%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE037+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 : n006.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 11:40:09 AM UTC 2026
% Result : Theorem 3.49s 1.43s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 20 unt; 0 def)
% Number of atoms : 36 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 7 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 44 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f17,conjecture,
! [X0] : leq(one,star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : leq(one,star(X0)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] : ~ leq(one,star(X0)),
inference(ennf_transformation,[],[f18]) ).
fof(f22,plain,
~ leq(one,star(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
~ leq(one,star(sK0)),
inference(cnf_transformation,[],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0,X1] :
( addition(X0,X1) = X0
| ~ leq(X1,X0) ),
inference(superposition,[],[f25,f37]) ).
fof(f63,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f36,f35]) ).
fof(f123,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f26,f63]) ).
fof(f130,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f123]) ).
fof(f165,plain,
! [X0,X1] : leq(X1,addition(X0,X1)),
inference(superposition,[],[f130,f37]) ).
fof(f176,plain,
! [X2,X0,X1] : leq(X2,addition(X0,addition(X1,X2))),
inference(superposition,[],[f165,f36]) ).
fof(f269,plain,
! [X2,X0,X1] : leq(X0,addition(X2,addition(X0,X1))),
inference(superposition,[],[f176,f37]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ leq(addition(X1,X2),X0)
| leq(X1,X0) ),
inference(superposition,[],[f269,f39]) ).
fof(f553,plain,
! [X0] : leq(one,star(X0)),
inference(resolution,[],[f298,f27]) ).
fof(f579,plain,
$false,
inference(resolution,[],[f553,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE037+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 : n006.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 13:04:41 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
% 3.49/1.43 % (2964631)Detected formulas, will run a generic FOF schedule.
% 3.49/1.43 % (2964638)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=646107275:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.43 % (2964640)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3704749087:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.43 % (2964637)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=1609200492:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.43 % (2964636)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=2088152038:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.43 % (2964639)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1873141224:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.43 % (2964641)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2172219971:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.43 % (2964639)Refutation not found, incomplete strategy
% 3.49/1.43 % (2964639)------------------------------
% 3.49/1.43 % (2964639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.43 % (2964639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.43 % (2964639)CaDiCaL version: 2.1.3
% 3.49/1.43 % (2964639)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.43 % (2964639)Time elapsed: 0.001 s
% 3.49/1.43 % (2964639)Peak memory usage: 88 MB
% 3.49/1.43 % (2964640)First to succeed.
% 3.49/1.43 % (2964642)dis-21_1_sil=8000:lcm=predicate:random_seed=3585168079: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)
% 3.49/1.43 % (2964640)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2964631"
% 3.49/1.43 % (2964642)Refutation not found, incomplete strategy
% 3.49/1.43 % (2964642)------------------------------
% 3.49/1.43 % (2964642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.43 % (2964642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.43 % (2964642)CaDiCaL version: 2.1.3
% 3.49/1.43 % (2964642)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.43 % (2964642)Time elapsed: 0.001 s
% 3.49/1.43 % (2964642)Peak memory usage: 88 MB
% 3.49/1.43 % (2964642)Instructions burned: 1 (million)
% 3.49/1.43 % (2964641)Also succeeded, but the first one will report.
% 3.49/1.43 % (2964639)------------------------------
% 3.49/1.43 % (2964639)------------------------------
% 3.49/1.43 % (2964642)------------------------------
% 3.49/1.43 % (2964642)------------------------------
% 3.49/1.43 % (2964640)Refutation found. Thanks to Tanya!
% 3.49/1.43 % SZS status Theorem for theBenchmark
% 3.49/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.43 % (2964640)------------------------------
% 3.49/1.43 % (2964640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.43 % (2964640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.43 % (2964640)CaDiCaL version: 2.1.3
% 3.49/1.43 % (2964640)Termination reason: Refutation
% 3.49/1.43 % (2964640)Time elapsed: 0.012 s
% 3.49/1.43 % (2964640)Peak memory usage: 88 MB
% 3.49/1.43 % (2964640)Instructions burned: 18 (million)
% 3.49/1.43 % (2964640)------------------------------
% 3.49/1.43 % (2964640)------------------------------
% 3.49/1.43 % (2964631)Success in time 0.406 s
% 3.49/1.43 % Vampire exiting
%------------------------------------------------------------------------------