%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE144+2 : 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 : n015.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 11:40:27 AM UTC 2026
% Result : Theorem 0.22s 1.91s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 54 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 12 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 63 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f12,axiom,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X0] :
( leq(strong_iteration(star(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(star(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X0))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
( ~ leq(strong_iteration(star(X0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(X0))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f24,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f25,plain,
( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f27,plain,
( ~ leq(strong_iteration(star(sK0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(sK0))) ),
inference(cnf_transformation,[],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f32,plain,
! [X0] : star(X0) = addition(one,multiplication(star(X0),X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f87,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f39,f38]) ).
fof(f149,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f36,f34]) ).
fof(f157,plain,
! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[],[f41,f34]) ).
fof(f235,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f29,f87]) ).
fof(f243,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f235]) ).
fof(f683,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(forward_subsumption_resolution,[],[f149,f243]) ).
fof(f686,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f683,f35]) ).
fof(f690,plain,
~ leq(strong_iteration(one),strong_iteration(star(sK0))),
inference(resolution,[],[f686,f27]) ).
fof(f718,plain,
! [X2,X0,X1] :
( ~ leq(X0,addition(addition(X0,multiplication(X1,X0)),X2))
| leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)) ),
inference(superposition,[],[f36,f157]) ).
fof(f752,plain,
! [X2,X0,X1] :
( ~ leq(X0,addition(X0,addition(multiplication(X1,X0),X2)))
| leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)) ),
inference(forward_demodulation,[],[f718,f39]) ).
fof(f765,plain,
! [X2,X0,X1] : leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)),
inference(forward_subsumption_resolution,[],[f752,f243]) ).
fof(f2544,plain,
! [X0,X1] : leq(X1,strong_iteration(addition(one,X0))),
inference(superposition,[],[f765,f35]) ).
fof(f2559,plain,
! [X0,X1] : leq(X1,strong_iteration(star(X0))),
inference(superposition,[],[f2544,f32]) ).
fof(f2599,plain,
$false,
inference(resolution,[],[f2559,f690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE144+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 % Computer : n015.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8046.5625MB
% 0.15/0.39 % OS : Linux 6.8.0-71-generic
% 0.15/0.39 % CPULimit : 300
% 0.15/0.39 % WCLimit : 300
% 0.15/0.39 % DateTime : Sun Sep 27 13:15:45 UTC 2026
% 0.19/0.39 % CPUTime :
% 0.19/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 Running first-order theorem proving
% 0.19/0.44 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
% 0.22/1.91 % (1669318)Detected formulas, will run a generic FOF schedule.
% 0.22/1.91 % (1669328)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=3552396905:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.22/1.91 % (1669332)dis-21_1_sil=8000:lcm=predicate:random_seed=2636457322: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)
% 0.22/1.91 % (1669332)Refutation not found, incomplete strategy
% 0.22/1.91 % (1669332)------------------------------
% 0.22/1.91 % (1669332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.91 % (1669332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.91 % (1669332)CaDiCaL version: 2.1.3
% 0.22/1.91 % (1669332)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.91 % (1669332)Time elapsed: 0.003 s
% 0.22/1.91 % (1669332)Peak memory usage: 88 MB
% 0.22/1.91 % (1669332)Instructions burned: 1 (million)
% 0.22/1.91 % (1669329)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2528729914:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.22/1.91 % (1669326)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=3822107327:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.22/1.91 % (1669329)Refutation not found, incomplete strategy
% 0.22/1.91 % (1669329)------------------------------
% 0.22/1.91 % (1669329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.91 % (1669329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.91 % (1669329)CaDiCaL version: 2.1.3
% 0.22/1.91 % (1669329)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.91 % (1669329)Time elapsed: 0.002 s
% 0.22/1.91 % (1669329)Peak memory usage: 88 MB
% 0.22/1.91 % (1669327)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=78278481:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.22/1.91 % (1669330)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1939294618:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.22/1.91 % (1669331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3346292518:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.22/1.91 % (1669330)First to succeed.
% 0.22/1.91 % (1669330)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1669318"
% 0.22/1.91 % (1669331)Instruction limit reached!
% 0.22/1.91 % (1669331)------------------------------
% 0.22/1.91 % (1669331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.91 % (1669331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.91 % (1669331)CaDiCaL version: 2.1.3
% 0.22/1.91 % (1669331)Termination reason: Instruction limit
% 0.22/1.91 % (1669331)Termination phase: Saturation
% 0.22/1.91 % (1669331)Time elapsed: 0.141 s
% 0.22/1.91 % (1669331)Peak memory usage: 90 MB
% 0.22/1.91 % (1669331)Instructions burned: 140 (million)
% 0.22/1.91 % (1669332)------------------------------
% 0.22/1.91 % (1669332)------------------------------
% 0.22/1.91 % (1669329)------------------------------
% 0.22/1.91 % (1669329)------------------------------
% 0.22/1.91 % (1669341)lrs+10_1_sil=8000:sp=occurrence:random_seed=451177734:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 0.22/1.91 % (1669328)Refutation not found, incomplete strategy
% 0.22/1.91 % (1669328)------------------------------
% 0.22/1.91 % (1669328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.91 % (1669328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.91 % (1669328)CaDiCaL version: 2.1.3
% 0.22/1.91 % (1669328)Termination reason: Refutation not found, incomplete strategy
% 0.22/1.91 % (1669328)Time elapsed: 0.531 s
% 0.22/1.91 % (1669328)Peak memory usage: 128 MB
% 0.22/1.91 % (1669328)Instructions burned: 895 (million)
% 0.22/1.91 % (1669330)Refutation found. Thanks to Tanya!
% 0.22/1.91 % SZS status Theorem for theBenchmark
% 0.22/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/1.91 % (1669330)------------------------------
% 0.22/1.91 % (1669330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.22/1.91 % (1669330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/1.91 % (1669330)CaDiCaL version: 2.1.3
% 0.22/1.91 % (1669330)Termination reason: Refutation
% 0.22/1.91 % (1669330)Time elapsed: 0.084 s
% 0.22/1.91 % (1669330)Peak memory usage: 89 MB
% 0.22/1.91 % (1669330)Instructions burned: 85 (million)
% 0.22/1.91 % (1669330)------------------------------
% 0.22/1.91 % (1669330)------------------------------
% 0.22/1.91 % (1669318)Success in time 0.764 s
% 0.22/1.91 % Vampire exiting
%------------------------------------------------------------------------------