%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 09:36:57 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.35s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 16 unt; 3 def)
% Number of atoms : 95 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 33 ~; 41 |; 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 : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ~ there_exists(domain(X0))
| there_exists(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',domain_has_elements) ).
fof(f6,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| there_exists(domain(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).
fof(f7,axiom,
! [X0,X1] :
( ~ there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',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/Axioms/CAT004-0.ax',domain_codomain_composition2) ).
fof(f9,axiom,
! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',associativity_of_compose) ).
fof(f10,axiom,
! [X0] : compose(X0,domain(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT004-0.ax',compose_domain) ).
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,
! [X0] :
( there_exists(domain(X0))
| ~ there_exists(X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f21,plain,
! [X0,X1] :
( ~ there_exists(domain(X0))
| there_exists(compose(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( there_exists(compose(X0,X1))
| domain(X0) = codomain(X1) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f23,plain,
! [X0,X1] :
( domain(X0) != codomain(X1)
| there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f24,plain,
~ there_exists(compose(a,b)),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f25,plain,
~ there_exists(compose(b,c)),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f26,plain,
there_exists(compose(a,compose(b,c))),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f36,plain,
domain(b) = codomain(c),
inference(resolution,[],[f22,f25]) ).
fof(f38,plain,
! [X0] :
( there_exists(X0)
| domain(X0) = codomain(domain(X0)) ),
inference(superposition,[],[f22,f10]) ).
fof(f46,plain,
! [X2,X0,X1] :
( there_exists(compose(X0,compose(X1,X2)))
| domain(compose(X0,X1)) = codomain(X2) ),
inference(superposition,[],[f22,f9]) ).
fof(f54,definition,
( spl0_1
<=> there_exists(b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f56,plain,
( ~ there_exists(b)
| spl0_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f68,plain,
! [X0] :
( domain(X0) != domain(b)
| there_exists(domain(X0))
| ~ there_exists(compose(X0,c)) ),
inference(superposition,[],[f23,f36]) ).
fof(f76,definition,
( spl0_4
<=> there_exists(domain(b)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f77,plain,
( ~ there_exists(domain(b))
| spl0_4 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( there_exists(domain(b))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f84,plain,
( domain(b) = codomain(domain(b))
| spl0_1 ),
inference(resolution,[],[f38,f56]) ).
fof(f152,plain,
! [X0,X1] :
( there_exists(compose(X1,X0))
| codomain(domain(X0)) = domain(compose(X1,X0)) ),
inference(superposition,[],[f46,f10]) ).
fof(f273,plain,
( ~ there_exists(b)
| spl0_4 ),
inference(resolution,[],[f77,f19]) ).
fof(f375,definition,
( spl0_12
<=> ! [X0] : there_exists(compose(b,X0)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f376,plain,
( ! [X0] : there_exists(compose(b,X0))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f456,plain,
( ! [X0] : there_exists(compose(b,X0))
| ~ spl0_4 ),
inference(resolution,[],[f78,f21]) ).
fof(f459,plain,
( spl0_12
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f456,f76,f375]) ).
fof(f468,plain,
( $false
| ~ spl0_12 ),
inference(backward_subsumption_resolution,[],[f25,f376]) ).
fof(f475,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f468]) ).
fof(f483,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f273,f76,f54]) ).
fof(f779,plain,
domain(compose(a,b)) = codomain(domain(b)),
inference(resolution,[],[f152,f24]) ).
fof(f2648,plain,
( domain(b) = domain(compose(a,b))
| spl0_1 ),
inference(forward_demodulation,[],[f779,f84]) ).
fof(f2685,plain,
( domain(b) != domain(b)
| there_exists(domain(b))
| ~ there_exists(compose(compose(a,b),c))
| spl0_1 ),
inference(superposition,[],[f68,f2648]) ).
fof(f2691,plain,
( there_exists(domain(b))
| ~ there_exists(compose(compose(a,b),c))
| spl0_1 ),
inference(trivial_inequality_removal,[],[f2685]) ).
fof(f2696,plain,
( ~ there_exists(compose(compose(a,b),c))
| spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f2691,f77]) ).
fof(f2702,plain,
( ~ there_exists(compose(a,compose(b,c)))
| spl0_1
| spl0_4 ),
inference(forward_demodulation,[],[f2696,f9]) ).
fof(f2704,plain,
( $false
| spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f2702,f26]) ).
fof(f2705,plain,
( spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f2704]) ).
cnf(s33,plain,
( ~ spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f459]) ).
cnf(s34,plain,
~ spl0_12,
inference(sat_conversion,[],[f475]) ).
cnf(s49,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f483]) ).
cnf(s111,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f2705]) ).
cnf(s121,plain,
~ spl0_4,
inference(rat,[],[s33,s34]) ).
cnf(s122,plain,
spl0_1,
inference(rat,[],[s111,s121]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s49,s121,s122]) ).
fof(f2706,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:13:37 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.35 % (783961)Will run a generic schedule for satisfiability detection.
% 0.23/0.35 % (783967)% WARNING: option uhcvi not known.
% 0.23/0.35 % (783967)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=557368203:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.35 % (783966)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3656043687_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.35 % TRYING [1]
% 0.23/0.35 % TRYING [2]
% 0.23/0.35 % TRYING [3]
% 0.23/0.35 % TRYING [4]
% 0.23/0.35 % (783972)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1651080601:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.35 % (783970)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3099079848:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.35 % (783971)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3861169588:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.35 % (783968)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=6407886:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.35 % (783969)dis+10_1_sil=32000:sp=arity:random_seed=2745926172:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.35 % TRYING [5]
% 0.23/0.35 % (783967) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-783961-783967"...
% 0.23/0.35 % (783967)...printing done.
% 0.23/0.35 % (783967)Refutation found. Thanks to Tanya!
% 0.23/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.35 % (783967)------------------------------
% 0.23/0.35 % (783967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (783967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (783967)CaDiCaL version: 2.1.3
% 0.23/0.35 % (783967)Termination reason: Refutation
% 0.23/0.35 % (783967)Time elapsed: 0.053 s
% 0.23/0.35 % (783967)Peak memory usage: 13 MB
% 0.23/0.35 % (783967)Instructions burned: 98 (million)
% 0.23/0.35 % (783961)Success in time 0.076 s
% 0.23/0.35 % Vampire exiting
%------------------------------------------------------------------------------