%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT009-4 : 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 : n004.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 2.72s 1.09s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 18 unt; 4 def)
% Number of atoms : 103 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 93 ( 46 ~; 43 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 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(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
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,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
fof(f13,negated_conjecture,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
fof(f21,plain,
domain(a) = codomain(b),
inference(resolution,[],[f7,f12]) ).
fof(f24,plain,
! [X0] :
( domain(X0) = codomain(domain(X0))
| ~ there_exists(X0) ),
inference(superposition,[],[f7,f10]) ).
fof(f27,plain,
( ~ there_exists(domain(a))
| there_exists(b) ),
inference(superposition,[],[f5,f21]) ).
fof(f29,definition,
( spl0_1
<=> there_exists(b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f31,plain,
( there_exists(b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f33,definition,
( spl0_2
<=> there_exists(domain(a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f35,plain,
( ~ there_exists(domain(a))
| spl0_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f27,f33,f29]) ).
fof(f37,plain,
! [X0,X1] : compose(X0,X1) = compose(X0,compose(domain(X0),X1)),
inference(superposition,[],[f9,f10]) ).
fof(f40,plain,
! [X0,X1] : compose(X0,X1) = compose(X0,compose(X1,domain(compose(X0,X1)))),
inference(superposition,[],[f9,f10]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ),
inference(superposition,[],[f7,f9]) ).
fof(f45,plain,
( ! [X0] : ~ there_exists(compose(a,X0))
| spl0_2 ),
inference(resolution,[],[f35,f6]) ).
fof(f49,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f45,f12]) ).
fof(f53,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f49]) ).
fof(f56,plain,
! [X0] :
( ~ there_exists(X0)
| domain(X0) = compose(domain(X0),domain(X0)) ),
inference(superposition,[],[f11,f24]) ).
fof(f66,plain,
! [X0] : compose(X0,domain(X0)) = compose(X0,domain(domain(X0))),
inference(superposition,[],[f37,f10]) ).
fof(f76,plain,
! [X0] : compose(X0,domain(domain(X0))) = X0,
inference(forward_demodulation,[],[f66,f10]) ).
fof(f108,plain,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(compose(X1,domain(compose(X0,X1)))) ),
inference(superposition,[],[f7,f40]) ).
fof(f135,plain,
! [X0,X1] :
( ~ there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ),
inference(superposition,[],[f42,f10]) ).
fof(f307,plain,
( domain(b) = compose(domain(b),domain(b))
| ~ spl0_1 ),
inference(resolution,[],[f56,f31]) ).
fof(f571,plain,
domain(compose(a,b)) = codomain(domain(b)),
inference(resolution,[],[f135,f12]) ).
fof(f606,definition,
( spl0_14
<=> there_exists(domain(b)) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f608,plain,
( ~ there_exists(domain(b))
| spl0_14 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f612,definition,
( spl0_15
<=> domain(domain(b)) = codomain(domain(b)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f614,plain,
( domain(domain(b)) = codomain(domain(b))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f649,plain,
( ! [X0] : ~ there_exists(compose(b,X0))
| spl0_14 ),
inference(resolution,[],[f608,f6]) ).
fof(f747,plain,
( ~ there_exists(b)
| spl0_14 ),
inference(superposition,[],[f649,f76]) ).
fof(f752,plain,
( $false
| ~ spl0_1
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f747,f31]) ).
fof(f753,plain,
( ~ spl0_1
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f752]) ).
fof(f771,plain,
( ~ there_exists(domain(b))
| domain(domain(b)) = codomain(compose(domain(b),domain(domain(b))))
| ~ spl0_1 ),
inference(superposition,[],[f108,f307]) ).
fof(f781,plain,
( domain(domain(b)) = codomain(domain(b))
| ~ there_exists(domain(b))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f771,f10]) ).
fof(f789,plain,
( ~ spl0_14
| spl0_15
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f781,f29,f612,f606]) ).
fof(f831,plain,
( domain(b) = domain(domain(b))
| ~ there_exists(b)
| ~ spl0_15 ),
inference(superposition,[],[f24,f614]) ).
fof(f839,plain,
( domain(b) = domain(domain(b))
| ~ spl0_1
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f831,f31]) ).
fof(f1278,plain,
( domain(compose(a,b)) = domain(domain(b))
| ~ spl0_15 ),
inference(forward_demodulation,[],[f571,f614]) ).
fof(f1279,plain,
( domain(compose(a,b)) = domain(b)
| ~ spl0_1
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1278,f839]) ).
fof(f1280,plain,
( $false
| ~ spl0_1
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1279,f13]) ).
fof(f1281,plain,
( ~ spl0_1
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1280]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f53]) ).
cnf(s16,plain,
( ~ spl0_1
| spl0_14 ),
inference(sat_conversion,[],[f753]) ).
cnf(s19,plain,
( ~ spl0_1
| ~ spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f789]) ).
cnf(s24,plain,
( ~ spl0_1
| ~ spl0_15 ),
inference(sat_conversion,[],[f1281]) ).
cnf(s30,plain,
spl0_1,
inference(rat,[],[s1,s2]) ).
cnf(s31,plain,
~ spl0_15,
inference(rat,[],[s24,s30]) ).
cnf(s33,plain,
~ spl0_14,
inference(rat,[],[s19,s31,s30]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s16,s33,s30]) ).
fof(f1282,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-4 : 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 : n004.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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:13:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.72/1.09 % (782083)Input is clausal, will run a generic CNF schedule.
% 2.72/1.09 % (782181)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2745537636:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.09 % (782181)First to succeed.
% 2.72/1.09 % (782181)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-782083"
% 2.72/1.09 % (782179)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3815679300:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.09 % (782183)dis-21_1_sil=8000:lcm=predicate:random_seed=2443054696: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)
% 2.72/1.09 % (782175)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1000940233:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.09 % (782177)lrs+10_1_sil=8000:sp=occurrence:random_seed=3883327907:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.09 % (782172)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=656713120:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.09 % (782183)Refutation not found, incomplete strategy
% 2.72/1.09 % (782183)------------------------------
% 2.72/1.09 % (782183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.09 % (782183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.09 % (782183)CaDiCaL version: 2.1.3
% 2.72/1.09 % (782183)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.09 % (782183)Time elapsed: 0.001 s
% 2.72/1.09 % (782183)Peak memory usage: 88 MB
% 2.72/1.09 % (782183)Instructions burned: 1 (million)
% 2.72/1.09 % (782177)Also succeeded, but the first one will report.
% 2.72/1.09 % (782179)Also succeeded, but the first one will report.
% 2.72/1.09 % (782174)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=774320221:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.09 % (782181)Refutation found. Thanks to Tanya!
% 2.72/1.09 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.09 % (782181)------------------------------
% 2.72/1.09 % (782181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.09 % (782181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.09 % (782181)CaDiCaL version: 2.1.3
% 2.72/1.09 % (782181)Termination reason: Refutation
% 2.72/1.09 % (782181)Time elapsed: 0.017 s
% 2.72/1.09 % (782181)Peak memory usage: 90 MB
% 2.72/1.09 % (782181)Instructions burned: 44 (million)
% 2.72/1.09 % (782181)------------------------------
% 2.72/1.09 % (782181)------------------------------
% 2.72/1.09 % (782083)Success in time 0.32 s
% 2.72/1.09 % Vampire exiting
%------------------------------------------------------------------------------