%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE139+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:40:26 AM UTC 2026
% Result : Theorem 9.26s 2.34s
% Output : Refutation 9.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
fof(f17,axiom,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
fof(f19,conjecture,
! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),one),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] : strong_iteration(X0) != addition(multiplication(strong_iteration(X0),X0),one),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
strong_iteration(sK0) != addition(multiplication(strong_iteration(sK0),sK0),one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f27,plain,
strong_iteration(sK0) != addition(multiplication(strong_iteration(sK0),sK0),one),
inference(cnf_transformation,[],[f25]) ).
fof(f29,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f35,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f47,plain,
strong_iteration(sK0) != addition(one,multiplication(strong_iteration(sK0),sK0)),
inference(forward_demodulation,[],[f27,f30]) ).
fof(f80,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),X0),X1)) = addition(star(X0),X1),
inference(superposition,[],[f29,f35]) ).
fof(f930,plain,
! [X0,X1] : addition(star(X0),multiplication(X1,X0)) = addition(one,multiplication(addition(star(X0),X1),X0)),
inference(superposition,[],[f80,f31]) ).
fof(f986,plain,
! [X0] : addition(star(X0),multiplication(multiplication(strong_iteration(X0),zero),X0)) = addition(one,multiplication(strong_iteration(X0),X0)),
inference(superposition,[],[f930,f39]) ).
fof(f1020,plain,
! [X0] : addition(one,multiplication(strong_iteration(X0),X0)) = addition(star(X0),multiplication(strong_iteration(X0),multiplication(zero,X0))),
inference(forward_demodulation,[],[f986,f33]) ).
fof(f1028,plain,
! [X0] : addition(star(X0),multiplication(strong_iteration(X0),zero)) = addition(one,multiplication(strong_iteration(X0),X0)),
inference(forward_demodulation,[],[f1020,f43]) ).
fof(f1031,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(strong_iteration(X0),X0)),
inference(forward_demodulation,[],[f1028,f39]) ).
fof(f1038,plain,
strong_iteration(sK0) != strong_iteration(sK0),
inference(superposition,[],[f47,f1031]) ).
fof(f1047,plain,
$false,
inference(trivial_inequality_removal,[],[f1038]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE139+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n009.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 13:12:15 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.47 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.26/2.34 % (2028235)Detected formulas, will run a generic FOF schedule.
% 9.26/2.34 % (2028250)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1247340283:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.26/2.34 % (2028252)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3284277913:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.26/2.34 % (2028251)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2567156626:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.26/2.34 % (2028253)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1832008775:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.26/2.34 % (2028249)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3071739551:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.26/2.34 % (2028252)Refutation not found, incomplete strategy
% 9.26/2.34 % (2028252)------------------------------
% 9.26/2.34 % (2028252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028252)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028252)Termination reason: Refutation not found, incomplete strategy
% 9.26/2.34 % (2028252)Time elapsed: 0.002 s
% 9.26/2.34 % (2028252)Peak memory usage: 88 MB
% 9.26/2.34 % (2028255)dis-21_1_sil=8000:lcm=predicate:random_seed=3638581470:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 9.26/2.34 % (2028254)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1104074591:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.26/2.34 % (2028255)Refutation not found, incomplete strategy
% 9.26/2.34 % (2028255)------------------------------
% 9.26/2.34 % (2028255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028255)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028255)Termination reason: Refutation not found, incomplete strategy
% 9.26/2.34 % (2028255)Time elapsed: 0.003 s
% 9.26/2.34 % (2028255)Peak memory usage: 88 MB
% 9.26/2.34 % (2028255)Instructions burned: 1 (million)
% 9.26/2.34 % (2028253)Instruction limit reached!
% 9.26/2.34 % (2028253)------------------------------
% 9.26/2.34 % (2028253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028253)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028253)Termination reason: Instruction limit
% 9.26/2.34 % (2028253)Termination phase: Saturation
% 9.26/2.34 % (2028253)Time elapsed: 0.120 s
% 9.26/2.34 % (2028253)Peak memory usage: 89 MB
% 9.26/2.34 % (2028253)Instructions burned: 119 (million)
% 9.26/2.34 % (2028254)Instruction limit reached!
% 9.26/2.34 % (2028254)------------------------------
% 9.26/2.34 % (2028254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028254)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028254)Termination reason: Instruction limit
% 9.26/2.34 % (2028254)Termination phase: Saturation
% 9.26/2.34 % (2028254)Time elapsed: 0.134 s
% 9.26/2.34 % (2028254)Peak memory usage: 89 MB
% 9.26/2.34 % (2028254)Instructions burned: 139 (million)
% 9.26/2.34 % (2028252)------------------------------
% 9.26/2.34 % (2028252)------------------------------
% 9.26/2.34 % (2028255)------------------------------
% 9.26/2.34 % (2028255)------------------------------
% 9.26/2.34 % (2028263)lrs+10_1_sil=8000:sp=occurrence:random_seed=4164470762:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 9.26/2.34 % (2028264)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2586017966:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 9.26/2.34 % (2028264)Instruction limit reached!
% 9.26/2.34 % (2028264)------------------------------
% 9.26/2.34 % (2028264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028264)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028264)Termination reason: Instruction limit
% 9.26/2.34 % (2028264)Termination phase: Saturation
% 9.26/2.34 % (2028264)Time elapsed: 0.162 s
% 9.26/2.34 % (2028264)Peak memory usage: 90 MB
% 9.26/2.34 % (2028264)Instructions burned: 157 (million)
% 9.26/2.34 % (2028250)First to succeed.
% 9.26/2.34 % (2028250)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2028235"
% 9.26/2.34 % (2028266)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1857857413:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 9.26/2.34 % (2028263)Instruction limit reached!
% 9.26/2.34 % (2028263)------------------------------
% 9.26/2.34 % (2028263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028263)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028263)Termination reason: Instruction limit
% 9.26/2.34 % (2028263)Termination phase: Saturation
% 9.26/2.34 % (2028263)Time elapsed: 0.300 s
% 9.26/2.34 % (2028263)Peak memory usage: 91 MB
% 9.26/2.34 % (2028263)Instructions burned: 286 (million)
% 9.26/2.34 % (2028267)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1245011952:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 9.26/2.34 % (2028269)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2297803560:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 9.26/2.34 % (2028269)Refutation not found, incomplete strategy
% 9.26/2.34 % (2028269)------------------------------
% 9.26/2.34 % (2028269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028269)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028269)Termination reason: Refutation not found, incomplete strategy
% 9.26/2.34 % (2028269)Time elapsed: 0.003 s
% 9.26/2.34 % (2028269)Peak memory usage: 88 MB
% 9.26/2.34 % (2028269)Instructions burned: 1 (million)
% 9.26/2.34 % (2028250)Refutation found. Thanks to Tanya!
% 9.26/2.34 % SZS status Theorem for theBenchmark
% 9.26/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 9.26/2.34 % (2028250)------------------------------
% 9.26/2.34 % (2028250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.26/2.34 % (2028250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.26/2.34 % (2028250)CaDiCaL version: 2.1.3
% 9.26/2.34 % (2028250)Termination reason: Refutation
% 9.26/2.34 % (2028250)Time elapsed: 0.756 s
% 9.26/2.34 % (2028250)Peak memory usage: 130 MB
% 9.26/2.34 % (2028250)Instructions burned: 1088 (million)
% 9.26/2.34 % (2028250)------------------------------
% 9.26/2.34 % (2028250)------------------------------
% 9.26/2.34 % (2028235)Success in time 1.222 s
% 9.26/2.34 % Vampire exiting
%------------------------------------------------------------------------------