%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE144+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 11:40:58 AM UTC 2026
% Result : Theorem 1.72s 0.82s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 26 unt; 2 def)
% Number of atoms : 74 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 22 ~; 18 |; 3 &)
% ( 3 <=>; 1 =>; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 63 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0] :
( leq(strong_iteration(star(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(star(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X0))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f24,plain,
? [X0] :
( ~ leq(strong_iteration(star(X0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(X0))) ),
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(strong_iteration(star(sK0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
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(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(sK0))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,definition,
( spl1_1
<=> leq(strong_iteration(one),strong_iteration(star(sK0))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ leq(strong_iteration(one),strong_iteration(star(sK0)))
| spl1_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl1_2
<=> leq(strong_iteration(star(sK0)),strong_iteration(one)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f54,plain,
( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
| spl1_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f319,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f28,f30]) ).
fof(f456,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f45,f319]) ).
fof(f458,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f456]) ).
fof(f537,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f35,f33]) ).
fof(f898,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f42,f33]) ).
fof(f906,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(forward_subsumption_resolution,[],[f898,f458]) ).
fof(f923,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f906,f32]) ).
fof(f944,plain,
( $false
| spl1_2 ),
inference(backward_subsumption_resolution,[],[f54,f923]) ).
fof(f945,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f944]) ).
fof(f2719,plain,
! [X2,X0,X1] :
( ~ leq(X0,addition(addition(X0,multiplication(X1,X0)),X2))
| leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)) ),
inference(superposition,[],[f42,f537]) ).
fof(f2761,plain,
! [X2,X0,X1] :
( ~ leq(X0,addition(X0,addition(multiplication(X1,X0),X2)))
| leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)) ),
inference(forward_demodulation,[],[f2719,f28]) ).
fof(f2780,plain,
! [X2,X0,X1] : leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)),
inference(forward_subsumption_resolution,[],[f2761,f458]) ).
fof(f3783,plain,
! [X0,X1] : leq(X1,strong_iteration(addition(one,X0))),
inference(superposition,[],[f2780,f32]) ).
fof(f3791,plain,
! [X0,X1] : leq(X1,strong_iteration(star(X0))),
inference(superposition,[],[f3783,f37]) ).
fof(f3822,plain,
( $false
| spl1_1 ),
inference(backward_subsumption_resolution,[],[f50,f3791]) ).
fof(f3831,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f3822]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s45,plain,
spl1_2,
inference(sat_conversion,[],[f945]) ).
cnf(s91,plain,
spl1_1,
inference(sat_conversion,[],[f3831]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s1,s45,s91]) ).
fof(f3832,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE144+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.20/0.46 % Computer : n013.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 27 13:11:51 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.49 Running first-order model finding
% 0.24/0.49 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
% 1.72/0.82 % (220191)Will run a generic schedule for satisfiability detection.
% 1.72/0.82 % (220197)% WARNING: option uhcvi not known.
% 1.72/0.82 % (220197)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=440365544:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.72/0.82 % (220196)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2329214743_2999 on theBenchmark for (2999ds/0Mi)
% 1.72/0.82 % (220200)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=418571349:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.72/0.82 % (220198)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3815194502:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.72/0.82 % (220199)dis+10_1_sil=32000:sp=arity:random_seed=813573685:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.72/0.82 % (220202)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2158093628:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.72/0.82 % TRYING [1]
% 1.72/0.82 % TRYING [2]
% 1.72/0.82 % TRYING [3]
% 1.72/0.82 % TRYING [4]
% 1.72/0.82 % (220201)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4221728541:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.72/0.82 % TRYING [5]
% 1.72/0.82 % (220199)Instruction limit reached!
% 1.72/0.82 % (220199)------------------------------
% 1.72/0.82 % (220199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220199)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220199)Termination reason: Instruction limit
% 1.72/0.82 % (220199)Termination phase: Saturation
% 1.72/0.82 % (220199)Time elapsed: 0.067 s
% 1.72/0.82 % (220199)Peak memory usage: 12 MB
% 1.72/0.82 % (220199)Instructions burned: 103 (million)
% 1.72/0.82 % (220200)Instruction limit reached!
% 1.72/0.82 % (220200)------------------------------
% 1.72/0.82 % (220200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220200)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220200)Termination reason: Instruction limit
% 1.72/0.82 % (220200)Termination phase: Saturation
% 1.72/0.82 % (220200)Time elapsed: 0.074 s
% 1.72/0.82 % (220200)Peak memory usage: 13 MB
% 1.72/0.82 % (220200)Instructions burned: 116 (million)
% 1.72/0.82 % (220210)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4273558837:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.72/0.82 % TRYING [6]
% 1.72/0.82 % TRYING [1]
% 1.72/0.82 % TRYING [2]
% 1.72/0.82 % (220211)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2968412914:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.72/0.82 % TRYING [3]
% 1.72/0.82 % TRYING [4]
% 1.72/0.82 % (220202)Instruction limit reached!
% 1.72/0.82 % (220202)------------------------------
% 1.72/0.82 % (220202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220202)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220202)Termination reason: Instruction limit
% 1.72/0.82 % (220202)Termination phase: Saturation
% 1.72/0.82 % (220202)Time elapsed: 0.103 s
% 1.72/0.82 % (220202)Peak memory usage: 13 MB
% 1.72/0.82 % (220202)Instructions burned: 159 (million)
% 1.72/0.82 % (220201)Instruction limit reached!
% 1.72/0.82 % (220201)------------------------------
% 1.72/0.82 % (220201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220201)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220201)Termination reason: Instruction limit
% 1.72/0.82 % (220201)Termination phase: Saturation
% 1.72/0.82 % (220201)Time elapsed: 0.102 s
% 1.72/0.82 % (220201)Peak memory usage: 13 MB
% 1.72/0.82 % (220201)Instructions burned: 132 (million)
% 1.72/0.82 % (220214)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2212562337:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.72/0.82 % TRYING [5]
% 1.72/0.82 % (220215)ott-21_1_sil=16000:fs=off:random_seed=1974766469:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.72/0.82 % (220211)Instruction limit reached!
% 1.72/0.82 % (220211)------------------------------
% 1.72/0.82 % (220211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220211)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220211)Termination reason: Instruction limit
% 1.72/0.82 % (220211)Termination phase: Saturation
% 1.72/0.82 % (220211)Time elapsed: 0.089 s
% 1.72/0.82 % (220211)Peak memory usage: 13 MB
% 1.72/0.82 % (220211)Instructions burned: 131 (million)
% 1.72/0.82 % TRYING [6]
% 1.72/0.82 % (220218)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=492235470:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.72/0.82 % (220215)Instruction limit reached!
% 1.72/0.82 % (220215)------------------------------
% 1.72/0.82 % (220215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220215)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220215)Termination reason: Instruction limit
% 1.72/0.82 % (220215)Termination phase: Saturation
% 1.72/0.82 % (220215)Time elapsed: 0.073 s
% 1.72/0.82 % (220215)Peak memory usage: 11 MB
% 1.72/0.82 % (220215)Instructions burned: 182 (million)
% 1.72/0.82 % (220220)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=472877489:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.72/0.82 % TRYING [1]
% 1.72/0.82 % TRYING [2]
% 1.72/0.82 % TRYING [3]
% 1.72/0.82 % TRYING [4]
% 1.72/0.82 % TRYING [7]
% 1.72/0.82 % (220218) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-220191-220218"...
% 1.72/0.82 % (220218)...printing done.
% 1.72/0.82 % (220218)Refutation found. Thanks to Tanya!
% 1.72/0.82 % SZS status Theorem for theBenchmark
% 1.72/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 1.72/0.82 % (220218)------------------------------
% 1.72/0.82 % (220218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.82 % (220218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.82 % (220218)CaDiCaL version: 2.1.3
% 1.72/0.82 % (220218)Termination reason: Refutation
% 1.72/0.82 % (220218)Time elapsed: 0.078 s
% 1.72/0.82 % (220218)Peak memory usage: 13 MB
% 1.72/0.82 % (220218)Instructions burned: 120 (million)
% 1.72/0.82 % (220191)Success in time 0.32 s
% 1.72/0.82 % Vampire exiting
%------------------------------------------------------------------------------