%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CAT018-4 : 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 : n001.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 09:36:39 AM UTC 2026
% Result : Unsatisfiable 3.94s 1.27s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 15 unt; 3 def)
% Number of atoms : 79 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 36 ~; 32 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ~ there_exists(codomain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f8,axiom,
! [X0,X1] :
( ~ there_exists(domain(X0))
| domain(X0) != codomain(X1)
| there_exists(compose(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f11,axiom,
! [X0] : compose(codomain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
fof(f12,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f13,axiom,
there_exists(compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f14,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_bc_exists) ).
fof(f19,plain,
domain(a) = codomain(b),
inference(resolution,[],[f7,f12]) ).
fof(f22,plain,
! [X0] :
( ~ there_exists(X0)
| codomain(X0) = domain(codomain(X0)) ),
inference(superposition,[],[f7,f11]) ).
fof(f24,plain,
( ~ there_exists(domain(a))
| there_exists(b) ),
inference(superposition,[],[f5,f19]) ).
fof(f26,definition,
( spl0_1
<=> there_exists(b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f28,plain,
( there_exists(b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl0_2
<=> there_exists(domain(a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f31,plain,
( there_exists(domain(a))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f32,plain,
( ~ there_exists(domain(a))
| spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f33,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f24,f30,f26]) ).
fof(f35,plain,
! [X0,X1] : compose(X0,X1) = compose(codomain(X0),compose(X0,X1)),
inference(superposition,[],[f9,f11]) ).
fof(f42,plain,
( ! [X0] : ~ there_exists(compose(a,X0))
| spl0_2 ),
inference(resolution,[],[f32,f6]) ).
fof(f44,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f42,f12]) ).
fof(f46,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f44]) ).
fof(f65,plain,
( ! [X0] :
( codomain(X0) != domain(a)
| there_exists(compose(a,X0)) )
| ~ spl0_2 ),
inference(resolution,[],[f31,f8]) ).
fof(f72,plain,
( codomain(b) = domain(codomain(b))
| ~ spl0_1 ),
inference(resolution,[],[f22,f28]) ).
fof(f73,plain,
( domain(a) = domain(domain(a))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f72,f19]) ).
fof(f104,plain,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(codomain(X0)) = codomain(compose(X0,X1)) ),
inference(superposition,[],[f7,f35]) ).
fof(f627,plain,
codomain(compose(b,c)) = domain(codomain(b)),
inference(resolution,[],[f104,f13]) ).
fof(f646,plain,
codomain(compose(b,c)) = domain(domain(a)),
inference(forward_demodulation,[],[f627,f19]) ).
fof(f650,plain,
( domain(a) = codomain(compose(b,c))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f646,f73]) ).
fof(f745,definition,
( spl0_29
<=> domain(a) = codomain(compose(b,c)) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f746,plain,
( domain(a) = codomain(compose(b,c))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f1714,plain,
( spl0_29
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f650,f26,f745]) ).
fof(f2105,plain,
( domain(a) != domain(a)
| there_exists(compose(a,compose(b,c)))
| ~ spl0_2
| ~ spl0_29 ),
inference(superposition,[],[f65,f746]) ).
fof(f2109,plain,
( there_exists(compose(a,compose(b,c)))
| ~ spl0_2
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f2105]) ).
fof(f2111,plain,
( $false
| ~ spl0_2
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f2109,f14]) ).
fof(f2112,plain,
( ~ spl0_2
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f2111]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f46]) ).
cnf(s57,plain,
( ~ spl0_1
| spl0_29 ),
inference(sat_conversion,[],[f1714]) ).
cnf(s73,plain,
( ~ spl0_2
| ~ spl0_29 ),
inference(sat_conversion,[],[f2112]) ).
cnf(s100,plain,
~ spl0_29,
inference(rat,[],[s73,s2]) ).
cnf(s102,plain,
~ spl0_1,
inference(rat,[],[s57,s100]) ).
cnf(s103,plain,
$false,
inference(rat,[],[s1,s2,s102]) ).
fof(f2114,plain,
$false,
inference(avatar_sat_refutation,[],[s103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.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 21:19:34 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.94/1.27 % (761220)Input is clausal, will run a generic CNF schedule.
% 3.94/1.27 % (761271)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4051283884:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.94/1.27 % (761271)Instruction limit reached!
% 3.94/1.27 % (761271)------------------------------
% 3.94/1.27 % (761271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.27 % (761271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.27 % (761271)CaDiCaL version: 2.1.3
% 3.94/1.27 % (761271)Termination reason: Instruction limit
% 3.94/1.27 % (761271)Termination phase: Saturation
% 3.94/1.27 % (761271)Time elapsed: 0.037 s
% 3.94/1.27 % (761271)Peak memory usage: 88 MB
% 3.94/1.27 % (761271)Instructions burned: 114 (million)
% 3.94/1.27 % (761267)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=2199684682:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.94/1.27 % (761268)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3265771267:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.94/1.27 % (761269)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3843892919:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.94/1.27 % (761272)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3965175086:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.94/1.27 % (761270)lrs+10_1_sil=8000:sp=occurrence:random_seed=3888408065:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.94/1.27 % (761273)dis-21_1_sil=8000:lcm=predicate:random_seed=2645920948: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)
% 3.94/1.27 % (761270)Refutation not found, incomplete strategy
% 3.94/1.27 % (761270)------------------------------
% 3.94/1.27 % (761270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.27 % (761270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.27 % (761270)CaDiCaL version: 2.1.3
% 3.94/1.27 % (761270)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.27 % (761270)Time elapsed: 0.001 s
% 3.94/1.27 % (761270)Peak memory usage: 87 MB
% 3.94/1.27 % (761273)Refutation not found, incomplete strategy
% 3.94/1.27 % (761273)------------------------------
% 3.94/1.27 % (761273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.27 % (761273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.27 % (761273)CaDiCaL version: 2.1.3
% 3.94/1.27 % (761273)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.27 % (761273)Time elapsed: 0.001 s
% 3.94/1.27 % (761273)Peak memory usage: 88 MB
% 3.94/1.27 % (761273)Instructions burned: 1 (million)
% 3.94/1.27 % (761272)First to succeed.
% 3.94/1.27 % (761272)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-761220"
% 3.94/1.27 % (761278)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2440820731:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.94/1.27 % (761278)Refutation not found, incomplete strategy
% 3.94/1.27 % (761278)------------------------------
% 3.94/1.27 % (761278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.27 % (761278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.27 % (761278)CaDiCaL version: 2.1.3
% 3.94/1.27 % (761278)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.27 % (761278)Time elapsed: 0.001 s
% 3.94/1.27 % (761278)Peak memory usage: 88 MB
% 3.94/1.27 % (761278)Instructions burned: 1 (million)
% 3.94/1.27 % (761270)------------------------------
% 3.94/1.27 % (761270)------------------------------
% 3.94/1.27 % (761273)------------------------------
% 3.94/1.27 % (761273)------------------------------
% 3.94/1.27 % (761278)------------------------------
% 3.94/1.27 % (761278)------------------------------
% 3.94/1.27 % (761272)Refutation found. Thanks to Tanya!
% 3.94/1.27 % SZS status Unsatisfiable for theBenchmark
% 3.94/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.27 % (761272)------------------------------
% 3.94/1.27 % (761272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.27 % (761272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.27 % (761272)CaDiCaL version: 2.1.3
% 3.94/1.27 % (761272)Termination reason: Refutation
% 3.94/1.27 % (761272)Time elapsed: 0.047 s
% 3.94/1.27 % (761272)Peak memory usage: 90 MB
% 3.94/1.27 % (761272)Instructions burned: 71 (million)
% 3.94/1.27 % (761272)------------------------------
% 3.94/1.27 % (761272)------------------------------
% 3.94/1.27 % (761220)Success in time 0.476 s
% 3.94/1.27 % Vampire exiting
%------------------------------------------------------------------------------