%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE150+2 : 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 : n019.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 11:41:00 AM UTC 2026
% Result : Theorem 1.66s 0.84s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 29 unt; 2 def)
% Number of atoms : 79 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 23 ~; 19 |; 3 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 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 : 52 ( 0 sgn 51 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X2),X1),X2)
=> leq(multiplication(star(X0),X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
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] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
? [X0] :
( ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
| ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
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(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X2),X1),X2)
| leq(multiplication(star(X0),X1),X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,definition,
( spl1_1
<=> leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ leq(addition(one,multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| spl1_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl1_2
<=> leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f54,plain,
( ~ leq(strong_iteration(multiplication(sK0,zero)),addition(one,multiplication(sK0,zero)))
| spl1_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f65,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f45,f30]) ).
fof(f70,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f65]) ).
fof(f134,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),
inference(superposition,[],[f37,f31]) ).
fof(f135,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one),
inference(superposition,[],[f41,f31]) ).
fof(f136,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f135,f27]) ).
fof(f203,plain,
! [X0] :
( ~ leq(strong_iteration(X0),strong_iteration(X0))
| leq(multiplication(star(X0),one),strong_iteration(X0)) ),
inference(superposition,[],[f39,f41]) ).
fof(f210,plain,
! [X0] : leq(multiplication(star(X0),one),strong_iteration(X0)),
inference(forward_subsumption_resolution,[],[f203,f70]) ).
fof(f212,plain,
! [X0] : leq(star(X0),strong_iteration(X0)),
inference(forward_demodulation,[],[f210,f32]) ).
fof(f2413,plain,
! [X0] : addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(superposition,[],[f134,f36]) ).
fof(f2455,plain,
( ~ leq(star(multiplication(sK0,zero)),strong_iteration(multiplication(sK0,zero)))
| spl1_1 ),
inference(backward_demodulation,[],[f50,f2413]) ).
fof(f2465,plain,
( $false
| spl1_1 ),
inference(forward_subsumption_resolution,[],[f2455,f212]) ).
fof(f2466,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f2465]) ).
fof(f2471,plain,
( ~ leq(strong_iteration(multiplication(sK0,zero)),star(multiplication(sK0,zero)))
| spl1_2 ),
inference(forward_demodulation,[],[f54,f2413]) ).
fof(f2480,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(superposition,[],[f136,f36]) ).
fof(f2521,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(forward_demodulation,[],[f2480,f2413]) ).
fof(f2531,plain,
( ~ leq(star(multiplication(sK0,zero)),star(multiplication(sK0,zero)))
| spl1_2 ),
inference(backward_demodulation,[],[f2471,f2521]) ).
fof(f2534,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f2531,f70]) ).
fof(f2535,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f2534]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s9,plain,
spl1_1,
inference(sat_conversion,[],[f2466]) ).
cnf(s10,plain,
spl1_2,
inference(sat_conversion,[],[f2535]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s10,s9]) ).
fof(f2537,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 13:13:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 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
% 1.66/0.84 % (3084902)Will run a generic schedule for satisfiability detection.
% 1.66/0.84 % (3084912)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=497105766:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.66/0.84 % (3084907)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1765966399_2999 on theBenchmark for (2999ds/0Mi)
% 1.66/0.84 % TRYING [1]
% 1.66/0.84 % TRYING [2]
% 1.66/0.84 % TRYING [3]
% 1.66/0.84 % (3084908)% WARNING: option uhcvi not known.
% 1.66/0.84 % (3084910)dis+10_1_sil=32000:sp=arity:random_seed=39792346:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.66/0.84 % (3084908)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4055378548:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.66/0.84 % (3084911)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3589161265:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.66/0.84 % (3084909)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3923091688:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.66/0.84 % (3084913)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1476310984:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.66/0.84 % TRYING [4]
% 1.66/0.84 % TRYING [5]
% 1.66/0.84 % (3084912)Instruction limit reached!
% 1.66/0.84 % (3084912)------------------------------
% 1.66/0.84 % (3084912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.66/0.84 % (3084912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/0.84 % (3084912)CaDiCaL version: 2.1.3
% 1.66/0.84 % (3084912)Termination reason: Instruction limit
% 1.66/0.84 % (3084912)Termination phase: Saturation
% 1.66/0.84 % (3084912)Time elapsed: 0.069 s
% 1.66/0.84 % (3084912)Peak memory usage: 13 MB
% 1.66/0.84 % (3084912)Instructions burned: 131 (million)
% 1.66/0.84 % (3084921)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4098914583:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.66/0.84 % TRYING [1]
% 1.66/0.84 % TRYING [2]
% 1.66/0.84 % TRYING [3]
% 1.66/0.84 % TRYING [4]
% 1.66/0.84 % (3084910)Instruction limit reached!
% 1.66/0.84 % (3084910)------------------------------
% 1.66/0.84 % (3084910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.66/0.84 % (3084910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/0.84 % (3084910)CaDiCaL version: 2.1.3
% 1.66/0.84 % (3084910)Termination reason: Instruction limit
% 1.66/0.84 % (3084910)Termination phase: Saturation
% 1.66/0.84 % (3084910)Time elapsed: 0.101 s
% 1.66/0.84 % (3084910)Peak memory usage: 12 MB
% 1.66/0.84 % (3084910)Instructions burned: 103 (million)
% 1.66/0.84 % (3084911)Instruction limit reached!
% 1.66/0.84 % (3084911)------------------------------
% 1.66/0.84 % (3084911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.66/0.84 % (3084911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/0.84 % (3084911)CaDiCaL version: 2.1.3
% 1.66/0.84 % (3084911)Termination reason: Instruction limit
% 1.66/0.84 % (3084911)Termination phase: Saturation
% 1.66/0.84 % (3084911)Time elapsed: 0.122 s
% 1.66/0.84 % (3084911)Peak memory usage: 13 MB
% 1.66/0.84 % (3084911)Instructions burned: 116 (million)
% 1.66/0.84 % TRYING [5]
% 1.66/0.84 % (3084923)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2064122911:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.66/0.84 % (3084924)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=578702604:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.66/0.84 % TRYING [6]
% 1.66/0.84 % (3084913)Instruction limit reached!
% 1.66/0.84 % (3084913)------------------------------
% 1.66/0.84 % (3084913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.66/0.84 % (3084913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/0.84 % (3084913)CaDiCaL version: 2.1.3
% 1.66/0.84 % (3084913)Termination reason: Instruction limit
% 1.66/0.84 % (3084913)Termination phase: Saturation
% 1.66/0.84 % (3084913)Time elapsed: 0.169 s
% 1.66/0.84 % (3084913)Peak memory usage: 13 MB
% 1.66/0.84 % (3084913)Instructions burned: 159 (million)
% 1.66/0.84 % TRYING [6]
% 1.66/0.84 % (3084927)ott-21_1_sil=16000:fs=off:random_seed=2983526342:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 1.66/0.84 % (3084923) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3084902-3084923"...
% 1.66/0.84 % (3084923)...printing done.
% 1.66/0.84 % (3084923)Refutation found. Thanks to Tanya!
% 1.66/0.84 % SZS status Theorem for theBenchmark
% 1.66/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 1.66/0.84 % (3084923)------------------------------
% 1.66/0.84 % (3084923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.66/0.84 % (3084923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/0.84 % (3084923)CaDiCaL version: 2.1.3
% 1.66/0.84 % (3084923)Termination reason: Refutation
% 1.66/0.84 % (3084923)Time elapsed: 0.143 s
% 1.66/0.84 % (3084923)Peak memory usage: 14 MB
% 1.66/0.84 % (3084923)Instructions burned: 126 (million)
% 1.66/0.84 % (3084902)Success in time 0.332 s
% 1.66/0.84 % Vampire exiting
%------------------------------------------------------------------------------