%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE022+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 : n017.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 11:40:39 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 17 unt; 2 def)
% Number of atoms : 111 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 36 |; 13 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 49 ( 0 sgn 47 !; 2 ?)
% 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)
=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ),
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(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))
| ~ leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) )
& test(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f30,plain,
( ( ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) )
& test(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f23]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
( ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f49]) ).
fof(f56,definition,
( spl3_1
<=> leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f58,plain,
( ~ leq(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl3_2
<=> leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f62,plain,
( ~ leq(sK1,addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))))
| spl3_2 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f53,f60,f56]) ).
fof(f75,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f42,f34]) ).
fof(f80,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f75]) ).
fof(f82,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f45,f54]) ).
fof(f83,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f82,f31]) ).
fof(f145,plain,
( ~ leq(multiplication(sK1,addition(sK2,c(sK2))),sK1)
| spl3_1 ),
inference(superposition,[],[f58,f38]) ).
fof(f254,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f83,f52]) ).
fof(f263,plain,
( ~ leq(multiplication(sK1,one),sK1)
| spl3_1 ),
inference(superposition,[],[f145,f254]) ).
fof(f276,plain,
( ~ leq(sK1,sK1)
| spl3_1 ),
inference(forward_demodulation,[],[f263,f36]) ).
fof(f277,plain,
( $false
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f276,f80]) ).
fof(f278,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f280,plain,
( ~ leq(sK1,multiplication(sK1,addition(sK2,c(sK2))))
| spl3_2 ),
inference(forward_demodulation,[],[f62,f38]) ).
fof(f282,plain,
( ~ leq(sK1,multiplication(sK1,one))
| spl3_2 ),
inference(forward_demodulation,[],[f280,f254]) ).
fof(f284,plain,
( ~ leq(sK1,sK1)
| spl3_2 ),
inference(forward_demodulation,[],[f282,f36]) ).
fof(f285,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f284,f80]) ).
fof(f286,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f285]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
spl3_1,
inference(sat_conversion,[],[f278]) ).
cnf(s7,plain,
spl3_2,
inference(sat_conversion,[],[f286]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s6]) ).
fof(f287,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE022+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 12:57:20 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.46 % (2531782)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2531790)dis+10_1_sil=32000:sp=arity:random_seed=3435716603:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (2531788)% WARNING: option uhcvi not known.
% 0.16/0.46 % (2531790) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2531782-2531790"...
% 0.16/0.46 % (2531790)...printing done.
% 0.16/0.46 % (2531790)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (2531790)------------------------------
% 0.16/0.46 % (2531790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (2531790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (2531790)CaDiCaL version: 2.1.3
% 0.16/0.46 % (2531790)Termination reason: Refutation
% 0.16/0.46 % (2531790)Time elapsed: 0.004 s
% 0.16/0.46 % (2531790)Peak memory usage: 12 MB
% 0.16/0.46 % (2531790)Instructions burned: 10 (million)
% 0.16/0.46 % (2531782)Success in time 0.03 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------