%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE148+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 : 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 11:40:28 AM UTC 2026
% Result : Theorem 0.26s 2.16s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 24 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
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(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',distributivity1) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f19,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,strong_iteration(X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,strong_iteration(X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != X0
& multiplication(X0,X1) = zero ),
inference(ennf_transformation,[],[f20]) ).
fof(f26,plain,
( sK0 != multiplication(sK0,strong_iteration(sK1))
& zero = multiplication(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
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(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f46,plain,
zero = multiplication(sK0,sK1),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
sK0 != multiplication(sK0,strong_iteration(sK1)),
inference(cnf_transformation,[],[f26]) ).
fof(f65,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[],[f41,f27]) ).
fof(f103,plain,
! [X0] : multiplication(zero,X0) = multiplication(sK0,multiplication(sK1,X0)),
inference(superposition,[],[f31,f46]) ).
fof(f108,plain,
! [X0] : zero = multiplication(sK0,multiplication(sK1,X0)),
inference(forward_demodulation,[],[f103,f36]) ).
fof(f127,plain,
! [X0,X1] : addition(multiplication(sK0,X0),zero) = multiplication(sK0,addition(X0,multiplication(sK1,X1))),
inference(superposition,[],[f34,f108]) ).
fof(f135,plain,
! [X0,X1] : multiplication(sK0,X0) = multiplication(sK0,addition(X0,multiplication(sK1,X1))),
inference(forward_demodulation,[],[f127,f29]) ).
fof(f615,plain,
multiplication(sK0,strong_iteration(sK1)) = multiplication(sK0,one),
inference(superposition,[],[f135,f65]) ).
fof(f629,plain,
sK0 = multiplication(sK0,strong_iteration(sK1)),
inference(forward_demodulation,[],[f615,f32]) ).
fof(f634,plain,
$false,
inference(forward_subsumption_resolution,[],[f629,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE148+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n004.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 13:12:37 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 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
% 0.26/2.16 % (3515413)Detected formulas, will run a generic FOF schedule.
% 0.26/2.16 % (3515423)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3482618217:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.26/2.16 % (3515423)Refutation not found, incomplete strategy
% 0.26/2.16 % (3515423)------------------------------
% 0.26/2.16 % (3515423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.26/2.16 % (3515423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/2.16 % (3515423)CaDiCaL version: 2.1.3
% 0.26/2.16 % (3515423)Termination reason: Refutation not found, incomplete strategy
% 0.26/2.16 % (3515423)Time elapsed: 0.002 s
% 0.26/2.16 % (3515423)Peak memory usage: 88 MB
% 0.26/2.16 % (3515423)Instructions burned: 1 (million)
% 0.26/2.16 % (3515422)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=2752016852:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.26/2.16 % (3515421)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=848259915:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.26/2.16 % (3515420)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=1071395408:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.26/2.16 % (3515426)dis-21_1_sil=8000:lcm=predicate:random_seed=2909289818: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)
% 0.26/2.16 % (3515426)Refutation not found, incomplete strategy
% 0.26/2.16 % (3515426)------------------------------
% 0.26/2.16 % (3515426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.26/2.16 % (3515426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/2.16 % (3515426)CaDiCaL version: 2.1.3
% 0.26/2.16 % (3515426)Termination reason: Refutation not found, incomplete strategy
% 0.26/2.16 % (3515426)Time elapsed: 0.003 s
% 0.26/2.16 % (3515426)Peak memory usage: 88 MB
% 0.26/2.16 % (3515426)Instructions burned: 1 (million)
% 0.26/2.16 % (3515425)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2165340399:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.26/2.16 % (3515424)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2533197387:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.26/2.16 % (3515425)First to succeed.
% 0.26/2.16 % (3515425)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3515413"
% 0.26/2.16 % (3515424)Instruction limit reached!
% 0.26/2.16 % (3515424)------------------------------
% 0.26/2.16 % (3515424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.26/2.16 % (3515424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/2.16 % (3515424)CaDiCaL version: 2.1.3
% 0.26/2.16 % (3515424)Termination reason: Instruction limit
% 0.26/2.16 % (3515424)Termination phase: Saturation
% 0.26/2.16 % (3515424)Time elapsed: 0.117 s
% 0.26/2.16 % (3515424)Peak memory usage: 89 MB
% 0.26/2.16 % (3515424)Instructions burned: 119 (million)
% 0.26/2.16 % (3515423)------------------------------
% 0.26/2.16 % (3515423)------------------------------
% 0.26/2.16 % (3515426)------------------------------
% 0.26/2.16 % (3515426)------------------------------
% 0.26/2.16 % (3515434)lrs+10_1_sil=8000:sp=occurrence:random_seed=2694747359:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 0.26/2.16 % (3515435)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3738115862:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 0.26/2.16 % (3515434)Also succeeded, but the first one will report.
% 0.26/2.16 % (3515425)Refutation found. Thanks to Tanya!
% 0.26/2.16 % SZS status Theorem for theBenchmark
% 0.26/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/2.16 % (3515425)------------------------------
% 0.26/2.16 % (3515425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.26/2.16 % (3515425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/2.16 % (3515425)CaDiCaL version: 2.1.3
% 0.26/2.16 % (3515425)Termination reason: Refutation
% 0.26/2.16 % (3515425)Time elapsed: 0.025 s
% 0.26/2.16 % (3515425)Peak memory usage: 89 MB
% 0.26/2.16 % (3515425)Instructions burned: 23 (million)
% 0.26/2.16 % (3515425)------------------------------
% 0.26/2.16 % (3515425)------------------------------
% 0.26/2.16 % (3515413)Success in time 0.728 s
% 0.26/2.16 % Vampire exiting
%------------------------------------------------------------------------------