%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE086+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:40:17 AM UTC 2026
% Result : Theorem 3.62s 1.54s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f21,conjecture,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
domain(zero) != zero,
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
zero != domain(zero),
inference(flattening,[],[f22]) ).
fof(f24,plain,
zero != domain(zero),
inference(cnf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f43,plain,
zero != antidomain(antidomain(zero)),
inference(definition_unfolding,[],[f24,f28]) ).
fof(f44,plain,
zero = antidomain(one),
inference(superposition,[],[f37,f40]) ).
fof(f49,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f34,f27]) ).
fof(f54,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f35,f34]) ).
fof(f60,plain,
one = addition(zero,antidomain(zero)),
inference(superposition,[],[f54,f44]) ).
fof(f61,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f60,f49]) ).
fof(f62,plain,
zero != antidomain(one),
inference(superposition,[],[f43,f61]) ).
fof(f66,plain,
$false,
inference(forward_subsumption_resolution,[],[f62,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE086+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n005.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 13:09:17 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.54 % (3978763)Detected formulas, will run a generic FOF schedule.
% 3.62/1.54 % (3978852)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=3366505309:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.54 % (3978853)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=540864219:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.54 % (3978854)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=791000332:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.54 % (3978856)dis-21_1_sil=8000:lcm=predicate:random_seed=1096686043: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)
% 3.62/1.54 % (3978855)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3150845223:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.54 % (3978851)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=3554845172:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.54 % (3978850)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=726668697:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.54 % (3978853)Refutation not found, incomplete strategy
% 3.62/1.54 % (3978853)------------------------------
% 3.62/1.54 % (3978853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.54 % (3978853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.54 % (3978853)CaDiCaL version: 2.1.3
% 3.62/1.54 % (3978853)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.54 % (3978853)Time elapsed: 0.001 s
% 3.62/1.54 % (3978853)Peak memory usage: 88 MB
% 3.62/1.54 % (3978856)Refutation not found, incomplete strategy
% 3.62/1.54 % (3978856)------------------------------
% 3.62/1.54 % (3978856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.54 % (3978856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.54 % (3978856)CaDiCaL version: 2.1.3
% 3.62/1.54 % (3978856)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.54 % (3978856)Time elapsed: 0.001 s
% 3.62/1.54 % (3978856)Peak memory usage: 88 MB
% 3.62/1.54 % (3978856)Instructions burned: 1 (million)
% 3.62/1.54 % (3978854)First to succeed.
% 3.62/1.54 % (3978854)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3978763"
% 3.62/1.54 % (3978855)Also succeeded, but the first one will report.
% 3.62/1.54 % (3978853)------------------------------
% 3.62/1.54 % (3978853)------------------------------
% 3.62/1.54 % (3978856)------------------------------
% 3.62/1.54 % (3978856)------------------------------
% 3.62/1.54 % (3978854)Refutation found. Thanks to Tanya!
% 3.62/1.54 % SZS status Theorem for theBenchmark
% 3.62/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.54 % (3978854)------------------------------
% 3.62/1.54 % (3978854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.54 % (3978854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.54 % (3978854)CaDiCaL version: 2.1.3
% 3.62/1.54 % (3978854)Termination reason: Refutation
% 3.62/1.54 % (3978854)Time elapsed: 0.003 s
% 3.62/1.54 % (3978854)Peak memory usage: 88 MB
% 3.62/1.54 % (3978854)Instructions burned: 3 (million)
% 3.62/1.54 % (3978854)------------------------------
% 3.62/1.54 % (3978854)------------------------------
% 3.62/1.54 % (3978763)Success in time 0.415 s
% 3.62/1.54 % Vampire exiting
%------------------------------------------------------------------------------