%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE040+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 : 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 11:40:44 AM UTC 2026
% Result : Theorem 1.64s 0.75s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 41 unt; 0 def)
% Number of atoms : 57 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 6 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 75 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+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/KLE002+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(f15,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(f17,conjecture,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
? [X0] : star(X0) != multiplication(star(X0),star(X0)),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f12]) ).
fof(f35,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
star(sK0) != multiplication(star(sK0),star(sK0)),
inference(cnf_transformation,[],[f21]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| leq(multiplication(star(X1),X0),X2) ),
inference(superposition,[],[f37,f22]) ).
fof(f154,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(resolution,[],[f34,f35]) ).
fof(f155,plain,
! [X0] : star(X0) = addition(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(resolution,[],[f34,f36]) ).
fof(f170,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(star(X0),X0))),
inference(forward_demodulation,[],[f155,f22]) ).
fof(f171,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[],[f154,f22]) ).
fof(f208,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f23,f25]) ).
fof(f282,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(superposition,[],[f208,f22]) ).
fof(f290,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f33,f208]) ).
fof(f297,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f290]) ).
fof(f361,plain,
! [X2,X0,X1] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[],[f297,f23]) ).
fof(f538,plain,
! [X2,X0,X1] : leq(addition(X2,X1),addition(X2,addition(X0,X1))),
inference(superposition,[],[f361,f22]) ).
fof(f847,plain,
! [X0] : leq(addition(star(X0),one),star(X0)),
inference(superposition,[],[f361,f170]) ).
fof(f884,plain,
! [X0] : leq(addition(one,star(X0)),star(X0)),
inference(forward_demodulation,[],[f847,f22]) ).
fof(f900,plain,
! [X0] : star(X0) = addition(addition(one,star(X0)),star(X0)),
inference(resolution,[],[f884,f34]) ).
fof(f908,plain,
! [X0] : star(X0) = addition(star(X0),addition(one,star(X0))),
inference(forward_demodulation,[],[f900,f22]) ).
fof(f909,plain,
! [X0] : star(X0) = addition(one,star(X0)),
inference(forward_demodulation,[],[f908,f282]) ).
fof(f928,plain,
! [X0] : leq(addition(star(X0),multiplication(X0,star(X0))),star(X0)),
inference(superposition,[],[f538,f171]) ).
fof(f2393,plain,
! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
inference(resolution,[],[f82,f928]) ).
fof(f2416,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),star(X0)),star(X0)),
inference(resolution,[],[f2393,f34]) ).
fof(f2421,plain,
! [X0] : star(X0) = addition(star(X0),multiplication(star(X0),star(X0))),
inference(forward_demodulation,[],[f2416,f22]) ).
fof(f9531,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f29,f27]) ).
fof(f10572,plain,
! [X0] : star(X0) = multiplication(star(X0),addition(one,star(X0))),
inference(superposition,[],[f2421,f9531]) ).
fof(f10599,plain,
! [X0] : star(X0) = multiplication(star(X0),star(X0)),
inference(forward_demodulation,[],[f10572,f909]) ).
fof(f10876,plain,
star(sK0) != star(sK0),
inference(superposition,[],[f39,f10599]) ).
fof(f10903,plain,
$false,
inference(trivial_inequality_removal,[],[f10876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE040+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 13:04:51 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.43 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
% 1.64/0.75 % (209449)Will run a generic schedule for satisfiability detection.
% 1.64/0.75 % (209458)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1638285244:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.64/0.75 % (209455)% WARNING: option uhcvi not known.
% 1.64/0.75 % (209454)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2397182101_2999 on theBenchmark for (2999ds/0Mi)
% 1.64/0.75 % (209459)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1379178234:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.64/0.75 % (209455)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2607662779:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.64/0.75 % (209456)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=765197234:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.64/0.75 % (209457)dis+10_1_sil=32000:sp=arity:random_seed=4164606835:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.64/0.75 % (209460)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3136411150:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.64/0.75 % TRYING [1]
% 1.64/0.75 % TRYING [2]
% 1.64/0.75 % TRYING [3]
% 1.64/0.75 % TRYING [4]
% 1.64/0.75 % TRYING [5]
% 1.64/0.75 % (209458)Instruction limit reached!
% 1.64/0.75 % (209458)------------------------------
% 1.64/0.75 % (209458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209458)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209458)Termination reason: Instruction limit
% 1.64/0.75 % (209458)Termination phase: Saturation
% 1.64/0.75 % (209458)Time elapsed: 0.039 s
% 1.64/0.75 % (209458)Peak memory usage: 13 MB
% 1.64/0.75 % (209458)Instructions burned: 118 (million)
% 1.64/0.75 % (209468)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=275923987:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.64/0.75 % TRYING [1]
% 1.64/0.75 % TRYING [2]
% 1.64/0.75 % TRYING [3]
% 1.64/0.75 % TRYING [4]
% 1.64/0.75 % TRYING [5]
% 1.64/0.75 % (209457)Instruction limit reached!
% 1.64/0.75 % (209457)------------------------------
% 1.64/0.75 % (209457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209457)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209457)Termination reason: Instruction limit
% 1.64/0.75 % (209457)Termination phase: Saturation
% 1.64/0.75 % (209457)Time elapsed: 0.062 s
% 1.64/0.75 % (209457)Peak memory usage: 12 MB
% 1.64/0.75 % (209457)Instructions burned: 103 (million)
% 1.64/0.75 % (209459)Instruction limit reached!
% 1.64/0.75 % (209459)------------------------------
% 1.64/0.75 % (209459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209459)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209459)Termination reason: Instruction limit
% 1.64/0.75 % (209459)Termination phase: Saturation
% 1.64/0.75 % (209459)Time elapsed: 0.075 s
% 1.64/0.75 % (209459)Peak memory usage: 13 MB
% 1.64/0.75 % (209459)Instructions burned: 132 (million)
% 1.64/0.75 % (209470)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3945863746:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.64/0.75 % TRYING [6]
% 1.64/0.75 % (209471)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=3151879718:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.64/0.75 % (209460)Instruction limit reached!
% 1.64/0.75 % (209460)------------------------------
% 1.64/0.75 % (209460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209460)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209460)Termination reason: Instruction limit
% 1.64/0.75 % (209460)Termination phase: Saturation
% 1.64/0.75 % (209460)Time elapsed: 0.098 s
% 1.64/0.75 % (209460)Peak memory usage: 13 MB
% 1.64/0.75 % (209460)Instructions burned: 160 (million)
% 1.64/0.75 % TRYING [6]
% 1.64/0.75 % (209474)ott-21_1_sil=16000:fs=off:random_seed=2237474391:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.64/0.75 % (209470)Instruction limit reached!
% 1.64/0.75 % (209470)------------------------------
% 1.64/0.75 % (209470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209470)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209470)Termination reason: Instruction limit
% 1.64/0.75 % (209470)Termination phase: Saturation
% 1.64/0.75 % (209470)Time elapsed: 0.090 s
% 1.64/0.75 % (209470)Peak memory usage: 13 MB
% 1.64/0.75 % (209470)Instructions burned: 132 (million)
% 1.64/0.75 % (209476)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2936313580:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.64/0.75 % (209474)Instruction limit reached!
% 1.64/0.75 % (209474)------------------------------
% 1.64/0.75 % (209474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209474)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209474)Termination reason: Instruction limit
% 1.64/0.75 % (209474)Termination phase: Saturation
% 1.64/0.75 % (209474)Time elapsed: 0.078 s
% 1.64/0.75 % (209474)Peak memory usage: 12 MB
% 1.64/0.75 % (209474)Instructions burned: 182 (million)
% 1.64/0.75 % TRYING [7]
% 1.64/0.75 % (209468)Instruction limit reached!
% 1.64/0.75 % (209468)------------------------------
% 1.64/0.75 % (209468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209468)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209468)Termination reason: Instruction limit
% 1.64/0.75 % (209468)Termination phase: Finite model building constraint generation
% 1.64/0.75 % (209468)Time elapsed: 0.171 s
% 1.64/0.75 % (209468)Peak memory usage: 31 MB
% 1.64/0.75 % (209468)Instructions burned: 722 (million)
% 1.64/0.75 % (209478)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1251447094:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.64/0.75 % TRYING [1]
% 1.64/0.75 % TRYING [2]
% 1.64/0.75 % TRYING [3]
% 1.64/0.75 % (209479)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2240954294:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.64/0.75 % TRYING [4]
% 1.64/0.75 % TRYING [7]
% 1.64/0.75 % (209471) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-209449-209471"...
% 1.64/0.75 % (209471)...printing done.
% 1.64/0.75 % (209471)Refutation found. Thanks to Tanya!
% 1.64/0.75 % SZS status Theorem for theBenchmark
% 1.64/0.75 % SZS output start Proof for theBenchmark
% See solution above
% 1.64/0.75 % (209471)------------------------------
% 1.64/0.75 % (209471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.64/0.75 % (209471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.64/0.75 % (209471)CaDiCaL version: 2.1.3
% 1.64/0.75 % (209471)Termination reason: Refutation
% 1.64/0.75 % (209471)Time elapsed: 0.167 s
% 1.64/0.75 % (209471)Peak memory usage: 15 MB
% 1.64/0.75 % (209471)Instructions burned: 300 (million)
% 1.64/0.75 % (209449)Success in time 0.311 s
% 1.64/0.75 % Vampire exiting
%------------------------------------------------------------------------------