%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE076+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 : n017.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 11:40:16 AM UTC 2026
% Result : Theorem 2.57s 1.23s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 1 def)
% Number of atoms : 17 ( 11 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f18,conjecture,
! [X0] : domain(multiplication(X0,domain(zero))) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0] : domain(multiplication(X0,domain(zero))) = zero,
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0] : zero != domain(multiplication(X0,domain(zero))),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
zero != domain(multiplication(sK0,domain(zero))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
fof(f22,plain,
zero != domain(multiplication(sK0,domain(zero))),
inference(cnf_transformation,[],[f21]) ).
fof(f23,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f33,definition,
~ sP1(zero),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f34,plain,
sP1(domain(multiplication(sK0,domain(zero)))),
inference(inequality_splitting,[],[f22,f33]) ).
fof(f35,plain,
sP1(domain(multiplication(sK0,zero))),
inference(forward_demodulation,[],[f34,f31]) ).
fof(f36,plain,
sP1(domain(zero)),
inference(forward_demodulation,[],[f35,f25]) ).
fof(f37,plain,
sP1(zero),
inference(forward_demodulation,[],[f36,f23]) ).
fof(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE076+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 13:04:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.57/1.23 % (2535961)Detected formulas, will run a generic FOF schedule.
% 2.57/1.23 % (2535969)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3538628387:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.23 % (2535969)First to succeed.
% 2.57/1.23 % (2535969)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2535961"
% 2.57/1.23 % (2535970)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2861189951:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.23 % (2535972)dis-21_1_sil=8000:lcm=predicate:random_seed=3520508188: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)
% 2.57/1.23 % (2535968)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=2125173747:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.23 % (2535966)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=1334176428:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.23 % (2535967)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=2827233136:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.23 % (2535971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2566744567:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.23 % (2535970)Also succeeded, but the first one will report.
% 2.57/1.23 % (2535972)Refutation not found, incomplete strategy
% 2.57/1.23 % (2535972)------------------------------
% 2.57/1.23 % (2535972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.23 % (2535972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.23 % (2535972)CaDiCaL version: 2.1.3
% 2.57/1.23 % (2535972)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.23 % (2535972)Time elapsed: 0.001 s
% 2.57/1.23 % (2535972)Peak memory usage: 88 MB
% 2.57/1.23 % (2535972)Instructions burned: 1 (million)
% 2.57/1.23 % (2535971)Also succeeded, but the first one will report.
% 2.57/1.23 % (2535969)Refutation found. Thanks to Tanya!
% 2.57/1.23 % SZS status Theorem for theBenchmark
% 2.57/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.23 % (2535969)------------------------------
% 2.57/1.23 % (2535969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.23 % (2535969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.23 % (2535969)CaDiCaL version: 2.1.3
% 2.57/1.23 % (2535969)Termination reason: Refutation
% 2.57/1.23 % (2535969)Time elapsed: 0.001 s
% 2.57/1.23 % (2535969)Peak memory usage: 88 MB
% 2.57/1.23 % (2535969)Instructions burned: 1 (million)
% 2.57/1.23 % (2535969)------------------------------
% 2.57/1.23 % (2535969)------------------------------
% 2.57/1.23 % (2535961)Success in time 0.294 s
% 2.57/1.23 % Vampire exiting
%------------------------------------------------------------------------------