%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE141+1 : 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 : n004.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 1.08s 0.67s
% Output : Refutation 1.08s
% 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 : 77 ( 0 sgn 76 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
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(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(f13,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X2),X1),X2)
=> leq(multiplication(star(X0),X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
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(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
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] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
file('/export/starexec/sandbox2/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,X1,X2] :
( leq(multiplication(star(X0),X1),X2)
| ~ leq(addition(multiplication(X0,X2),X1),X2) ),
inference(ennf_transformation,[],[f13]) ).
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] : strong_iteration(one) != multiplication(strong_iteration(one),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,
strong_iteration(one) != multiplication(strong_iteration(one),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(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(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f38,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X2),X1),X2)
| leq(multiplication(star(X0),X1),X2) ),
inference(cnf_transformation,[],[f21]) ).
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(f43,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
strong_iteration(one) != multiplication(strong_iteration(one),sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f56,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f45,f30]) ).
fof(f61,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f56]) ).
fof(f95,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f28,f30]) ).
fof(f193,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(multiplication(star(one),X1),X0) ),
inference(superposition,[],[f39,f33]) ).
fof(f254,definition,
( spl1_3
<=> leq(star(one),one) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f256,plain,
( leq(star(one),one)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl1_4
<=> one = star(one) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f259,plain,
( one = star(one)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f260,plain,
( one != star(one)
| spl1_4 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f263,plain,
! [X0,X1] :
( ~ leq(one,addition(X0,X1))
| leq(one,multiplication(strong_iteration(X0),X1)) ),
inference(superposition,[],[f42,f32]) ).
fof(f300,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(superposition,[],[f95,f38]) ).
fof(f307,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f45,f95]) ).
fof(f312,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f307]) ).
fof(f1052,plain,
! [X0] :
( ~ leq(X0,X0)
| leq(multiplication(star(one),X0),X0) ),
inference(superposition,[],[f193,f30]) ).
fof(f1079,plain,
! [X0] : leq(multiplication(star(one),X0),X0),
inference(forward_subsumption_resolution,[],[f1052,f61]) ).
fof(f1104,plain,
leq(star(one),one),
inference(superposition,[],[f1079,f32]) ).
fof(f1105,plain,
spl1_3,
inference(avatar_split_clause,[],[f1104,f254]) ).
fof(f1157,plain,
( one = addition(star(one),one)
| ~ spl1_3 ),
inference(resolution,[],[f256,f44]) ).
fof(f1158,plain,
( one = addition(one,star(one))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f1157,f27]) ).
fof(f1159,plain,
( one = star(one)
| ~ spl1_3 ),
inference(forward_demodulation,[],[f1158,f300]) ).
fof(f1160,plain,
( $false
| ~ spl1_3
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f1159,f260]) ).
fof(f1161,plain,
( ~ spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f1160]) ).
fof(f1228,plain,
( strong_iteration(one) = addition(one,multiplication(strong_iteration(one),zero))
| ~ spl1_4 ),
inference(superposition,[],[f43,f259]) ).
fof(f1233,plain,
! [X0] : leq(one,multiplication(strong_iteration(one),X0)),
inference(resolution,[],[f263,f312]) ).
fof(f1267,plain,
! [X0] : multiplication(strong_iteration(one),X0) = addition(one,multiplication(strong_iteration(one),X0)),
inference(resolution,[],[f1233,f44]) ).
fof(f1269,plain,
( strong_iteration(one) = multiplication(strong_iteration(one),zero)
| ~ spl1_4 ),
inference(backward_demodulation,[],[f1228,f1267]) ).
fof(f2214,plain,
( ! [X0] : multiplication(strong_iteration(one),X0) = multiplication(strong_iteration(one),multiplication(zero,X0))
| ~ spl1_4 ),
inference(superposition,[],[f31,f1269]) ).
fof(f2255,plain,
( ! [X0] : multiplication(strong_iteration(one),X0) = multiplication(strong_iteration(one),zero)
| ~ spl1_4 ),
inference(forward_demodulation,[],[f2214,f36]) ).
fof(f2266,plain,
( ! [X0] : strong_iteration(one) = multiplication(strong_iteration(one),X0)
| ~ spl1_4 ),
inference(forward_demodulation,[],[f2255,f1269]) ).
fof(f2270,plain,
( strong_iteration(one) != strong_iteration(one)
| ~ spl1_4 ),
inference(backward_demodulation,[],[f46,f2266]) ).
fof(f2276,plain,
( $false
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f2270]) ).
fof(f2277,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f2276]) ).
cnf(s4,plain,
spl1_3,
inference(sat_conversion,[],[f1105]) ).
cnf(s5,plain,
( ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f1161]) ).
cnf(s8,plain,
~ spl1_4,
inference(sat_conversion,[],[f2277]) ).
cnf(s9,plain,
~ spl1_3,
inference(rat,[],[s5,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s9]) ).
fof(f2278,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE141+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 % Computer : n004.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 13:12:07 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.45 Running first-order model finding
% 0.14/0.45 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
% 1.08/0.67 % (3514037)Will run a generic schedule for satisfiability detection.
% 1.08/0.67 % (3514057)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3246793489:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.08/0.67 % (3514054)% WARNING: option uhcvi not known.
% 1.08/0.67 % (3514055)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1485550977:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.08/0.67 % (3514053)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3827786787_2999 on theBenchmark for (2999ds/0Mi)
% 1.08/0.67 % (3514054)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1476467213:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.08/0.67 % (3514056)dis+10_1_sil=32000:sp=arity:random_seed=3920650069:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.08/0.67 % (3514060)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1415606656:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.08/0.67 % (3514059)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=356528984:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.67 % TRYING [1]
% 1.08/0.67 % TRYING [2]
% 1.08/0.67 % TRYING [3]
% 1.08/0.67 % TRYING [4]
% 1.08/0.67 % TRYING [5]
% 1.08/0.67 % (3514057)Instruction limit reached!
% 1.08/0.67 % (3514057)------------------------------
% 1.08/0.67 % (3514057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.67 % (3514057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.67 % (3514057)CaDiCaL version: 2.1.3
% 1.08/0.67 % (3514057)Termination reason: Instruction limit
% 1.08/0.67 % (3514057)Termination phase: Saturation
% 1.08/0.67 % (3514057)Time elapsed: 0.040 s
% 1.08/0.67 % (3514057)Peak memory usage: 13 MB
% 1.08/0.67 % (3514057)Instructions burned: 116 (million)
% 1.08/0.67 % (3514089)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3275499339:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.08/0.67 % TRYING [1]
% 1.08/0.67 % TRYING [2]
% 1.08/0.67 % TRYING [3]
% 1.08/0.67 % TRYING [4]
% 1.08/0.67 % TRYING [5]
% 1.08/0.67 % (3514056)Instruction limit reached!
% 1.08/0.67 % (3514056)------------------------------
% 1.08/0.67 % (3514056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.67 % (3514056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.67 % (3514056)CaDiCaL version: 2.1.3
% 1.08/0.67 % (3514056)Termination reason: Instruction limit
% 1.08/0.67 % (3514056)Termination phase: Saturation
% 1.08/0.67 % (3514056)Time elapsed: 0.062 s
% 1.08/0.67 % (3514056)Peak memory usage: 12 MB
% 1.08/0.67 % (3514056)Instructions burned: 103 (million)
% 1.08/0.67 % (3514097)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3166198367:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.08/0.67 % TRYING [6]
% 1.08/0.67 % (3514059)Instruction limit reached!
% 1.08/0.67 % (3514059)------------------------------
% 1.08/0.67 % (3514059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.67 % (3514059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.67 % (3514059)CaDiCaL version: 2.1.3
% 1.08/0.67 % (3514059)Termination reason: Instruction limit
% 1.08/0.67 % (3514059)Termination phase: Saturation
% 1.08/0.67 % (3514059)Time elapsed: 0.087 s
% 1.08/0.67 % (3514059)Peak memory usage: 13 MB
% 1.08/0.67 % (3514059)Instructions burned: 131 (million)
% 1.08/0.67 % TRYING [6]
% 1.08/0.67 % (3514060)Instruction limit reached!
% 1.08/0.67 % (3514060)------------------------------
% 1.08/0.67 % (3514060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.67 % (3514060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.67 % (3514060)CaDiCaL version: 2.1.3
% 1.08/0.67 % (3514060)Termination reason: Instruction limit
% 1.08/0.67 % (3514060)Termination phase: Saturation
% 1.08/0.67 % (3514060)Time elapsed: 0.103 s
% 1.08/0.67 % (3514060)Peak memory usage: 13 MB
% 1.08/0.67 % (3514060)Instructions burned: 159 (million)
% 1.08/0.67 % (3514107)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=65809568:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.08/0.67 % (3514115)ott-21_1_sil=16000:fs=off:random_seed=3962672115:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.08/0.67 % (3514097) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3514037-3514097"...
% 1.08/0.67 % (3514097)...printing done.
% 1.08/0.67 % (3514097)Refutation found. Thanks to Tanya!
% 1.08/0.67 % SZS status Theorem for theBenchmark
% 1.08/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 1.08/0.67 % (3514097)------------------------------
% 1.08/0.67 % (3514097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.67 % (3514097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.67 % (3514097)CaDiCaL version: 2.1.3
% 1.08/0.67 % (3514097)Termination reason: Refutation
% 1.08/0.67 % (3514097)Time elapsed: 0.079 s
% 1.08/0.67 % (3514097)Peak memory usage: 14 MB
% 1.08/0.67 % (3514097)Instructions burned: 113 (million)
% 1.08/0.67 % (3514037)Success in time 0.209 s
% 1.08/0.67 % Vampire exiting
%------------------------------------------------------------------------------