%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 09:36:51 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 15 unt; 2 def)
% Number of atoms : 102 ( 67 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 65 ~; 58 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( codomain(X0) != domain(X1)
| codomain(compose(X0,X1)) = codomain(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain2) ).
fof(f10,axiom,
! [X2,X0,X1] :
( codomain(X0) != domain(X1)
| codomain(X1) != domain(X2)
| compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',star_property) ).
fof(f11,axiom,
! [X2,X0,X1] :
( codomain(compose(a,b)) != domain(X0)
| compose(compose(a,b),X0) != X1
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X2) != X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',endomorphism) ).
fof(f12,plain,
! [X2,X0,X1] :
( domain(X0) != codomain(compose(a,b))
| compose(compose(a,b),X0) != X1
| domain(X2) != codomain(compose(a,b))
| compose(compose(a,b),X2) != X1
| X0 = X2 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
fof(f14,axiom,
codomain(b) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
fof(f15,axiom,
codomain(b) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
fof(f16,axiom,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_bg) ).
fof(f17,negated_conjecture,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
fof(f18,plain,
h != g,
inference(reorient_equations,[],[f17]) ).
fof(f47,plain,
! [X0] :
( codomain(X0) != codomain(a)
| codomain(b) = codomain(compose(X0,b)) ),
inference(superposition,[],[f9,f13]) ).
fof(f55,plain,
! [X0,X1] :
( codomain(X0) != codomain(a)
| domain(X1) != codomain(b)
| compose(X0,compose(b,X1)) = compose(compose(X0,b),X1) ),
inference(superposition,[],[f10,f13]) ).
fof(f60,plain,
! [X0,X1] :
( codomain(compose(a,b)) != codomain(b)
| compose(compose(a,b),h) != X0
| domain(X1) != codomain(compose(a,b))
| compose(compose(a,b),X1) != X0
| h = X1 ),
inference(superposition,[],[f12,f14]) ).
fof(f66,definition,
( spl0_2
<=> codomain(compose(a,b)) = codomain(b) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f67,plain,
( codomain(compose(a,b)) = codomain(b)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( codomain(compose(a,b)) != codomain(b)
| spl0_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f71,definition,
( spl0_3
<=> ! [X0,X1] :
( compose(compose(a,b),h) != X0
| h = X1
| domain(X1) != codomain(compose(a,b))
| compose(compose(a,b),X1) != X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0,X1] :
( compose(compose(a,b),h) != X0
| h = X1
| domain(X1) != codomain(compose(a,b))
| compose(compose(a,b),X1) != X0 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f60,f66,f71]) ).
fof(f165,plain,
codomain(compose(a,b)) = codomain(b),
inference(equality_resolution,[],[f47]) ).
fof(f167,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f165,f68]) ).
fof(f168,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f169,plain,
( ! [X0,X1] :
( domain(X1) != codomain(b)
| compose(compose(a,b),h) != X0
| h = X1
| compose(compose(a,b),X1) != X0 )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f72,f67]) ).
fof(f367,plain,
! [X0] :
( domain(X0) != codomain(b)
| compose(compose(a,b),X0) = compose(a,compose(b,X0)) ),
inference(equality_resolution,[],[f55]) ).
fof(f445,plain,
( ! [X0] :
( codomain(b) != codomain(b)
| compose(compose(a,b),h) != X0
| h = g
| compose(compose(a,b),g) != X0 )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f169,f15]) ).
fof(f446,plain,
( ! [X0] :
( compose(compose(a,b),h) != X0
| h = g
| compose(compose(a,b),g) != X0 )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f445]) ).
fof(f447,plain,
( ! [X0] :
( compose(compose(a,b),g) != X0
| compose(compose(a,b),h) != X0 )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f446,f18]) ).
fof(f448,plain,
( compose(compose(a,b),h) != compose(compose(a,b),g)
| ~ spl0_2
| ~ spl0_3 ),
inference(equality_resolution,[],[f447]) ).
fof(f1218,plain,
( codomain(b) != codomain(b)
| compose(compose(a,b),h) = compose(a,compose(b,h)) ),
inference(superposition,[],[f367,f14]) ).
fof(f1219,plain,
( codomain(b) != codomain(b)
| compose(compose(a,b),g) = compose(a,compose(b,g)) ),
inference(superposition,[],[f367,f15]) ).
fof(f1220,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(trivial_inequality_removal,[],[f1219]) ).
fof(f1221,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(trivial_inequality_removal,[],[f1218]) ).
fof(f1222,plain,
compose(compose(a,b),g) = compose(a,compose(b,h)),
inference(forward_demodulation,[],[f1220,f16]) ).
fof(f1292,plain,
( compose(compose(a,b),h) != compose(a,compose(b,h))
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f448,f1222]) ).
fof(f1293,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1292,f1221]) ).
fof(f1294,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f1293]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f168]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f1294]) ).
cnf(s20,plain,
~ spl0_3,
inference(rat,[],[s19,s4]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s2,s20,s4]) ).
fof(f1299,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:13:00 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.31 % (3483301)Will run a generic schedule for satisfiability detection.
% 0.19/0.31 % (3483316)% WARNING: option uhcvi not known.
% 0.19/0.31 % (3483321)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=672548515:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.31 % (3483315)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=480126792_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.31 % (3483316)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3161323746:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.31 % (3483317)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3187893486:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.31 % (3483318)dis+10_1_sil=32000:sp=arity:random_seed=3141324436:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.31 % (3483320)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1907781381:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.31 % TRYING [1]
% 0.19/0.31 % (3483319)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4268866116:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.31 % TRYING [2]
% 0.19/0.31 % TRYING [3]
% 0.19/0.31 % TRYING [4]
% 0.19/0.31 % TRYING [5]
% 0.19/0.31 % (3483320) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3483301-3483320"...
% 0.19/0.31 % (3483320)...printing done.
% 0.19/0.31 % (3483320)Refutation found. Thanks to Tanya!
% 0.19/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.31 % (3483320)------------------------------
% 0.19/0.31 % (3483320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (3483320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (3483320)CaDiCaL version: 2.1.3
% 0.19/0.31 % (3483320)Termination reason: Refutation
% 0.19/0.31 % (3483320)Time elapsed: 0.039 s
% 0.19/0.31 % (3483320)Peak memory usage: 13 MB
% 0.19/0.31 % (3483320)Instructions burned: 54 (million)
% 0.19/0.31 % (3483301)Success in time 0.09 s
% 0.19/0.31 % Vampire exiting
%------------------------------------------------------------------------------