%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 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 11:41:02 AM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 24 unt; 3 def)
% Number of atoms : 94 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 34 ~; 29 |; 3 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) )
& leq(X0,multiplication(X0,star(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) )
& leq(X0,multiplication(X0,star(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f24,plain,
? [X0,X1] :
( ( ~ leq(multiplication(X0,star(X1)),X0)
& multiplication(X0,X1) = zero )
| ~ leq(X0,multiplication(X0,star(X1))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X2,X0),X1),X2)
| leq(multiplication(X1,star(X0)),X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ~ leq(multiplication(sK0,star(sK1)),sK0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,definition,
( spl2_1
<=> zero = multiplication(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f49,plain,
( zero = multiplication(sK0,sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl2_2
<=> leq(sK0,multiplication(sK0,star(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f53,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| spl2_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f44,f51,f47]) ).
fof(f56,definition,
( spl2_3
<=> leq(multiplication(sK0,star(sK1)),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f58,plain,
( ~ leq(multiplication(sK0,star(sK1)),sK0)
| spl2_3 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
( ~ spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f45,f51,f56]) ).
fof(f63,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f27,f25]) ).
fof(f64,plain,
( multiplication(sK0,star(sK1)) != addition(sK0,multiplication(sK0,star(sK1)))
| spl2_2 ),
inference(resolution,[],[f42,f53]) ).
fof(f96,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f26,f28]) ).
fof(f147,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f96,f36]) ).
fof(f162,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f32,f30]) ).
fof(f698,plain,
( multiplication(sK0,star(sK1)) != multiplication(sK0,addition(one,star(sK1)))
| spl2_2 ),
inference(superposition,[],[f64,f162]) ).
fof(f699,plain,
( multiplication(sK0,star(sK1)) != multiplication(sK0,star(sK1))
| spl2_2 ),
inference(forward_demodulation,[],[f698,f147]) ).
fof(f700,plain,
( $false
| spl2_2 ),
inference(trivial_inequality_removal,[],[f699]) ).
fof(f701,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f700]) ).
fof(f737,plain,
( ! [X0] :
( ~ leq(addition(zero,X0),sK0)
| leq(multiplication(X0,star(sK1)),sK0) )
| ~ spl2_1 ),
inference(superposition,[],[f38,f49]) ).
fof(f743,plain,
( ! [X0] :
( leq(multiplication(X0,star(sK1)),sK0)
| ~ leq(X0,sK0) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f737,f63]) ).
fof(f790,plain,
( ~ leq(sK0,sK0)
| ~ spl2_1
| spl2_3 ),
inference(resolution,[],[f743,f58]) ).
fof(f806,plain,
( sK0 != addition(sK0,sK0)
| ~ spl2_1
| spl2_3 ),
inference(resolution,[],[f790,f42]) ).
fof(f807,plain,
( $false
| ~ spl2_1
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f806,f28]) ).
fof(f808,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f807]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f54]) ).
cnf(s2,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f59]) ).
cnf(s5,plain,
spl2_2,
inference(sat_conversion,[],[f701]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f808]) ).
cnf(s9,plain,
~ spl2_3,
inference(rat,[],[s2,s5]) ).
cnf(s10,plain,
~ spl2_1,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s5,s10]) ).
fof(f809,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:14:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.16/0.48 % (2031245)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (2031251)% WARNING: option uhcvi not known.
% 0.16/0.48 % (2031251)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2176640061:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (2031252)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2830945490:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (2031250)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=792607961_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (2031253)dis+10_1_sil=32000:sp=arity:random_seed=1020589286:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (2031254)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3723402928:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (2031255)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1174648432:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (2031256)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=251729129:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (2031254) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2031245-2031254"...
% 0.16/0.48 % (2031254)...printing done.
% 0.16/0.48 % (2031254)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (2031254)------------------------------
% 0.16/0.48 % (2031254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (2031254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (2031254)CaDiCaL version: 2.1.3
% 0.16/0.48 % (2031254)Termination reason: Refutation
% 0.16/0.48 % (2031254)Time elapsed: 0.020 s
% 0.16/0.48 % (2031254)Peak memory usage: 13 MB
% 0.16/0.48 % (2031254)Instructions burned: 28 (million)
% 0.16/0.48 % (2031245)Success in time 0.071 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------