TSTP Solution File: KLE075+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE075+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 : n002.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 13:11:52 EDT 2024
% Result : Theorem 0.19s 0.35s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 40
% Syntax : Number of formulae : 109 ( 61 unt; 0 def)
% Number of atoms : 173 ( 85 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 112 ( 48 ~; 41 |; 0 &)
% ( 22 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 107 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f298,plain,
$false,
inference(avatar_sat_refutation,[],[f50,f56,f61,f65,f69,f73,f77,f81,f85,f89,f94,f106,f110,f114,f138,f142,f146,f192,f196,f201,f275,f279,f295]) ).
fof(f295,plain,
( spl1_2
| ~ spl1_22 ),
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f294,plain,
( $false
| spl1_2
| ~ spl1_22 ),
inference(trivial_inequality_removal,[],[f288]) ).
fof(f288,plain,
( domain(sK0) != domain(sK0)
| spl1_2
| ~ spl1_22 ),
inference(superposition,[],[f55,f278]) ).
fof(f278,plain,
( ! [X0] : domain(X0) = domain(domain(X0))
| ~ spl1_22 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f277,plain,
( spl1_22
<=> ! [X0] : domain(X0) = domain(domain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f55,plain,
( domain(sK0) != domain(domain(sK0))
| spl1_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl1_2
<=> domain(sK0) = domain(domain(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f279,plain,
( spl1_22
| ~ spl1_8
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f132,f108,f79,f277]) ).
fof(f79,plain,
( spl1_8
<=> ! [X0] : multiplication(one,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f108,plain,
( spl1_13
<=> ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f132,plain,
( ! [X0] : domain(X0) = domain(domain(X0))
| ~ spl1_8
| ~ spl1_13 ),
inference(forward_demodulation,[],[f127,f80]) ).
fof(f80,plain,
( ! [X0] : multiplication(one,X0) = X0
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f127,plain,
( ! [X0] : domain(multiplication(one,X0)) = domain(domain(X0))
| ~ spl1_8
| ~ spl1_13 ),
inference(superposition,[],[f109,f80]) ).
fof(f109,plain,
( ! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f275,plain,
( spl1_21
| ~ spl1_10
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f96,f92,f87,f273]) ).
fof(f273,plain,
( spl1_21
<=> ! [X0] : one = addition(one,domain(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f87,plain,
( spl1_10
<=> ! [X0] : one = addition(domain(X0),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f92,plain,
( spl1_11
<=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f96,plain,
( ! [X0] : one = addition(one,domain(X0))
| ~ spl1_10
| ~ spl1_11 ),
inference(superposition,[],[f93,f88]) ).
fof(f88,plain,
( ! [X0] : one = addition(domain(X0),one)
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f93,plain,
( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f201,plain,
( spl1_20
| ~ spl1_7
| ~ spl1_10
| ~ spl1_11
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f151,f136,f92,f87,f75,f198]) ).
fof(f198,plain,
( spl1_20
<=> one = domain(one) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f75,plain,
( spl1_7
<=> ! [X0] : multiplication(X0,one) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f136,plain,
( spl1_15
<=> ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f151,plain,
( one = domain(one)
| ~ spl1_7
| ~ spl1_10
| ~ spl1_11
| ~ spl1_15 ),
inference(forward_demodulation,[],[f150,f96]) ).
fof(f150,plain,
( domain(one) = addition(one,domain(one))
| ~ spl1_7
| ~ spl1_15 ),
inference(superposition,[],[f137,f76]) ).
fof(f76,plain,
( ! [X0] : multiplication(X0,one) = X0
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f137,plain,
( ! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f196,plain,
spl1_19,
inference(avatar_split_clause,[],[f45,f194]) ).
fof(f194,plain,
( spl1_19
<=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f45,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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f192,plain,
spl1_18,
inference(avatar_split_clause,[],[f44,f190]) ).
fof(f190,plain,
( spl1_18
<=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f44,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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f146,plain,
spl1_17,
inference(avatar_split_clause,[],[f43,f144]) ).
fof(f144,plain,
( spl1_17
<=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f142,plain,
spl1_16,
inference(avatar_split_clause,[],[f42,f140]) ).
fof(f140,plain,
( spl1_16
<=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f42,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f138,plain,
spl1_15,
inference(avatar_split_clause,[],[f38,f136]) ).
fof(f38,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] : multiplication(domain(X3),X3) = addition(X3,multiplication(domain(X3),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f114,plain,
( spl1_14
| ~ spl1_6
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f95,f92,f71,f112]) ).
fof(f112,plain,
( spl1_14
<=> ! [X0] : addition(zero,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f71,plain,
( spl1_6
<=> ! [X0] : addition(X0,zero) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f95,plain,
( ! [X0] : addition(zero,X0) = X0
| ~ spl1_6
| ~ spl1_11 ),
inference(superposition,[],[f93,f72]) ).
fof(f72,plain,
( ! [X0] : addition(X0,zero) = X0
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f110,plain,
spl1_13,
inference(avatar_split_clause,[],[f41,f108]) ).
fof(f41,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] : domain(multiplication(X3,X4)) = domain(multiplication(X3,domain(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f106,plain,
spl1_12,
inference(avatar_split_clause,[],[f40,f104]) ).
fof(f104,plain,
( spl1_12
<=> ! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f40,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X3,X4] : domain(addition(X3,X4)) = addition(domain(X3),domain(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
fof(f94,plain,
spl1_11,
inference(avatar_split_clause,[],[f39,f92]) ).
fof(f39,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(f89,plain,
spl1_10,
inference(avatar_split_clause,[],[f37,f87]) ).
fof(f37,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0] : one = addition(domain(X0),one),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3] : one = addition(domain(X3),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
fof(f85,plain,
spl1_9,
inference(avatar_split_clause,[],[f36,f83]) ).
fof(f83,plain,
( spl1_9
<=> ! [X0] : addition(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f81,plain,
spl1_8,
inference(avatar_split_clause,[],[f35,f79]) ).
fof(f35,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(f77,plain,
spl1_7,
inference(avatar_split_clause,[],[f34,f75]) ).
fof(f34,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(f73,plain,
spl1_6,
inference(avatar_split_clause,[],[f33,f71]) ).
fof(f33,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(f69,plain,
spl1_5,
inference(avatar_split_clause,[],[f32,f67]) ).
fof(f67,plain,
( spl1_5
<=> ! [X0] : zero = multiplication(zero,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f32,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(f65,plain,
spl1_4,
inference(avatar_split_clause,[],[f31,f63]) ).
fof(f63,plain,
( spl1_4
<=> ! [X0] : zero = multiplication(X0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f31,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(f61,plain,
spl1_3,
inference(avatar_split_clause,[],[f30,f58]) ).
fof(f58,plain,
( spl1_3
<=> zero = domain(zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f30,plain,
zero = domain(zero),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
zero = domain(zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
fof(f56,plain,
( ~ spl1_2
| spl1_1 ),
inference(avatar_split_clause,[],[f51,f47,f53]) ).
fof(f47,plain,
( spl1_1
<=> domain(sK0) = domain(multiplication(one,domain(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f51,plain,
( domain(sK0) != domain(domain(sK0))
| spl1_1 ),
inference(forward_demodulation,[],[f49,f35]) ).
fof(f49,plain,
( domain(sK0) != domain(multiplication(one,domain(sK0)))
| spl1_1 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f29,f47]) ).
fof(f29,plain,
domain(sK0) != domain(multiplication(one,domain(sK0))),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
domain(sK0) != domain(multiplication(one,domain(sK0))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).
fof(f27,plain,
( ? [X0] : domain(X0) != domain(multiplication(one,domain(X0)))
=> domain(sK0) != domain(multiplication(one,domain(sK0))) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
? [X0] : domain(X0) != domain(multiplication(one,domain(X0))),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ! [X0] : domain(X0) = domain(multiplication(one,domain(X0))),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X3] : domain(X3) = domain(multiplication(one,domain(X3))),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X3] : domain(X3) = domain(multiplication(one,domain(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE075+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 30 05:20:55 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % (5946)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.35 % (5950)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.35 % (5951)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)
% 0.19/0.35 TRYING [1]
% 0.19/0.35 TRYING [2]
% 0.19/0.35 TRYING [3]
% 0.19/0.35 % (5951)First to succeed.
% 0.19/0.35 % (5949)WARNING: value z3 for option sas not known
% 0.19/0.35 % (5951)Refutation found. Thanks to Tanya!
% 0.19/0.35 % SZS status Theorem for theBenchmark
% 0.19/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.35 % (5951)------------------------------
% 0.19/0.35 % (5951)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.35 % (5951)Termination reason: Refutation
% 0.19/0.35
% 0.19/0.35 % (5951)Memory used [KB]: 912
% 0.19/0.35 % (5951)Time elapsed: 0.006 s
% 0.19/0.35 % (5951)Instructions burned: 14 (million)
% 0.19/0.35 % (5951)------------------------------
% 0.19/0.35 % (5951)------------------------------
% 0.19/0.35 % (5946)Success in time 0.009 s
%------------------------------------------------------------------------------