%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE137+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 : n012.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 11:40:26 AM UTC 2026
% Result : Theorem 3.03s 1.17s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 36 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 7 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 41 ( 40 !; 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(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(X0,strong_iteration(one)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] : leq(X0,strong_iteration(one)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] : ~ leq(X0,strong_iteration(one)),
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(sK0,strong_iteration(one)),
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(sK0,strong_iteration(one)),
inference(cnf_transformation,[],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f32,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f33,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f87,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f37,f36]) ).
fof(f149,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f34,f32]) ).
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,f33]) ).
fof(f690,plain,
$false,
inference(resolution,[],[f686,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE137+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 13:11:50 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.33 Running first-order theorem proving
% 0.05/0.33 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
% 3.03/1.17 % (2379558)Detected formulas, will run a generic FOF schedule.
% 3.03/1.17 % (2379608)dis-21_1_sil=8000:lcm=predicate:random_seed=2097413214: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)
% 3.03/1.17 % (2379608)Refutation not found, incomplete strategy
% 3.03/1.17 % (2379608)------------------------------
% 3.03/1.17 % (2379608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.17 % (2379608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.17 % (2379608)CaDiCaL version: 2.1.3
% 3.03/1.17 % (2379608)Termination reason: Refutation not found, incomplete strategy
% 3.03/1.17 % (2379608)Time elapsed: 0.001 s
% 3.03/1.17 % (2379608)Peak memory usage: 88 MB
% 3.03/1.17 % (2379608)Instructions burned: 1 (million)
% 3.03/1.17 % (2379602)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=1288583275:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.03/1.17 % (2379603)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=2713625423:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.03/1.17 % (2379606)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=978023156:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.03/1.17 % (2379604)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=1227856299:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.03/1.17 % (2379605)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2559631319:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.03/1.17 % (2379605)Refutation not found, incomplete strategy
% 3.03/1.17 % (2379605)------------------------------
% 3.03/1.17 % (2379605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.17 % (2379605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.17 % (2379605)CaDiCaL version: 2.1.3
% 3.03/1.17 % (2379605)Termination reason: Refutation not found, incomplete strategy
% 3.03/1.17 % (2379605)Time elapsed: 0.001 s
% 3.03/1.17 % (2379605)Peak memory usage: 88 MB
% 3.03/1.17 % (2379606)First to succeed.
% 3.03/1.17 % (2379606)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2379558"
% 3.03/1.17 % (2379607)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=165387049:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.03/1.17 % (2379607)Also succeeded, but the first one will report.
% 3.03/1.17 % (2379608)------------------------------
% 3.03/1.17 % (2379608)------------------------------
% 3.03/1.17 % (2379606)Refutation found. Thanks to Tanya!
% 3.03/1.17 % SZS status Theorem for theBenchmark
% 3.03/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 3.03/1.17 % (2379606)------------------------------
% 3.03/1.17 % (2379606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.17 % (2379606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.17 % (2379606)CaDiCaL version: 2.1.3
% 3.03/1.17 % (2379606)Termination reason: Refutation
% 3.03/1.17 % (2379606)Time elapsed: 0.008 s
% 3.03/1.17 % (2379606)Peak memory usage: 88 MB
% 3.03/1.17 % (2379606)Instructions burned: 22 (million)
% 3.03/1.17 % (2379606)------------------------------
% 3.03/1.17 % (2379606)------------------------------
% 3.03/1.17 % (2379558)Success in time 0.376 s
% 3.03/1.17 % Vampire exiting
%------------------------------------------------------------------------------