%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE151+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 : 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 11:40:29 AM UTC 2026
% Result : Theorem 3.34s 1.55s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 27 unt; 0 def)
% Number of atoms : 43 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 6 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
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,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f24,plain,
? [X0,X1] : ~ leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(strong_iteration(multiplication(sK0,sK1)),sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f42,plain,
! [X2,X0,X1] :
( leq(X2,multiplication(strong_iteration(X0),X1))
| ~ leq(X2,addition(multiplication(X0,X2),X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(strong_iteration(multiplication(sK0,sK1)),sK0)),
inference(cnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f45,f30]) ).
fof(f49,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f48]) ).
fof(f85,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one),
inference(superposition,[],[f41,f31]) ).
fof(f116,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f34,f32]) ).
fof(f198,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),addition(multiplication(multiplication(sK0,sK1),multiplication(sK0,strong_iteration(multiplication(sK1,sK0)))),sK0)),
inference(resolution,[],[f42,f46]) ).
fof(f204,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),addition(sK0,multiplication(multiplication(sK0,sK1),multiplication(sK0,strong_iteration(multiplication(sK1,sK0)))))),
inference(forward_demodulation,[],[f198,f27]) ).
fof(f206,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),addition(sK0,multiplication(sK0,multiplication(sK1,multiplication(sK0,strong_iteration(multiplication(sK1,sK0))))))),
inference(forward_demodulation,[],[f204,f31]) ).
fof(f264,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(sK0,addition(one,multiplication(sK1,multiplication(sK0,strong_iteration(multiplication(sK1,sK0))))))),
inference(superposition,[],[f206,f116]) ).
fof(f531,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(forward_demodulation,[],[f85,f27]) ).
fof(f646,plain,
~ leq(multiplication(sK0,strong_iteration(multiplication(sK1,sK0))),multiplication(sK0,strong_iteration(multiplication(sK1,sK0)))),
inference(superposition,[],[f264,f531]) ).
fof(f655,plain,
$false,
inference(forward_subsumption_resolution,[],[f646,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 13:12:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.34/1.55 % (2969261)Detected formulas, will run a generic FOF schedule.
% 3.34/1.55 % (2969372)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1860782684:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.55 % (2969372)First to succeed.
% 3.34/1.55 % (2969372)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2969261"
% 3.34/1.55 % (2969371)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3773873251:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.55 % (2969367)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=2585024733:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.55 % (2969368)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=2684901180:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.55 % (2969370)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2014803702:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.55 % (2969369)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=649921939:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.55 % (2969370)Refutation not found, incomplete strategy
% 3.34/1.55 % (2969370)------------------------------
% 3.34/1.55 % (2969370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.55 % (2969370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.55 % (2969370)CaDiCaL version: 2.1.3
% 3.34/1.55 % (2969370)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.55 % (2969370)Time elapsed: 0.001 s
% 3.34/1.55 % (2969370)Peak memory usage: 88 MB
% 3.34/1.55 % (2969373)dis-21_1_sil=8000:lcm=predicate:random_seed=2299732406: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)
% 3.34/1.55 % (2969373)Refutation not found, incomplete strategy
% 3.34/1.55 % (2969373)------------------------------
% 3.34/1.55 % (2969373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.55 % (2969373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.55 % (2969373)CaDiCaL version: 2.1.3
% 3.34/1.55 % (2969373)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.55 % (2969373)Time elapsed: 0.002 s
% 3.34/1.55 % (2969373)Peak memory usage: 88 MB
% 3.34/1.55 % (2969373)Instructions burned: 1 (million)
% 3.34/1.55 % (2969371)Instruction limit reached!
% 3.34/1.55 % (2969371)------------------------------
% 3.34/1.55 % (2969371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.55 % (2969371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.55 % (2969371)CaDiCaL version: 2.1.3
% 3.34/1.55 % (2969371)Termination reason: Instruction limit
% 3.34/1.55 % (2969371)Termination phase: Saturation
% 3.34/1.55 % (2969371)Time elapsed: 0.095 s
% 3.34/1.55 % (2969371)Peak memory usage: 89 MB
% 3.34/1.55 % (2969371)Instructions burned: 120 (million)
% 3.34/1.55 % (2969372)Refutation found. Thanks to Tanya!
% 3.34/1.55 % SZS status Theorem for theBenchmark
% 3.34/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/1.55 % (2969372)------------------------------
% 3.34/1.55 % (2969372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.55 % (2969372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.55 % (2969372)CaDiCaL version: 2.1.3
% 3.34/1.55 % (2969372)Termination reason: Refutation
% 3.34/1.55 % (2969372)Time elapsed: 0.010 s
% 3.34/1.55 % (2969372)Peak memory usage: 89 MB
% 3.34/1.55 % (2969372)Instructions burned: 23 (million)
% 3.34/1.55 % (2969372)------------------------------
% 3.34/1.55 % (2969372)------------------------------
% 3.34/1.55 % (2969261)Success in time 0.373 s
% 3.34/1.55 % Vampire exiting
%------------------------------------------------------------------------------