%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KLE009+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 11:40:36 AM UTC 2026
% Result : Theorem 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 59 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 7 |; 8 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 48 !; 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(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_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(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
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(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1] :
( one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1] :
( one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X1)
& test(X0) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| complement(X0,X1)
| c(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
test(sK1),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
test(sK2),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
one != addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f47]) ).
fof(f74,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f42,f54]) ).
fof(f75,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f74,f29]) ).
fof(f104,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f29,f30]) ).
fof(f156,plain,
one != addition(addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(superposition,[],[f53,f36]) ).
fof(f158,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f30,f36]) ).
fof(f161,plain,
one != addition(multiplication(c(sK1),c(sK2)),addition(multiplication(sK1,addition(sK2,c(sK2))),multiplication(c(sK1),sK2))),
inference(forward_demodulation,[],[f156,f29]) ).
fof(f171,plain,
one != addition(multiplication(c(sK1),sK2),addition(multiplication(c(sK1),c(sK2)),multiplication(sK1,addition(sK2,c(sK2))))),
inference(forward_demodulation,[],[f161,f104]) ).
fof(f176,plain,
one != addition(multiplication(c(sK1),addition(sK2,c(sK2))),multiplication(sK1,addition(sK2,c(sK2)))),
inference(forward_demodulation,[],[f171,f158]) ).
fof(f179,plain,
one != multiplication(addition(c(sK1),sK1),addition(sK2,c(sK2))),
inference(forward_demodulation,[],[f176,f37]) ).
fof(f180,plain,
one != multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),
inference(forward_demodulation,[],[f179,f29]) ).
fof(f438,plain,
one = addition(sK1,c(sK1)),
inference(resolution,[],[f75,f51]) ).
fof(f439,plain,
one = addition(sK2,c(sK2)),
inference(resolution,[],[f75,f52]) ).
fof(f595,plain,
one != multiplication(one,addition(sK2,c(sK2))),
inference(superposition,[],[f180,f438]) ).
fof(f599,plain,
one != addition(sK2,c(sK2)),
inference(forward_demodulation,[],[f595,f35]) ).
fof(f600,plain,
$false,
inference(forward_subsumption_resolution,[],[f599,f439]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 % Computer : n017.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Sun Sep 27 12:53:35 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.47 Running first-order model finding
% 0.22/0.47 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
% 0.22/0.52 % (2525649)Will run a generic schedule for satisfiability detection.
% 0.22/0.52 % (2525658)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2338297171:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.52 % (2525656)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=167206083:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.52 % (2525655)% WARNING: option uhcvi not known.
% 0.22/0.52 % (2525660)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=23911780:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.52 % (2525657)dis+10_1_sil=32000:sp=arity:random_seed=1247042543:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.52 % (2525654)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3124617116_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.52 % (2525658) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2525649-2525658"...
% 0.22/0.52 % (2525655)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2540403355:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.52 % (2525659)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3045236627:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.52 % (2525658)...printing done.
% 0.22/0.52 % (2525658)Refutation found. Thanks to Tanya!
% 0.22/0.52 % SZS status Theorem for theBenchmark
% 0.22/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.52 % (2525658)------------------------------
% 0.22/0.52 % (2525658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.52 % (2525658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.52 % (2525658)CaDiCaL version: 2.1.3
% 0.22/0.52 % (2525658)Termination reason: Refutation
% 0.22/0.52 % (2525658)Time elapsed: 0.014 s
% 0.22/0.52 % (2525658)Peak memory usage: 12 MB
% 0.22/0.52 % (2525658)Instructions burned: 22 (million)
% 0.22/0.52 % (2525649)Success in time 0.037 s
% 0.22/0.52 % Vampire exiting
%------------------------------------------------------------------------------