%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 11:40:32 AM UTC 2026
% Result : Theorem 5.43s 1.90s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 23 unt; 3 def)
% Number of atoms : 104 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 39 ~; 33 |; 5 &)
% ( 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 : 50 ( 0 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/sandbox2/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] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
( ( ~ leq(multiplication(sK0,star(sK1)),sK0)
& zero = multiplication(sK0,sK1) )
| ~ leq(sK0,multiplication(sK0,star(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f40,plain,
! [X2,X0,X1] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( zero = multiplication(sK0,sK1)
| ~ leq(sK0,multiplication(sK0,star(sK1))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
( ~ leq(multiplication(sK0,star(sK1)),sK0)
| ~ leq(sK0,multiplication(sK0,star(sK1))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f49,definition,
( spl2_1
<=> leq(sK0,multiplication(sK0,star(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f51,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| spl2_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl2_2
<=> zero = multiplication(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f55,plain,
( zero = multiplication(sK0,sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f46,f53,f49]) ).
fof(f58,definition,
( spl2_3
<=> leq(multiplication(sK0,star(sK1)),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f60,plain,
( ~ leq(multiplication(sK0,star(sK1)),sK0)
| spl2_3 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f47,f58,f49]) ).
fof(f70,plain,
( multiplication(sK0,star(sK1)) != addition(sK0,multiplication(sK0,star(sK1)))
| spl2_1 ),
inference(resolution,[],[f45,f51]) ).
fof(f93,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f28,f30]) ).
fof(f124,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f34,f32]) ).
fof(f186,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f93,f37]) ).
fof(f678,plain,
( multiplication(sK0,star(sK1)) != multiplication(sK0,addition(one,star(sK1)))
| spl2_1 ),
inference(superposition,[],[f70,f124]) ).
fof(f679,plain,
( multiplication(sK0,star(sK1)) != multiplication(sK0,star(sK1))
| spl2_1 ),
inference(forward_demodulation,[],[f678,f186]) ).
fof(f680,plain,
( $false
| spl2_1 ),
inference(trivial_inequality_removal,[],[f679]) ).
fof(f681,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f709,plain,
( multiplication(sK0,addition(one,sK1)) = addition(sK0,zero)
| ~ spl2_2 ),
inference(superposition,[],[f124,f55]) ).
fof(f720,plain,
( sK0 = multiplication(sK0,addition(one,sK1))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f709,f29]) ).
fof(f723,plain,
( ~ leq(addition(multiplication(sK0,sK1),sK0),sK0)
| spl2_3 ),
inference(resolution,[],[f60,f40]) ).
fof(f726,plain,
( ~ leq(addition(sK0,multiplication(sK0,sK1)),sK0)
| spl2_3 ),
inference(forward_demodulation,[],[f723,f27]) ).
fof(f728,plain,
( ~ leq(multiplication(sK0,addition(one,sK1)),sK0)
| spl2_3 ),
inference(forward_demodulation,[],[f726,f124]) ).
fof(f748,plain,
( ~ leq(sK0,sK0)
| ~ spl2_2
| spl2_3 ),
inference(superposition,[],[f728,f720]) ).
fof(f786,plain,
( sK0 != addition(sK0,sK0)
| ~ spl2_2
| spl2_3 ),
inference(resolution,[],[f748,f45]) ).
fof(f787,plain,
( $false
| ~ spl2_2
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f786,f30]) ).
fof(f788,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f787]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f681]) ).
cnf(s4,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f788]) ).
cnf(s5,plain,
~ spl2_3,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
~ spl2_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s3]) ).
fof(f789,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 % Computer : n003.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 13:16:10 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 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
% 5.43/1.90 % (525483)Detected formulas, will run a generic FOF schedule.
% 5.43/1.90 % (525489)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2701555856:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.43/1.90 % (525494)dis-21_1_sil=8000:lcm=predicate:random_seed=867122825:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.43/1.90 % (525494)Refutation not found, incomplete strategy
% 5.43/1.90 % (525494)------------------------------
% 5.43/1.90 % (525494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.90 % (525494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.90 % (525494)CaDiCaL version: 2.1.3
% 5.43/1.90 % (525494)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.90 % (525494)Time elapsed: 0.003 s
% 5.43/1.90 % (525494)Peak memory usage: 88 MB
% 5.43/1.90 % (525494)Instructions burned: 1 (million)
% 5.43/1.90 % (525493)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1651232068:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.43/1.90 % (525488)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=1903567388:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.43/1.90 % (525490)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3840961114:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.43/1.90 % (525491)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3187127786:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.43/1.90 % (525491)Refutation not found, incomplete strategy
% 5.43/1.90 % (525491)------------------------------
% 5.43/1.90 % (525491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.90 % (525491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.90 % (525491)CaDiCaL version: 2.1.3
% 5.43/1.90 % (525491)Termination reason: Refutation not found, incomplete strategy
% 5.43/1.90 % (525491)Time elapsed: 0.002 s
% 5.43/1.90 % (525491)Peak memory usage: 88 MB
% 5.43/1.90 % (525493)First to succeed.
% 5.43/1.90 % (525493)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-525483"
% 5.43/1.90 % (525492)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3526367925:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.43/1.90 % (525492)Instruction limit reached!
% 5.43/1.90 % (525492)------------------------------
% 5.43/1.90 % (525492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.90 % (525492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.90 % (525492)CaDiCaL version: 2.1.3
% 5.43/1.90 % (525492)Termination reason: Instruction limit
% 5.43/1.90 % (525492)Termination phase: Saturation
% 5.43/1.90 % (525492)Time elapsed: 0.119 s
% 5.43/1.90 % (525492)Peak memory usage: 89 MB
% 5.43/1.90 % (525492)Instructions burned: 120 (million)
% 5.43/1.90 % (525494)------------------------------
% 5.43/1.90 % (525494)------------------------------
% 5.43/1.90 % (525493)Refutation found. Thanks to Tanya!
% 5.43/1.90 % SZS status Theorem for theBenchmark
% 5.43/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 5.43/1.90 % (525493)------------------------------
% 5.43/1.90 % (525493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.90 % (525493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.90 % (525493)CaDiCaL version: 2.1.3
% 5.43/1.90 % (525493)Termination reason: Refutation
% 5.43/1.90 % (525493)Time elapsed: 0.027 s
% 5.43/1.90 % (525493)Peak memory usage: 90 MB
% 5.43/1.90 % (525493)Instructions burned: 27 (million)
% 5.43/1.90 % (525493)------------------------------
% 5.43/1.90 % (525493)------------------------------
% 5.43/1.90 % (525483)Success in time 0.665 s
% 5.43/1.90 % Vampire exiting
%------------------------------------------------------------------------------