%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE119+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 : n007.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 11:40:23 AM UTC 2026
% Result : Theorem 3.68s 1.49s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',backward_diamond) ).
fof(f27,conjecture,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1] : domain(X1) != addition(backward_diamond(zero,domain(X0)),domain(X1)),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f46,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f53,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f56,plain,
domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)),
inference(cnf_transformation,[],[f30]) ).
fof(f63,plain,
zero = coantidomain(one),
inference(superposition,[],[f46,f37]) ).
fof(f66,plain,
coantidomain(zero) = codomain(one),
inference(superposition,[],[f49,f63]) ).
fof(f69,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f31,f33]) ).
fof(f83,plain,
! [X0] : one = addition(coantidomain(X0),coantidomain(coantidomain(X0))),
inference(forward_demodulation,[],[f48,f31]) ).
fof(f84,plain,
! [X0] : one = addition(coantidomain(X0),codomain(X0)),
inference(forward_demodulation,[],[f83,f49]) ).
fof(f85,plain,
one = addition(zero,codomain(one)),
inference(superposition,[],[f84,f63]) ).
fof(f87,plain,
one = codomain(one),
inference(forward_demodulation,[],[f85,f69]) ).
fof(f94,plain,
! [X0] : backward_diamond(zero,X0) = codomain(zero),
inference(superposition,[],[f53,f40]) ).
fof(f227,plain,
one = coantidomain(zero),
inference(forward_demodulation,[],[f66,f87]) ).
fof(f262,plain,
coantidomain(one) = codomain(zero),
inference(superposition,[],[f49,f227]) ).
fof(f264,plain,
zero = codomain(zero),
inference(forward_demodulation,[],[f262,f63]) ).
fof(f302,plain,
! [X0] : zero = backward_diamond(zero,X0),
inference(forward_demodulation,[],[f94,f264]) ).
fof(f304,plain,
domain(sK1) != addition(zero,domain(sK1)),
inference(superposition,[],[f56,f302]) ).
fof(f305,plain,
$false,
inference(forward_subsumption_resolution,[],[f304,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:08:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.68/1.49 % (1404288)Detected formulas, will run a generic FOF schedule.
% 3.68/1.49 % (1404297)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2408298316:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.49 % (1404297)Instruction limit reached!
% 3.68/1.49 % (1404297)------------------------------
% 3.68/1.49 % (1404297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (1404297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (1404297)CaDiCaL version: 2.1.3
% 3.68/1.49 % (1404297)Termination reason: Instruction limit
% 3.68/1.49 % (1404297)Termination phase: Saturation
% 3.68/1.49 % (1404297)Time elapsed: 0.036 s
% 3.68/1.49 % (1404297)Peak memory usage: 89 MB
% 3.68/1.49 % (1404297)Instructions burned: 122 (million)
% 3.68/1.49 % (1404296)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1892668156:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.49 % (1404295)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=844491789:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.49 % (1404298)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2334918809:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.49 % (1404293)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=1250485253:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.49 % (1404294)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=2168188419:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.49 % (1404299)dis-21_1_sil=8000:lcm=predicate:random_seed=1842517805: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)
% 3.68/1.49 % (1404296)Refutation not found, incomplete strategy
% 3.68/1.49 % (1404296)------------------------------
% 3.68/1.49 % (1404296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (1404296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (1404296)CaDiCaL version: 2.1.3
% 3.68/1.49 % (1404296)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.49 % (1404296)Time elapsed: 0.001 s
% 3.68/1.49 % (1404296)Peak memory usage: 88 MB
% 3.68/1.49 % (1404299)Refutation not found, incomplete strategy
% 3.68/1.49 % (1404299)------------------------------
% 3.68/1.49 % (1404299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (1404299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (1404299)CaDiCaL version: 2.1.3
% 3.68/1.49 % (1404299)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.49 % (1404299)Time elapsed: 0.002 s
% 3.68/1.49 % (1404299)Peak memory usage: 88 MB
% 3.68/1.49 % (1404299)Instructions burned: 1 (million)
% 3.68/1.49 % (1404298)First to succeed.
% 3.68/1.49 % (1404298)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1404288"
% 3.68/1.49 % (1404301)lrs+10_1_sil=8000:sp=occurrence:random_seed=644660422:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.68/1.49 % (1404301)Also succeeded, but the first one will report.
% 3.68/1.49 % (1404296)------------------------------
% 3.68/1.49 % (1404296)------------------------------
% 3.68/1.49 % (1404299)------------------------------
% 3.68/1.49 % (1404299)------------------------------
% 3.68/1.49 % (1404298)Refutation found. Thanks to Tanya!
% 3.68/1.49 % SZS status Theorem for theBenchmark
% 3.68/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.49 % (1404298)------------------------------
% 3.68/1.49 % (1404298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (1404298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (1404298)CaDiCaL version: 2.1.3
% 3.68/1.49 % (1404298)Termination reason: Refutation
% 3.68/1.49 % (1404298)Time elapsed: 0.009 s
% 3.68/1.49 % (1404298)Peak memory usage: 88 MB
% 3.68/1.49 % (1404298)Instructions burned: 11 (million)
% 3.68/1.49 % (1404298)------------------------------
% 3.68/1.49 % (1404298)------------------------------
% 3.68/1.49 % (1404288)Success in time 0.44 s
% 3.68/1.49 % Vampire exiting
%------------------------------------------------------------------------------