TSTP Solution File: KLE131+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE131+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 : n006.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 13:11:59 EDT 2024
% Result : Theorem 1.67s 0.58s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 90 ( 84 unt; 0 def)
% Number of atoms : 98 ( 97 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 0 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 3 con; 0-2 aty)
% Number of variables : 108 ( 106 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9953,plain,
$false,
inference(trivial_inequality_removal,[],[f9945]) ).
fof(f9945,plain,
zero != zero,
inference(superposition,[],[f54,f9905]) ).
fof(f9905,plain,
zero = divergence(sK0),
inference(superposition,[],[f9895,f57]) ).
fof(f57,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f9895,plain,
zero = addition(divergence(sK0),zero),
inference(forward_demodulation,[],[f9894,f8793]) ).
fof(f8793,plain,
! [X0] : divergence(X0) = domain(divergence(X0)),
inference(forward_demodulation,[],[f8792,f3796]) ).
fof(f3796,plain,
! [X0] : multiplication(domain(X0),X0) = X0,
inference(forward_demodulation,[],[f3776,f59]) ).
fof(f59,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f3776,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(superposition,[],[f772,f82]) ).
fof(f82,plain,
! [X0] : one = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[],[f68,f65]) ).
fof(f65,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/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f68,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/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f772,plain,
! [X0,X1] : multiplication(X1,X0) = multiplication(addition(X1,antidomain(X0)),X0),
inference(forward_demodulation,[],[f738,f57]) ).
fof(f738,plain,
! [X0,X1] : addition(multiplication(X1,X0),zero) = multiplication(addition(X1,antidomain(X0)),X0),
inference(superposition,[],[f80,f62]) ).
fof(f62,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/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f80,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f8792,plain,
! [X0] : domain(divergence(X0)) = multiplication(domain(divergence(X0)),divergence(X0)),
inference(forward_demodulation,[],[f8791,f65]) ).
fof(f8791,plain,
! [X0] : antidomain(antidomain(divergence(X0))) = multiplication(antidomain(antidomain(divergence(X0))),divergence(X0)),
inference(forward_demodulation,[],[f8707,f58]) ).
fof(f58,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8707,plain,
! [X0] : multiplication(antidomain(antidomain(divergence(X0))),divergence(X0)) = multiplication(antidomain(antidomain(divergence(X0))),one),
inference(superposition,[],[f538,f7111]) ).
fof(f7111,plain,
! [X0] : one = addition(antidomain(divergence(X0)),divergence(X0)),
inference(superposition,[],[f273,f66]) ).
fof(f66,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X3] : divergence(X3) = forward_diamond(X3,divergence(X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
fof(f273,plain,
! [X0,X1] : one = addition(antidomain(forward_diamond(X0,X1)),forward_diamond(X0,X1)),
inference(forward_demodulation,[],[f264,f262]) ).
fof(f262,plain,
! [X0,X1] : domain(antidomain(multiplication(X0,domain(X1)))) = antidomain(forward_diamond(X0,X1)),
inference(superposition,[],[f89,f74]) ).
fof(f74,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/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
fof(f89,plain,
! [X0] : antidomain(domain(X0)) = domain(antidomain(X0)),
inference(superposition,[],[f65,f65]) ).
fof(f264,plain,
! [X0,X1] : one = addition(domain(antidomain(multiplication(X0,domain(X1)))),forward_diamond(X0,X1)),
inference(superposition,[],[f107,f74]) ).
fof(f107,plain,
! [X0] : one = addition(domain(antidomain(X0)),domain(X0)),
inference(superposition,[],[f82,f65]) ).
fof(f538,plain,
! [X0,X1] : multiplication(antidomain(X0),X1) = multiplication(antidomain(X0),addition(X0,X1)),
inference(forward_demodulation,[],[f509,f97]) ).
fof(f97,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f69,f57]) ).
fof(f69,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/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f509,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X0,X1)) = addition(zero,multiplication(antidomain(X0),X1)),
inference(superposition,[],[f79,f62]) ).
fof(f79,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9894,plain,
zero = addition(domain(divergence(sK0)),zero),
inference(forward_demodulation,[],[f9893,f268]) ).
fof(f268,plain,
! [X0] : zero = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f267,f122]) ).
fof(f122,plain,
zero = domain(zero),
inference(forward_demodulation,[],[f116,f87]) ).
fof(f87,plain,
zero = antidomain(one),
inference(superposition,[],[f62,f58]) ).
fof(f116,plain,
antidomain(one) = domain(zero),
inference(backward_demodulation,[],[f93,f109]) ).
fof(f109,plain,
one = domain(one),
inference(superposition,[],[f106,f57]) ).
fof(f106,plain,
one = addition(domain(one),zero),
inference(superposition,[],[f82,f87]) ).
fof(f93,plain,
domain(zero) = antidomain(domain(one)),
inference(superposition,[],[f65,f91]) ).
fof(f91,plain,
antidomain(zero) = domain(one),
inference(superposition,[],[f65,f87]) ).
fof(f267,plain,
! [X0] : domain(zero) = forward_diamond(X0,zero),
inference(forward_demodulation,[],[f254,f55]) ).
fof(f55,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f254,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(superposition,[],[f74,f122]) ).
fof(f9893,plain,
forward_diamond(star(sK0),zero) = addition(domain(divergence(sK0)),forward_diamond(star(sK0),zero)),
inference(forward_demodulation,[],[f9854,f200]) ).
fof(f200,plain,
! [X0] : zero = domain_difference(X0,X0),
inference(superposition,[],[f73,f90]) ).
fof(f90,plain,
! [X0] : zero = multiplication(domain(X0),antidomain(X0)),
inference(superposition,[],[f62,f65]) ).
fof(f73,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/sandbox/benchmark/theBenchmark.p',domain_difference) ).
fof(f9854,plain,
forward_diamond(star(sK0),domain_difference(divergence(sK0),divergence(sK0))) = addition(domain(divergence(sK0)),forward_diamond(star(sK0),domain_difference(divergence(sK0),divergence(sK0)))),
inference(superposition,[],[f9750,f66]) ).
fof(f9750,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(X1,forward_diamond(sK0,X1))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(X1,forward_diamond(sK0,X1)))),
inference(backward_demodulation,[],[f9725,f9726]) ).
fof(f9726,plain,
! [X0,X1] : forward_diamond(X1,domain(X0)) = forward_diamond(X1,X0),
inference(forward_demodulation,[],[f9693,f74]) ).
fof(f9693,plain,
! [X0,X1] : forward_diamond(X1,domain(X0)) = domain(multiplication(X1,domain(X0))),
inference(superposition,[],[f74,f9059]) ).
fof(f9059,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[],[f8817,f65]) ).
fof(f8817,plain,
! [X0] : antidomain(antidomain(X0)) = domain(domain(X0)),
inference(backward_demodulation,[],[f164,f8813]) ).
fof(f8813,plain,
! [X0] : antidomain(X0) = domain(antidomain(X0)),
inference(forward_demodulation,[],[f8812,f3796]) ).
fof(f8812,plain,
! [X0] : domain(antidomain(X0)) = multiplication(domain(antidomain(X0)),antidomain(X0)),
inference(forward_demodulation,[],[f8811,f58]) ).
fof(f8811,plain,
! [X0] : multiplication(domain(antidomain(X0)),antidomain(X0)) = multiplication(domain(antidomain(X0)),one),
inference(forward_demodulation,[],[f8709,f89]) ).
fof(f8709,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(superposition,[],[f538,f82]) ).
fof(f164,plain,
! [X0] : domain(domain(X0)) = antidomain(domain(antidomain(X0))),
inference(superposition,[],[f65,f89]) ).
fof(f9725,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(X1,forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(X1,forward_diamond(sK0,domain(X1))))),
inference(backward_demodulation,[],[f53,f9718]) ).
fof(f9718,plain,
! [X0,X1] : domain_difference(X0,X1) = domain_difference(domain(X0),X1),
inference(forward_demodulation,[],[f9692,f73]) ).
fof(f9692,plain,
! [X0,X1] : multiplication(domain(X0),antidomain(X1)) = domain_difference(domain(X0),X1),
inference(superposition,[],[f73,f9059]) ).
fof(f53,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( zero != divergence(sK0)
& ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f49,f51]) ).
fof(f51,plain,
( ? [X0] :
( zero != divergence(X0)
& ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) )
=> ( zero != divergence(sK0)
& ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0] :
( zero != divergence(X0)
& ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0] :
( ! [X1] : forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) = addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))))
=> zero = divergence(X0) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X3] :
( ! [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)))))
=> zero = divergence(X3) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X3] :
( ! [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)))))
=> zero = divergence(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f54,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 04:57:35 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (13016)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (13019)WARNING: value z3 for option sas not known
% 0.15/0.38 % (13017)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (13019)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)
% 0.15/0.38 % (13018)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (13021)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)
% 0.15/0.38 % (13022)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)
% 0.15/0.38 % (13020)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (13023)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [1]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 TRYING [2]
% 0.22/0.42 TRYING [3]
% 0.22/0.42 TRYING [4]
% 0.22/0.49 TRYING [4]
% 0.22/0.50 TRYING [1]
% 0.22/0.50 TRYING [2]
% 0.22/0.51 TRYING [3]
% 0.22/0.53 TRYING [4]
% 0.22/0.54 TRYING [5]
% 0.22/0.58 % (13022)First to succeed.
% 1.67/0.58 % (13022)Refutation found. Thanks to Tanya!
% 1.67/0.58 % SZS status Theorem for theBenchmark
% 1.67/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.67/0.58 % (13022)------------------------------
% 1.67/0.58 % (13022)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.67/0.58 % (13022)Termination reason: Refutation
% 1.67/0.58
% 1.67/0.58 % (13022)Memory used [KB]: 4064
% 1.67/0.58 % (13022)Time elapsed: 0.202 s
% 1.67/0.58 % (13022)Instructions burned: 474 (million)
% 1.67/0.58 % (13022)------------------------------
% 1.67/0.58 % (13022)------------------------------
% 1.67/0.58 % (13016)Success in time 0.208 s
%------------------------------------------------------------------------------