%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE113+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 : 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 11:40:22 AM UTC 2026
% Result : Theorem 5.28s 1.76s
% Output : Refutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 28 !; 1 ?)
% 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(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
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(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f27,conjecture,
! [X0] : forward_diamond(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0] : forward_diamond(X0,zero) = zero,
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0] : zero != forward_diamond(X0,zero),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
zero != forward_diamond(sK0,zero),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
zero != forward_diamond(sK0,zero),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
zero = antidomain(one),
inference(superposition,[],[f42,f36]) ).
fof(f60,plain,
antidomain(zero) = domain(one),
inference(superposition,[],[f45,f57]) ).
fof(f66,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f31,f33]) ).
fof(f70,plain,
! [X0] : one = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(forward_demodulation,[],[f44,f31]) ).
fof(f71,plain,
! [X0] : one = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[],[f70,f45]) ).
fof(f76,plain,
one = addition(zero,domain(one)),
inference(superposition,[],[f71,f57]) ).
fof(f78,plain,
one = domain(one),
inference(forward_demodulation,[],[f76,f66]) ).
fof(f136,plain,
one = antidomain(zero),
inference(forward_demodulation,[],[f60,f78]) ).
fof(f178,plain,
antidomain(one) = domain(zero),
inference(superposition,[],[f45,f136]) ).
fof(f180,plain,
zero = domain(zero),
inference(forward_demodulation,[],[f178,f57]) ).
fof(f219,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(superposition,[],[f52,f180]) ).
fof(f222,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[],[f219,f40]) ).
fof(f223,plain,
! [X0] : zero = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f222,f180]) ).
fof(f225,plain,
zero != zero,
inference(superposition,[],[f56,f223]) ).
fof(f226,plain,
$false,
inference(trivial_inequality_removal,[],[f225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 13:11:07 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 5.28/1.76 % (3511348)Detected formulas, will run a generic FOF schedule.
% 5.28/1.76 % (3511362)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=3889946863:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.28/1.76 % (3511368)dis-21_1_sil=8000:lcm=predicate:random_seed=2530375220: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)
% 5.28/1.76 % (3511368)Refutation not found, incomplete strategy
% 5.28/1.76 % (3511368)------------------------------
% 5.28/1.76 % (3511368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.76 % (3511368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.76 % (3511368)CaDiCaL version: 2.1.3
% 5.28/1.76 % (3511368)Termination reason: Refutation not found, incomplete strategy
% 5.28/1.76 % (3511368)Time elapsed: 0.002 s
% 5.28/1.76 % (3511368)Peak memory usage: 88 MB
% 5.28/1.76 % (3511368)Instructions burned: 1 (million)
% 5.28/1.76 % (3511364)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=1041274581:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.28/1.76 % (3511367)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3916762507:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.28/1.76 % (3511363)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=754038565:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.28/1.76 % (3511365)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2568397550:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.28/1.76 % (3511365)Refutation not found, incomplete strategy
% 5.28/1.76 % (3511365)------------------------------
% 5.28/1.76 % (3511365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.76 % (3511365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.76 % (3511365)CaDiCaL version: 2.1.3
% 5.28/1.76 % (3511365)Termination reason: Refutation not found, incomplete strategy
% 5.28/1.76 % (3511365)Time elapsed: 0.002 s
% 5.28/1.76 % (3511365)Peak memory usage: 88 MB
% 5.28/1.76 % (3511367)First to succeed.
% 5.28/1.76 % (3511367)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3511348"
% 5.28/1.76 % (3511366)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1419455817:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.28/1.76 % (3511366)Instruction limit reached!
% 5.28/1.76 % (3511366)------------------------------
% 5.28/1.76 % (3511366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.76 % (3511366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.76 % (3511366)CaDiCaL version: 2.1.3
% 5.28/1.76 % (3511366)Termination reason: Instruction limit
% 5.28/1.76 % (3511366)Termination phase: Saturation
% 5.28/1.76 % (3511366)Time elapsed: 0.111 s
% 5.28/1.76 % (3511366)Peak memory usage: 88 MB
% 5.28/1.76 % (3511366)Instructions burned: 120 (million)
% 5.28/1.76 % (3511368)------------------------------
% 5.28/1.76 % (3511368)------------------------------
% 5.28/1.76 % (3511365)------------------------------
% 5.28/1.76 % (3511365)------------------------------
% 5.28/1.76 % (3511367)Refutation found. Thanks to Tanya!
% 5.28/1.76 % SZS status Theorem for theBenchmark
% 5.28/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.28/1.76 % (3511367)------------------------------
% 5.28/1.76 % (3511367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.28/1.76 % (3511367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.28/1.76 % (3511367)CaDiCaL version: 2.1.3
% 5.28/1.76 % (3511367)Termination reason: Refutation
% 5.28/1.76 % (3511367)Time elapsed: 0.010 s
% 5.28/1.76 % (3511367)Peak memory usage: 89 MB
% 5.28/1.76 % (3511367)Instructions burned: 8 (million)
% 5.28/1.76 % (3511367)------------------------------
% 5.28/1.76 % (3511367)------------------------------
% 5.28/1.76 % (3511348)Success in time 0.665 s
% 5.28/1.76 % Vampire exiting
%------------------------------------------------------------------------------