%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 11:40:57 AM UTC 2026
% Result : Theorem 0.26s 0.58s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 18 unt; 2 def)
% Number of atoms : 62 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 16 |; 3 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',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/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0] :
( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
& leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
& leq(strong_iteration(one),multiplication(strong_iteration(one),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] :
( ~ leq(multiplication(strong_iteration(one),X0),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),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(strong_iteration(one),sK0),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),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(strong_iteration(one),sK0),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f48,definition,
( spl1_1
<=> leq(strong_iteration(one),multiplication(strong_iteration(one),sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f50,plain,
( ~ leq(strong_iteration(one),multiplication(strong_iteration(one),sK0))
| spl1_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl1_2
<=> leq(multiplication(strong_iteration(one),sK0),strong_iteration(one)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f54,plain,
( ~ leq(multiplication(strong_iteration(one),sK0),strong_iteration(one))
| spl1_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f98,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f28,f30]) ).
fof(f223,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(superposition,[],[f42,f33]) ).
fof(f286,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,addition(X0,X1)) ),
inference(superposition,[],[f45,f98]) ).
fof(f291,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(trivial_inequality_removal,[],[f286]) ).
fof(f1209,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(forward_subsumption_resolution,[],[f223,f291]) ).
fof(f1237,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f1209,f50]) ).
fof(f1238,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(superposition,[],[f1209,f32]) ).
fof(f1239,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f1237]) ).
fof(f1263,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f1238,f54]) ).
fof(f1265,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f1263]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f55]) ).
cnf(s12,plain,
spl1_1,
inference(sat_conversion,[],[f1239]) ).
cnf(s13,plain,
spl1_2,
inference(sat_conversion,[],[f1265]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s13,s12]) ).
fof(f1266,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.18/0.46 % Computer : n002.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 27 13:14:36 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.51 Running first-order model finding
% 0.22/0.51 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.58 % (3520064)Will run a generic schedule for satisfiability detection.
% 0.26/0.58 % (3520072)dis+10_1_sil=32000:sp=arity:random_seed=667894662:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.26/0.58 % (3520070)% WARNING: option uhcvi not known.
% 0.26/0.58 % (3520073)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2326641616:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.26/0.58 % (3520069)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2473199107_2999 on theBenchmark for (2999ds/0Mi)
% 0.26/0.58 % (3520071)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1203054721:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.58 % (3520070)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2147664481:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.26/0.58 % (3520075)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3512660854:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.26/0.58 % (3520074)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2245428167:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.26/0.58 % TRYING [1]
% 0.26/0.58 % TRYING [2]
% 0.26/0.58 % TRYING [3]
% 0.26/0.58 % (3520072) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3520064-3520072"...
% 0.26/0.58 % (3520072)...printing done.
% 0.26/0.58 % (3520072)Refutation found. Thanks to Tanya!
% 0.26/0.58 % SZS status Theorem for theBenchmark
% 0.26/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.58 % (3520072)------------------------------
% 0.26/0.58 % (3520072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.58 % (3520072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.58 % (3520072)CaDiCaL version: 2.1.3
% 0.26/0.58 % (3520072)Termination reason: Refutation
% 0.26/0.58 % (3520072)Time elapsed: 0.025 s
% 0.26/0.58 % (3520072)Peak memory usage: 13 MB
% 0.26/0.58 % (3520072)Instructions burned: 45 (million)
% 0.26/0.58 % (3520064)Success in time 0.051 s
% 0.26/0.58 % Vampire exiting
%------------------------------------------------------------------------------