%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE065+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 11:40:14 AM UTC 2026
% Result : Theorem 0.15s 1.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 25 unt; 0 def)
% Number of atoms : 33 ( 32 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f18,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( zero != multiplication(X0,domain(X1))
& multiplication(X0,X1) = zero ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( zero != multiplication(sK0,domain(sK1))
& zero = multiplication(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
zero = multiplication(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
zero != multiplication(sK0,domain(sK1)),
inference(cnf_transformation,[],[f21]) ).
fof(f24,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f81,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(superposition,[],[f33,f32]) ).
fof(f144,plain,
! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))),
inference(superposition,[],[f28,f30]) ).
fof(f2955,plain,
! [X0,X1] : multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1)),
inference(forward_demodulation,[],[f81,f144]) ).
fof(f2972,plain,
multiplication(domain(zero),multiplication(sK0,domain(sK1))) = multiplication(addition(sK0,multiplication(domain(zero),sK0)),domain(sK1)),
inference(superposition,[],[f2955,f22]) ).
fof(f3034,plain,
multiplication(zero,multiplication(sK0,domain(sK1))) = multiplication(addition(sK0,multiplication(zero,sK0)),domain(sK1)),
inference(forward_demodulation,[],[f2972,f24]) ).
fof(f3058,plain,
multiplication(zero,multiplication(sK0,domain(sK1))) = multiplication(addition(sK0,zero),domain(sK1)),
inference(forward_demodulation,[],[f3034,f25]) ).
fof(f3068,plain,
multiplication(sK0,domain(sK1)) = multiplication(zero,multiplication(sK0,domain(sK1))),
inference(forward_demodulation,[],[f3058,f27]) ).
fof(f3071,plain,
zero = multiplication(sK0,domain(sK1)),
inference(forward_demodulation,[],[f3068,f25]) ).
fof(f3072,plain,
$false,
inference(forward_subsumption_resolution,[],[f3071,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n009.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 13:08:46 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.15/1.51 % (2022926)Detected formulas, will run a generic FOF schedule.
% 0.15/1.51 % (2022933)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=265694771:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.51 % (2022931)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=3431179270:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.51 % (2022936)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3158436600:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.51 % (2022932)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=1010749528:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.51 % (2022937)dis-21_1_sil=8000:lcm=predicate:random_seed=4231521076: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)
% 0.15/1.51 % (2022935)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3228836863:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.51 % (2022934)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2471311240:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.51 % (2022937)Refutation not found, incomplete strategy
% 0.15/1.51 % (2022937)------------------------------
% 0.15/1.51 % (2022937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (2022937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (2022937)CaDiCaL version: 2.1.3
% 0.15/1.51 % (2022937)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.51 % (2022937)Time elapsed: 0.001 s
% 0.15/1.51 % (2022934)Refutation not found, incomplete strategy
% 0.15/1.51 % (2022934)------------------------------
% 0.15/1.51 % (2022934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (2022937)Peak memory usage: 88 MB
% 0.15/1.51 % (2022937)Instructions burned: 1 (million)
% 0.15/1.51 % (2022934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (2022934)CaDiCaL version: 2.1.3
% 0.15/1.51 % (2022934)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.51 % (2022934)Time elapsed: 0.001 s
% 0.15/1.51 % (2022934)Peak memory usage: 88 MB
% 0.15/1.51 % (2022934)Instructions burned: 1 (million)
% 0.15/1.51 % (2022935)First to succeed.
% 0.15/1.51 % (2022935)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2022926"
% 0.15/1.51 % (2022936)Instruction limit reached!
% 0.15/1.51 % (2022936)------------------------------
% 0.15/1.51 % (2022936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (2022936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (2022936)CaDiCaL version: 2.1.3
% 0.15/1.51 % (2022936)Termination reason: Instruction limit
% 0.15/1.51 % (2022936)Termination phase: Saturation
% 0.15/1.51 % (2022936)Time elapsed: 0.085 s
% 0.15/1.51 % (2022936)Peak memory usage: 89 MB
% 0.15/1.51 % (2022936)Instructions burned: 141 (million)
% 0.15/1.51 % (2022945)lrs+10_1_sil=8000:sp=occurrence:random_seed=3750417588:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.15/1.51 % (2022934)------------------------------
% 0.15/1.51 % (2022934)------------------------------
% 0.15/1.51 % (2022937)------------------------------
% 0.15/1.51 % (2022937)------------------------------
% 0.15/1.51 % (2022935)Refutation found. Thanks to Tanya!
% 0.15/1.51 % SZS status Theorem for theBenchmark
% 0.15/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.51 % (2022935)------------------------------
% 0.15/1.51 % (2022935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.51 % (2022935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.51 % (2022935)CaDiCaL version: 2.1.3
% 0.15/1.51 % (2022935)Termination reason: Refutation
% 0.15/1.51 % (2022935)Time elapsed: 0.061 s
% 0.15/1.51 % (2022935)Peak memory usage: 89 MB
% 0.15/1.51 % (2022935)Instructions burned: 111 (million)
% 0.15/1.51 % (2022935)------------------------------
% 0.15/1.51 % (2022935)------------------------------
% 0.15/1.51 % (2022926)Success in time 0.47 s
% 0.15/1.51 % Vampire exiting
%------------------------------------------------------------------------------