%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE089+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 : n011.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 11:40:18 AM UTC 2026
% Result : Theorem 3.54s 1.44s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 17 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 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 : 22 ( 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
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(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f21,conjecture,
! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( zero != multiplication(domain(X0),X1)
& addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
( zero != multiplication(domain(sK0),sK1)
& antidomain(sK1) = addition(domain(sK0),antidomain(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).
fof(f25,plain,
antidomain(sK1) = addition(domain(sK0),antidomain(sK1)),
inference(cnf_transformation,[],[f24]) ).
fof(f26,plain,
zero != multiplication(domain(sK0),sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f27,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
zero != multiplication(antidomain(antidomain(sK0)),sK1),
inference(definition_unfolding,[],[f26,f38]) ).
fof(f40,plain,
antidomain(sK1) = addition(antidomain(antidomain(sK0)),antidomain(sK1)),
inference(definition_unfolding,[],[f25,f38]) ).
fof(f86,plain,
! [X0,X1] : addition(multiplication(X0,X1),zero) = multiplication(addition(X0,antidomain(X1)),X1),
inference(superposition,[],[f27,f37]) ).
fof(f94,plain,
! [X0,X1] : multiplication(X0,X1) = multiplication(addition(X0,antidomain(X1)),X1),
inference(forward_demodulation,[],[f86,f34]) ).
fof(f446,plain,
multiplication(antidomain(antidomain(sK0)),sK1) = multiplication(antidomain(sK1),sK1),
inference(superposition,[],[f94,f40]) ).
fof(f464,plain,
zero = multiplication(antidomain(antidomain(sK0)),sK1),
inference(forward_demodulation,[],[f446,f37]) ).
fof(f467,plain,
$false,
inference(forward_subsumption_resolution,[],[f464,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 13:09:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.54/1.44 % (2392177)Detected formulas, will run a generic FOF schedule.
% 3.54/1.44 % (2392182)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=1113383257:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/1.44 % (2392187)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1349146073:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/1.44 % (2392186)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=763631954:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/1.44 % (2392185)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1769502310:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/1.44 % (2392184)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=1282326459:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/1.44 % (2392183)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=1527148982:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/1.44 % (2392188)dis-21_1_sil=8000:lcm=predicate:random_seed=2581381837: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)
% 3.54/1.44 % (2392188)Refutation not found, incomplete strategy
% 3.54/1.44 % (2392188)------------------------------
% 3.54/1.44 % (2392188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.44 % (2392188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.44 % (2392188)CaDiCaL version: 2.1.3
% 3.54/1.44 % (2392188)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.44 % (2392188)Time elapsed: 0.001 s
% 3.54/1.44 % (2392188)Peak memory usage: 88 MB
% 3.54/1.44 % (2392188)Instructions burned: 1 (million)
% 3.54/1.44 % (2392186)First to succeed.
% 3.54/1.44 % (2392186)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2392177"
% 3.54/1.44 % (2392187)Also succeeded, but the first one will report.
% 3.54/1.44 % (2392185)Instruction limit reached!
% 3.54/1.44 % (2392185)------------------------------
% 3.54/1.44 % (2392185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.44 % (2392185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.44 % (2392185)CaDiCaL version: 2.1.3
% 3.54/1.44 % (2392185)Termination reason: Instruction limit
% 3.54/1.44 % (2392185)Termination phase: Saturation
% 3.54/1.44 % (2392185)Time elapsed: 0.063 s
% 3.54/1.44 % (2392185)Peak memory usage: 89 MB
% 3.54/1.44 % (2392185)Instructions burned: 111 (million)
% 3.54/1.44 % (2392196)lrs+10_1_sil=8000:sp=occurrence:random_seed=3264961605:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.54/1.44 % (2392196)Also succeeded, but the first one will report.
% 3.54/1.44 % (2392188)------------------------------
% 3.54/1.44 % (2392188)------------------------------
% 3.54/1.44 % (2392186)Refutation found. Thanks to Tanya!
% 3.54/1.44 % SZS status Theorem for theBenchmark
% 3.54/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.44 % (2392186)------------------------------
% 3.54/1.44 % (2392186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.44 % (2392186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.44 % (2392186)CaDiCaL version: 2.1.3
% 3.54/1.44 % (2392186)Termination reason: Refutation
% 3.54/1.44 % (2392186)Time elapsed: 0.014 s
% 3.54/1.44 % (2392186)Peak memory usage: 88 MB
% 3.54/1.44 % (2392186)Instructions burned: 18 (million)
% 3.54/1.44 % (2392186)------------------------------
% 3.54/1.44 % (2392186)------------------------------
% 3.54/1.44 % (2392177)Success in time 0.417 s
% 3.54/1.44 % Vampire exiting
%------------------------------------------------------------------------------