%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE007+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 11:40:35 AM UTC 2026
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 20 unt; 2 def)
% Number of atoms : 111 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 44 ~; 32 |; 10 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',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/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
? [X0,X1] :
( ( ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
| ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
? [X0,X1] :
( ( ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
| ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) )
& test(X1)
& test(X0) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f46,plain,
( ~ leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
test(sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
test(sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f44]) ).
fof(f50,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f53,plain,
! [X0] :
( complement(X0,c(X0))
| test(X0) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f56,plain,
~ test(sK2),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f57,plain,
~ test(sK1),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f58,plain,
( leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f60,definition,
( spl3_1
<=> leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f62,plain,
( leq(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl3_2
<=> leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f66,plain,
( leq(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f58,f64,f60]) ).
fof(f75,plain,
! [X0] :
( one = addition(c(X0),X0)
| test(X0) ),
inference(resolution,[],[f39,f53]) ).
fof(f76,plain,
! [X0] :
( test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f75,f25]) ).
fof(f81,plain,
( one != addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))),one)
| ~ spl3_2 ),
inference(resolution,[],[f50,f66]) ).
fof(f101,plain,
( one != addition(one,addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK1,c(sK1)),c(sK2))))
| ~ spl3_2 ),
inference(superposition,[],[f81,f25]) ).
fof(f132,plain,
( one != addition(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| ~ spl3_2 ),
inference(superposition,[],[f101,f32]) ).
fof(f208,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f76,f57]) ).
fof(f209,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f76,f56]) ).
fof(f235,plain,
( one != addition(one,multiplication(addition(sK1,c(sK1)),one))
| ~ spl3_2 ),
inference(superposition,[],[f132,f209]) ).
fof(f241,plain,
( one != addition(one,addition(sK1,c(sK1)))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f235,f30]) ).
fof(f244,plain,
( one != addition(one,one)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f241,f208]) ).
fof(f247,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f244,f28]) ).
fof(f248,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f249,plain,
( leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f62,f32]) ).
fof(f251,plain,
( leq(one,multiplication(addition(sK1,c(sK1)),one))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f249,f209]) ).
fof(f253,plain,
( leq(one,addition(sK1,c(sK1)))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f251,f30]) ).
fof(f255,plain,
( leq(one,one)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f253,f208]) ).
fof(f257,plain,
( one != addition(one,one)
| ~ spl3_1 ),
inference(resolution,[],[f255,f50]) ).
fof(f258,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f257,f28]) ).
fof(f259,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f258]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f259]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f260,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE007+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n003.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 12:59:56 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.44 Running first-order model finding
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 % (514314)Will run a generic schedule for satisfiability detection.
% 0.20/0.47 % (514324)% WARNING: option uhcvi not known.
% 0.20/0.47 % (514324)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3567156574:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.47 % (514324) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-514314-514324"...
% 0.20/0.47 % (514324)...printing done.
% 0.20/0.47 % (514324)Refutation found. Thanks to Tanya!
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47 % (514324)------------------------------
% 0.20/0.47 % (514324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.47 % (514324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.47 % (514324)CaDiCaL version: 2.1.3
% 0.20/0.47 % (514324)Termination reason: Refutation
% 0.20/0.47 % (514324)Time elapsed: 0.005 s
% 0.20/0.47 % (514324)Peak memory usage: 13 MB
% 0.20/0.47 % (514324)Instructions burned: 11 (million)
% 0.20/0.47 % (514314)Success in time 0.02 s
% 0.20/0.47 % Vampire exiting
%------------------------------------------------------------------------------