%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE139+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 : n017.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 11:40:57 AM UTC 2026
% Result : Theorem 0.17s 0.55s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 49 unt; 2 def)
% Number of atoms : 113 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 31 ~; 27 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 85 ( 0 sgn 84 !; 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(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(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(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_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(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
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(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
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(X0),addition(multiplication(strong_iteration(X0),X0),one))
& leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one))
& leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0] :
( ~ leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one))
| ~ leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(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(sK0),addition(multiplication(strong_iteration(sK0),sK0),one))
| ~ leq(addition(multiplication(strong_iteration(sK0),sK0),one),strong_iteration(sK0)) ),
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(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(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(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
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(f38,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f43,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(strong_iteration(sK0),addition(multiplication(strong_iteration(sK0),sK0),one))
| ~ leq(addition(multiplication(strong_iteration(sK0),sK0),one),strong_iteration(sK0)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,definition,
( spl1_1
<=> leq(addition(multiplication(strong_iteration(sK0),sK0),one),strong_iteration(sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ leq(addition(multiplication(strong_iteration(sK0),sK0),one),strong_iteration(sK0))
| spl1_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl1_2
<=> leq(strong_iteration(sK0),addition(multiplication(strong_iteration(sK0),sK0),one)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f54,plain,
( ~ leq(strong_iteration(sK0),addition(multiplication(strong_iteration(sK0),sK0),one))
| spl1_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f56,plain,
( ~ leq(addition(one,multiplication(strong_iteration(sK0),sK0)),strong_iteration(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f50,f27]) ).
fof(f66,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f45,f30]) ).
fof(f71,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f66]) ).
fof(f74,plain,
star(zero) = addition(one,zero),
inference(superposition,[],[f37,f36]) ).
fof(f80,plain,
one = star(zero),
inference(forward_demodulation,[],[f74,f29]) ).
fof(f122,plain,
! [X2,X0,X1] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f28,f27]) ).
fof(f126,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,star(X0)),X1)) = addition(star(X0),X1),
inference(superposition,[],[f28,f37]) ).
fof(f139,plain,
! [X0,X1] : addition(star(X0),X1) = addition(star(zero),addition(multiplication(X0,star(X0)),X1)),
inference(forward_demodulation,[],[f126,f80]) ).
fof(f177,plain,
! [X0,X1] : multiplication(X1,star(X0)) = addition(multiplication(X1,one),multiplication(X1,multiplication(star(X0),X0))),
inference(superposition,[],[f34,f38]) ).
fof(f199,plain,
! [X0,X1] : multiplication(X1,star(X0)) = addition(X1,multiplication(X1,multiplication(star(X0),X0))),
inference(forward_demodulation,[],[f177,f32]) ).
fof(f233,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(one,X1),multiplication(multiplication(X0,star(X0)),X1)),
inference(superposition,[],[f35,f37]) ).
fof(f235,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(star(X0),X1),multiplication(multiplication(strong_iteration(X0),zero),X1)),
inference(superposition,[],[f35,f43]) ).
fof(f254,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(star(X0),X1),multiplication(strong_iteration(X0),multiplication(zero,X1))),
inference(forward_demodulation,[],[f235,f31]) ).
fof(f256,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(one,X1),multiplication(X0,multiplication(star(X0),X1))),
inference(forward_demodulation,[],[f233,f31]) ).
fof(f265,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(star(X0),X1),multiplication(strong_iteration(X0),zero)),
inference(forward_demodulation,[],[f254,f36]) ).
fof(f267,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(X0,multiplication(star(X0),X1))),
inference(forward_demodulation,[],[f256,f33]) ).
fof(f617,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f28,f122]) ).
fof(f1961,plain,
! [X0] : multiplication(X0,star(X0)) = multiplication(star(X0),X0),
inference(superposition,[],[f199,f267]) ).
fof(f3293,plain,
( ~ leq(addition(one,addition(multiplication(star(sK0),sK0),multiplication(strong_iteration(sK0),zero))),strong_iteration(sK0))
| spl1_1 ),
inference(superposition,[],[f56,f265]) ).
fof(f3347,plain,
! [X2,X0,X1] : addition(multiplication(strong_iteration(X0),X1),X2) = addition(multiplication(strong_iteration(X0),zero),addition(multiplication(star(X0),X1),X2)),
inference(superposition,[],[f122,f265]) ).
fof(f3390,plain,
( ~ leq(addition(one,addition(multiplication(sK0,star(sK0)),multiplication(strong_iteration(sK0),zero))),strong_iteration(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f3293,f1961]) ).
fof(f3417,plain,
( ~ leq(addition(star(zero),addition(multiplication(sK0,star(sK0)),multiplication(strong_iteration(sK0),zero))),strong_iteration(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f3390,f80]) ).
fof(f3436,plain,
( ~ leq(addition(star(sK0),multiplication(strong_iteration(sK0),zero)),strong_iteration(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f3417,f139]) ).
fof(f3446,plain,
( ~ leq(strong_iteration(sK0),strong_iteration(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f3436,f43]) ).
fof(f3451,plain,
( $false
| spl1_1 ),
inference(forward_subsumption_resolution,[],[f3446,f71]) ).
fof(f3452,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f3451]) ).
fof(f3457,plain,
( ~ leq(strong_iteration(sK0),addition(multiplication(strong_iteration(sK0),zero),addition(multiplication(star(sK0),sK0),one)))
| spl1_2 ),
inference(forward_demodulation,[],[f54,f3347]) ).
fof(f3459,plain,
( ~ leq(strong_iteration(sK0),addition(addition(multiplication(star(sK0),sK0),one),multiplication(strong_iteration(sK0),zero)))
| spl1_2 ),
inference(forward_demodulation,[],[f3457,f27]) ).
fof(f3461,plain,
( ~ leq(strong_iteration(sK0),addition(multiplication(star(sK0),sK0),addition(one,multiplication(strong_iteration(sK0),zero))))
| spl1_2 ),
inference(forward_demodulation,[],[f3459,f28]) ).
fof(f3463,plain,
( ~ leq(strong_iteration(sK0),addition(one,addition(multiplication(star(sK0),sK0),multiplication(strong_iteration(sK0),zero))))
| spl1_2 ),
inference(forward_demodulation,[],[f3461,f617]) ).
fof(f3465,plain,
( ~ leq(strong_iteration(sK0),addition(one,addition(multiplication(sK0,star(sK0)),multiplication(strong_iteration(sK0),zero))))
| spl1_2 ),
inference(forward_demodulation,[],[f3463,f1961]) ).
fof(f3467,plain,
( ~ leq(strong_iteration(sK0),addition(star(zero),addition(multiplication(sK0,star(sK0)),multiplication(strong_iteration(sK0),zero))))
| spl1_2 ),
inference(forward_demodulation,[],[f3465,f80]) ).
fof(f3469,plain,
( ~ leq(strong_iteration(sK0),addition(star(sK0),multiplication(strong_iteration(sK0),zero)))
| spl1_2 ),
inference(forward_demodulation,[],[f3467,f139]) ).
fof(f3471,plain,
( ~ leq(strong_iteration(sK0),strong_iteration(sK0))
| spl1_2 ),
inference(forward_demodulation,[],[f3469,f43]) ).
fof(f3472,plain,
( $false
| spl1_2 ),
inference(forward_subsumption_resolution,[],[f3471,f71]) ).
fof(f3473,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f3472]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s8,plain,
spl1_1,
inference(sat_conversion,[],[f3452]) ).
cnf(s9,plain,
spl1_2,
inference(sat_conversion,[],[f3473]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
fof(f3474,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE139+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:07:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.17/0.55 % (2540965)Will run a generic schedule for satisfiability detection.
% 0.17/0.55 % (2540975)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=948446884:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.55 % (2540972)% WARNING: option uhcvi not known.
% 0.17/0.55 % (2540972)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3526391437:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.55 % (2540970)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1446269289_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.55 % (2540973)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=888101887:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.55 % (2540974)dis+10_1_sil=32000:sp=arity:random_seed=1755375302:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.55 % (2540976)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=845536121:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.55 % (2540977)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2915423060:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.55 % TRYING [1]
% 0.17/0.55 % TRYING [2]
% 0.17/0.55 % TRYING [3]
% 0.17/0.55 % TRYING [4]
% 0.17/0.55 % TRYING [5]
% 0.17/0.55 % (2540975)Instruction limit reached!
% 0.17/0.55 % (2540975)------------------------------
% 0.17/0.55 % (2540975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (2540975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (2540975)CaDiCaL version: 2.1.3
% 0.17/0.55 % (2540975)Termination reason: Instruction limit
% 0.17/0.55 % (2540975)Termination phase: Saturation
% 0.17/0.55 % (2540975)Time elapsed: 0.042 s
% 0.17/0.55 % (2540975)Peak memory usage: 13 MB
% 0.17/0.55 % (2540975)Instructions burned: 119 (million)
% 0.17/0.55 % (2540998)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3071726408:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.55 % TRYING [1]
% 0.17/0.55 % TRYING [2]
% 0.17/0.55 % TRYING [3]
% 0.17/0.55 % TRYING [4]
% 0.17/0.55 % (2540974)Instruction limit reached!
% 0.17/0.55 % (2540974)------------------------------
% 0.17/0.55 % (2540974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (2540974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (2540974)CaDiCaL version: 2.1.3
% 0.17/0.55 % (2540974)Termination reason: Instruction limit
% 0.17/0.55 % (2540974)Termination phase: Saturation
% 0.17/0.55 % (2540974)Time elapsed: 0.063 s
% 0.17/0.55 % (2540974)Peak memory usage: 12 MB
% 0.17/0.55 % (2540974)Instructions burned: 103 (million)
% 0.17/0.55 % TRYING [5]
% 0.17/0.55 % (2540976) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2540965-2540976"...
% 0.17/0.55 % (2540976)...printing done.
% 0.17/0.55 % (2540976)Refutation found. Thanks to Tanya!
% 0.17/0.55 % SZS status Theorem for theBenchmark
% 0.17/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.55 % (2540976)------------------------------
% 0.17/0.55 % (2540976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (2540976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (2540976)CaDiCaL version: 2.1.3
% 0.17/0.55 % (2540976)Termination reason: Refutation
% 0.17/0.55 % (2540976)Time elapsed: 0.081 s
% 0.17/0.55 % (2540976)Peak memory usage: 14 MB
% 0.17/0.55 % (2540976)Instructions burned: 127 (million)
% 0.17/0.55 % (2540965)Success in time 0.131 s
% 0.17/0.55 % Vampire exiting
%------------------------------------------------------------------------------