]) ).
fof(f93,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f92]) ).
fof(f94,plain,
~ there_exists(d),
inference(forward_subsumption_resolution,[],[f47,f69]) ).
fof(f95,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f94,f44]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f93]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s4,s5]) ).
fof(f96,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n020.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Mon Sep 28 21:13:50 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running first-order theorem proving
% 0.11/0.22 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
% 2.62/1.23 % (567075)Input is clausal, will run a generic CNF schedule.
% 2.62/1.23 % (567099)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2088380246:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.23 % (567099)First to succeed.
% 2.62/1.23 % (567099)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-567075"
% 2.62/1.23 % (567095)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=1732439574:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.23 % (567101)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2933706556:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.23 % (567098)lrs+10_1_sil=8000:sp=occurrence:random_seed=2624293023:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.23 % (567102)dis-21_1_sil=8000:lcm=predicate:random_seed=662104748: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)
% 2.62/1.23 % (567097)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4252027571:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.23 % (567098)Also succeeded, but the first one will report.
% 2.62/1.23 % (567101)Also succeeded, but the first one will report.
% 2.62/1.23 % (567096)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2649803638:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.23 % (567102)Instruction limit reached!
% 2.62/1.23 % (567102)------------------------------
% 2.62/1.23 % (567102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.23 % (567102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.23 % (567102)CaDiCaL version: 2.1.3
% 2.62/1.23 % (567102)Termination reason: Instruction limit
% 2.62/1.23 % (567102)Termination phase: Saturation
% 2.62/1.23 % (567102)Time elapsed: 0.056 s
% 2.62/1.23 % (567102)Peak memory usage: 90 MB
% 2.62/1.23 % (567102)Instructions burned: 119 (million)
% 2.62/1.23 % (567099)Refutation found. Thanks to Tanya!
% 2.62/1.23 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.23 % (567099)------------------------------
% 2.62/1.23 % (567099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.23 % (567099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.23 % (567099)CaDiCaL version: 2.1.3
% 2.62/1.23 % (567099)Termination reason: Refutation
% 2.62/1.23 % (567099)Time elapsed: 0.002 s
% 2.62/1.23 % (567099)Peak memory usage: 89 MB
% 2.62/1.23 % (567099)Instructions burned: 3 (million)
% 2.62/1.23 % (567099)------------------------------
% 2.62/1.23 % (567099)------------------------------
% 2.62/1.23 % (567075)Success in time 0.256 s
% 2.62/1.23 % Vampire exiting
%------------------------------------------------------------------------------