TSTP Solution File: KLE133+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE133+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:12:00 EDT 2024
% Result : Theorem 0.14s 0.43s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 68 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 34 ( 14 ~; 0 |; 15 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 87 ( 77 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1541,plain,
$false,
inference(trivial_inequality_removal,[],[f1540]) ).
fof(f1540,plain,
forward_diamond(star(sK0),domain(domain(sK1))) != forward_diamond(star(sK0),domain(domain(sK1))),
inference(superposition,[],[f1218,f1159]) ).
fof(f1159,plain,
! [X0] : addition(sK0,X0) = X0,
inference(backward_demodulation,[],[f101,f1150]) ).
fof(f1150,plain,
zero = sK0,
inference(forward_demodulation,[],[f1132,f63]) ).
fof(f63,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f1132,plain,
zero = multiplication(one,sK0),
inference(superposition,[],[f66,f1122]) ).
fof(f1122,plain,
one = antidomain(sK0),
inference(superposition,[],[f920,f101]) ).
fof(f920,plain,
one = addition(zero,antidomain(sK0)),
inference(superposition,[],[f86,f898]) ).
fof(f898,plain,
zero = domain(sK0),
inference(superposition,[],[f897,f62]) ).
fof(f62,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f897,plain,
zero = addition(domain(sK0),zero),
inference(forward_demodulation,[],[f896,f243]) ).
fof(f243,plain,
! [X0] : zero = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f242,f126]) ).
fof(f126,plain,
zero = domain(zero),
inference(forward_demodulation,[],[f120,f91]) ).
fof(f91,plain,
zero = antidomain(one),
inference(superposition,[],[f66,f61]) ).
fof(f61,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f120,plain,
antidomain(one) = domain(zero),
inference(backward_demodulation,[],[f97,f113]) ).
fof(f113,plain,
one = domain(one),
inference(superposition,[],[f110,f62]) ).
fof(f110,plain,
one = addition(domain(one),zero),
inference(superposition,[],[f86,f91]) ).
fof(f97,plain,
domain(zero) = antidomain(domain(one)),
inference(superposition,[],[f69,f94]) ).
fof(f94,plain,
antidomain(zero) = domain(one),
inference(superposition,[],[f69,f91]) ).
fof(f69,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3] : antidomain(antidomain(X3)) = domain(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f242,plain,
! [X0] : domain(zero) = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f229,f59]) ).
fof(f59,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f229,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(superposition,[],[f78,f126]) ).
fof(f78,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X3,X4] : forward_diamond(X3,X4) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
fof(f896,plain,
forward_diamond(star(sK0),zero) = addition(domain(sK0),forward_diamond(star(sK0),zero)),
inference(forward_demodulation,[],[f888,f198]) ).
fof(f198,plain,
! [X0] : zero = domain_difference(X0,X0),
inference(superposition,[],[f96,f77]) ).
fof(f77,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X3,X4] : domain_difference(X3,X4) = multiplication(domain(X3),antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_difference) ).
fof(f96,plain,
! [X0] : zero = multiplication(domain(X0),antidomain(X0)),
inference(superposition,[],[f66,f69]) ).
fof(f888,plain,
forward_diamond(star(sK0),domain_difference(domain(sK0),domain(sK0))) = addition(domain(sK0),forward_diamond(star(sK0),domain_difference(domain(sK0),domain(sK0)))),
inference(superposition,[],[f56,f241]) ).
fof(f241,plain,
domain(sK0) = forward_diamond(sK0,domain(sK0)),
inference(backward_demodulation,[],[f148,f240]) ).
fof(f240,plain,
! [X0] : domain(X0) = forward_diamond(X0,one),
inference(forward_demodulation,[],[f228,f61]) ).
fof(f228,plain,
! [X0] : forward_diamond(X0,one) = domain(multiplication(X0,one)),
inference(superposition,[],[f78,f113]) ).
fof(f148,plain,
forward_diamond(sK0,one) = forward_diamond(sK0,forward_diamond(sK0,one)),
inference(superposition,[],[f57,f113]) ).
fof(f57,plain,
! [X2] : forward_diamond(sK0,domain(X2)) = forward_diamond(sK0,forward_diamond(sK0,domain(X2))),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
( forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1)))) != addition(forward_diamond(sK0,domain(sK1)),forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1)))))
& ! [X2] : forward_diamond(sK0,domain(X2)) = forward_diamond(sK0,forward_diamond(sK0,domain(X2)))
& ! [X3] : forward_diamond(star(sK0),domain_difference(domain(X3),forward_diamond(sK0,domain(X3)))) = addition(domain(X3),forward_diamond(star(sK0),domain_difference(domain(X3),forward_diamond(sK0,domain(X3))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f52,f54,f53]) ).
fof(f53,plain,
( ? [X0] :
( ? [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) != addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))
& ! [X2] : forward_diamond(X0,domain(X2)) = forward_diamond(X0,forward_diamond(X0,domain(X2)))
& ! [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) = addition(domain(X3),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) )
=> ( ? [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) != addition(forward_diamond(sK0,domain(X1)),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))))
& ! [X2] : forward_diamond(sK0,domain(X2)) = forward_diamond(sK0,forward_diamond(sK0,domain(X2)))
& ! [X3] : forward_diamond(star(sK0),domain_difference(domain(X3),forward_diamond(sK0,domain(X3)))) = addition(domain(X3),forward_diamond(star(sK0),domain_difference(domain(X3),forward_diamond(sK0,domain(X3))))) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
( ? [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) != addition(forward_diamond(sK0,domain(X1)),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))))
=> forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1)))) != addition(forward_diamond(sK0,domain(sK1)),forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1))))) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0] :
( ? [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) != addition(forward_diamond(X0,domain(X1)),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))
& ! [X2] : forward_diamond(X0,domain(X2)) = forward_diamond(X0,forward_diamond(X0,domain(X2)))
& ! [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) = addition(domain(X3),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
? [X0] :
( ? [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) != addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))))
& ! [X1] : forward_diamond(X0,domain(X1)) = forward_diamond(X0,forward_diamond(X0,domain(X1)))
& ! [X2] : forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2)))) = addition(domain(X2),forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2))))) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
? [X0] :
( ? [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) != addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))))
& ! [X1] : forward_diamond(X0,domain(X1)) = forward_diamond(X0,forward_diamond(X0,domain(X1)))
& ! [X2] : forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2)))) = addition(domain(X2),forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2))))) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0] :
( ( ! [X1] : forward_diamond(X0,domain(X1)) = forward_diamond(X0,forward_diamond(X0,domain(X1)))
& ! [X2] : forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2)))) = addition(domain(X2),forward_diamond(star(X0),domain_difference(domain(X2),forward_diamond(X0,domain(X2))))) )
=> ! [X3] : forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) = addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X3] :
( ( ! [X5] : forward_diamond(X3,domain(X5)) = forward_diamond(X3,forward_diamond(X3,domain(X5)))
& ! [X4] : forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))) = addition(domain(X4),forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4))))) )
=> ! [X6] : forward_diamond(star(X3),domain_difference(domain(X6),forward_diamond(X3,domain(X6)))) = addition(forward_diamond(X3,domain(X6)),forward_diamond(star(X3),domain_difference(domain(X6),forward_diamond(X3,domain(X6))))) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X3] :
( ( ! [X5] : forward_diamond(X3,domain(X5)) = forward_diamond(X3,forward_diamond(X3,domain(X5)))
& ! [X4] : forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4)))) = addition(domain(X4),forward_diamond(star(X3),domain_difference(domain(X4),forward_diamond(X3,domain(X4))))) )
=> ! [X6] : forward_diamond(star(X3),domain_difference(domain(X6),forward_diamond(X3,domain(X6)))) = addition(forward_diamond(X3,domain(X6)),forward_diamond(star(X3),domain_difference(domain(X6),forward_diamond(X3,domain(X6))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f56,plain,
! [X3] : forward_diamond(star(sK0),domain_difference(domain(X3),forward_diamond(sK0,domain(X3)))) = addition(domain(X3),forward_diamond(star(sK0),domain_difference(domain(X3),forward_diamond(sK0,domain(X3))))),
inference(cnf_transformation,[],[f55]) ).
fof(f86,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[],[f72,f69]) ).
fof(f72,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(antidomain(antidomain(X3)),antidomain(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f66,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : zero = multiplication(antidomain(X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f101,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f73,f62]) ).
fof(f73,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f1218,plain,
forward_diamond(star(sK0),domain(domain(sK1))) != addition(sK0,forward_diamond(star(sK0),domain(domain(sK1)))),
inference(forward_demodulation,[],[f1210,f1165]) ).
fof(f1165,plain,
! [X0] : domain(X0) = domain_difference(X0,sK0),
inference(backward_demodulation,[],[f182,f1150]) ).
fof(f182,plain,
! [X0] : domain(X0) = domain_difference(X0,zero),
inference(forward_demodulation,[],[f176,f61]) ).
fof(f176,plain,
! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
inference(superposition,[],[f77,f119]) ).
fof(f119,plain,
one = antidomain(zero),
inference(backward_demodulation,[],[f94,f113]) ).
fof(f1210,plain,
forward_diamond(star(sK0),domain_difference(domain(sK1),sK0)) != addition(sK0,forward_diamond(star(sK0),domain_difference(domain(sK1),sK0))),
inference(backward_demodulation,[],[f58,f1171]) ).
fof(f1171,plain,
! [X0] : sK0 = forward_diamond(sK0,X0),
inference(backward_demodulation,[],[f245,f1150]) ).
fof(f245,plain,
! [X0] : zero = forward_diamond(zero,X0),
inference(forward_demodulation,[],[f231,f126]) ).
fof(f231,plain,
! [X0] : domain(zero) = forward_diamond(zero,X0),
inference(superposition,[],[f78,f60]) ).
fof(f60,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
fof(f58,plain,
forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1)))) != addition(forward_diamond(sK0,domain(sK1)),forward_diamond(star(sK0),domain_difference(domain(sK1),forward_diamond(sK0,domain(sK1))))),
inference(cnf_transformation,[],[f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE133+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 04:53:48 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (7873)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (7880)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (7874)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (7876)WARNING: value z3 for option sas not known
% 0.14/0.38 % (7878)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (7877)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (7875)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (7879)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (7876)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [3]
% 0.14/0.42 % (7879)First to succeed.
% 0.14/0.43 % (7879)Refutation found. Thanks to Tanya!
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.43 % (7879)------------------------------
% 0.14/0.43 % (7879)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.43 % (7879)Termination reason: Refutation
% 0.14/0.43
% 0.14/0.43 % (7879)Memory used [KB]: 1407
% 0.14/0.43 % (7879)Time elapsed: 0.043 s
% 0.14/0.43 % (7879)Instructions burned: 72 (million)
% 0.14/0.43 % (7879)------------------------------
% 0.14/0.43 % (7879)------------------------------
% 0.14/0.43 % (7873)Success in time 0.062 s
%------------------------------------------------------------------------------