%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT005-4 : 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 : 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 09:36:34 AM UTC 2026
% Result : Unsatisfiable 3.60s 1.22s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 12 unt; 2 def)
% Number of atoms : 45 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 15 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 12 ( 0 sgn 12 !; 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(compose(X0,X1))
| there_exists(domain(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,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(f12,axiom,
there_exists(compose(a,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ad_exists) ).
fof(f13,axiom,
! [X0] :
( compose(X0,d) = X0
| ~ there_exists(compose(X0,d)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xd_equals_x) ).
fof(f15,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
fof(f16,plain,
d != domain(a),
inference(reorient_equations,[],[f15]) ).
fof(f20,plain,
( d = codomain(d)
| ~ there_exists(d) ),
inference(superposition,[],[f13,f11]) ).
fof(f28,definition,
( spl0_2
<=> d = codomain(d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f29,plain,
( d = codomain(d)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f33,definition,
( spl0_3
<=> there_exists(d) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f34,plain,
( ~ there_exists(d)
| spl0_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f35,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f20,f28,f33]) ).
fof(f49,plain,
! [X0] :
( ~ there_exists(compose(a,X0))
| codomain(X0) != d ),
inference(superposition,[],[f16,f7]) ).
fof(f53,plain,
! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(superposition,[],[f5,f7]) ).
fof(f54,plain,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(X1) ),
inference(forward_subsumption_resolution,[],[f53,f6]) ).
fof(f55,plain,
d != codomain(d),
inference(resolution,[],[f49,f12]) ).
fof(f105,plain,
there_exists(d),
inference(resolution,[],[f54,f12]) ).
fof(f111,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f105,f34]) ).
fof(f112,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f113,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f29,f55]) ).
fof(f114,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
spl0_3,
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
~ spl0_2,
inference(sat_conversion,[],[f114]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s5,s6]) ).
fof(f121,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:13:49 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.60/1.22 % (566945)Input is clausal, will run a generic CNF schedule.
% 3.60/1.22 % (567082)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1595909254:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.60/1.22 % (567080)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=1206342020:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.60/1.22 % (567081)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2920894143:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.60/1.22 % (567084)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=611343249:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.60/1.22 % (567085)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1649760407:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.60/1.22 % (567084)First to succeed.
% 3.60/1.22 % (567084)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-566945"
% 3.60/1.22 % (567085)Also succeeded, but the first one will report.
% 3.60/1.22 % (567086)dis-21_1_sil=8000:lcm=predicate:random_seed=2567788487: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)
% 3.60/1.22 % (567086)Refutation not found, incomplete strategy
% 3.60/1.22 % (567086)------------------------------
% 3.60/1.22 % (567086)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.22 % (567086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.22 % (567086)CaDiCaL version: 2.1.3
% 3.60/1.22 % (567086)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.22 % (567086)Time elapsed: 0.002 s
% 3.60/1.22 % (567086)Peak memory usage: 88 MB
% 3.60/1.22 % (567086)Instructions burned: 1 (million)
% 3.60/1.22 % (567083)lrs+10_1_sil=8000:sp=occurrence:random_seed=1216782595:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.60/1.22 % (567083)Also succeeded, but the first one will report.
% 3.60/1.22 % (567084)Refutation found. Thanks to Tanya!
% 3.60/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.60/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.22 % (567084)------------------------------
% 3.60/1.22 % (567084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.22 % (567084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.22 % (567084)CaDiCaL version: 2.1.3
% 3.60/1.22 % (567084)Termination reason: Refutation
% 3.60/1.22 % (567084)Time elapsed: 0.005 s
% 3.60/1.22 % (567084)Peak memory usage: 89 MB
% 3.60/1.22 % (567084)Instructions burned: 4 (million)
% 3.60/1.22 % (567084)------------------------------
% 3.60/1.22 % (567084)------------------------------
% 3.60/1.22 % (566945)Success in time 0.434 s
% 3.60/1.22 % Vampire exiting
%------------------------------------------------------------------------------