%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE141+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 11:40:26 AM UTC 2026
% Result : Theorem 3.05s 1.38s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 38 unt; 2 def)
% Number of atoms : 107 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 37 ~; 30 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 78 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',star_induction2) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] : strong_iteration(one) != multiplication(strong_iteration(one),X0),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,star(X0)),X2)
| ~ leq(addition(multiplication(X2,X0),X1),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
strong_iteration(one) != multiplication(strong_iteration(one),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f27,plain,
strong_iteration(one) != multiplication(strong_iteration(one),sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f33,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f34,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X2,X0),X1),X2)
| leq(multiplication(X1,star(X0)),X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f56,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f46,f38]) ).
fof(f62,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f56]) ).
fof(f102,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f39,f38]) ).
fof(f187,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f37,f34]) ).
fof(f223,definition,
( spl1_3
<=> leq(star(one),one) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f225,plain,
( leq(star(one),one)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f227,definition,
( spl1_4
<=> one = star(one) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f228,plain,
( one = star(one)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f229,plain,
( one != star(one)
| spl1_4 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f231,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(multiplication(X1,star(one)),X0) ),
inference(superposition,[],[f41,f35]) ).
fof(f269,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f102,f33]) ).
fof(f277,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f46,f102]) ).
fof(f282,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f277]) ).
fof(f1141,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(resolution,[],[f187,f282]) ).
fof(f1217,plain,
! [X0,X1] : multiplication(strong_iteration(one),X1) = addition(X0,multiplication(strong_iteration(one),X1)),
inference(resolution,[],[f1141,f45]) ).
fof(f1222,plain,
! [X0] :
( ~ leq(X0,X0)
| leq(multiplication(X0,star(one)),X0) ),
inference(superposition,[],[f231,f38]) ).
fof(f1261,plain,
! [X0] : leq(multiplication(X0,star(one)),X0),
inference(forward_subsumption_resolution,[],[f1222,f62]) ).
fof(f1281,plain,
leq(star(one),one),
inference(superposition,[],[f1261,f34]) ).
fof(f1282,plain,
spl1_3,
inference(avatar_split_clause,[],[f1281,f223]) ).
fof(f1291,plain,
( one = addition(star(one),one)
| ~ spl1_3 ),
inference(resolution,[],[f225,f45]) ).
fof(f1292,plain,
( one = addition(one,star(one))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f1291,f40]) ).
fof(f1293,plain,
( one = star(one)
| ~ spl1_3 ),
inference(forward_demodulation,[],[f1292,f269]) ).
fof(f1294,plain,
( $false
| ~ spl1_3
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f1293,f229]) ).
fof(f1295,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f1294]) ).
fof(f1382,plain,
( strong_iteration(one) = addition(one,multiplication(strong_iteration(one),zero))
| ~ spl1_4 ),
inference(superposition,[],[f36,f228]) ).
fof(f1392,plain,
( strong_iteration(one) = multiplication(strong_iteration(one),zero)
| ~ spl1_4 ),
inference(forward_demodulation,[],[f1382,f1217]) ).
fof(f2516,plain,
( ! [X0] : multiplication(strong_iteration(one),X0) = multiplication(strong_iteration(one),multiplication(zero,X0))
| ~ spl1_4 ),
inference(superposition,[],[f30,f1392]) ).
fof(f2549,plain,
( ! [X0] : multiplication(strong_iteration(one),X0) = multiplication(strong_iteration(one),zero)
| ~ spl1_4 ),
inference(forward_demodulation,[],[f2516,f43]) ).
fof(f2561,plain,
( ! [X0] : strong_iteration(one) = multiplication(strong_iteration(one),X0)
| ~ spl1_4 ),
inference(forward_demodulation,[],[f2549,f1392]) ).
fof(f4222,plain,
( strong_iteration(one) != strong_iteration(one)
| ~ spl1_4 ),
inference(superposition,[],[f27,f2561]) ).
fof(f4291,plain,
( $false
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f4222]) ).
fof(f4292,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f4291]) ).
cnf(s4,plain,
spl1_3,
inference(sat_conversion,[],[f1282]) ).
cnf(s5,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f1295]) ).
cnf(s10,plain,
~ spl1_4,
inference(sat_conversion,[],[f4292]) ).
cnf(s11,plain,
~ spl1_3,
inference(rat,[],[s5,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s4,s11]) ).
fof(f4393,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE141+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 13:12:01 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.05/1.38 % (805682)Detected formulas, will run a generic FOF schedule.
% 3.05/1.38 % (805792)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1990860731:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.05/1.38 % (805790)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=1247157925:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.05/1.38 % (805794)dis-21_1_sil=8000:lcm=predicate:random_seed=1064519011: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)
% 3.05/1.38 % (805793)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=843259278:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.05/1.38 % (805789)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=3469905703:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.05/1.38 % (805788)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=295301858:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.05/1.38 % (805791)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4021837531:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.05/1.38 % (805791)Refutation not found, incomplete strategy
% 3.05/1.38 % (805791)------------------------------
% 3.05/1.38 % (805791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.38 % (805791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.38 % (805791)CaDiCaL version: 2.1.3
% 3.05/1.38 % (805791)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.38 % (805791)Time elapsed: 0.001 s
% 3.05/1.38 % (805791)Peak memory usage: 88 MB
% 3.05/1.38 % (805794)Refutation not found, incomplete strategy
% 3.05/1.38 % (805794)------------------------------
% 3.05/1.38 % (805794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.38 % (805794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.38 % (805794)CaDiCaL version: 2.1.3
% 3.05/1.38 % (805794)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.38 % (805794)Time elapsed: 0.002 s
% 3.05/1.38 % (805794)Peak memory usage: 88 MB
% 3.05/1.38 % (805794)Instructions burned: 1 (million)
% 3.05/1.38 % (805792)Instruction limit reached!
% 3.05/1.38 % (805792)------------------------------
% 3.05/1.38 % (805792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.38 % (805792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.38 % (805792)CaDiCaL version: 2.1.3
% 3.05/1.38 % (805792)Termination reason: Instruction limit
% 3.05/1.38 % (805792)Termination phase: Saturation
% 3.05/1.38 % (805792)Time elapsed: 0.038 s
% 3.05/1.38 % (805792)Peak memory usage: 89 MB
% 3.05/1.38 % (805792)Instructions burned: 120 (million)
% 3.05/1.38 % (805793)Instruction limit reached!
% 3.05/1.38 % (805793)------------------------------
% 3.05/1.38 % (805793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.38 % (805793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.38 % (805793)CaDiCaL version: 2.1.3
% 3.05/1.38 % (805793)Termination reason: Instruction limit
% 3.05/1.38 % (805793)Termination phase: Saturation
% 3.05/1.38 % (805793)Time elapsed: 0.082 s
% 3.05/1.38 % (805793)Peak memory usage: 90 MB
% 3.05/1.38 % (805793)Instructions burned: 139 (million)
% 3.05/1.38 % (805802)lrs+10_1_sil=8000:sp=occurrence:random_seed=709772655:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.05/1.38 % (805802)First to succeed.
% 3.05/1.38 % (805802)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-805682"
% 3.05/1.38 % (805791)------------------------------
% 3.05/1.38 % (805791)------------------------------
% 3.05/1.38 % (805816)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1667257986:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.05/1.38 % (805794)------------------------------
% 3.05/1.38 % (805794)------------------------------
% 3.05/1.38 % (805802)Refutation found. Thanks to Tanya!
% 3.05/1.38 % SZS status Theorem for theBenchmark
% 3.05/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 4.21/1.58 % (805802)------------------------------
% 4.21/1.58 % (805802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.58 % (805802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.58 % (805802)CaDiCaL version: 2.1.3
% 4.21/1.58 % (805802)Termination reason: Refutation
% 4.21/1.58 % (805802)Time elapsed: 0.053 s
% 4.21/1.58 % (805802)Peak memory usage: 91 MB
% 4.21/1.58 % (805802)Instructions burned: 149 (million)
% 4.21/1.58 % (805802)------------------------------
% 4.21/1.58 % (805802)------------------------------
% 4.21/1.58 % (805682)Success in time 0.513 s
% 4.21/1.58 % Vampire exiting
%------------------------------------------------------------------------------