TSTP Solution File: RNG023-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG023-7 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n031.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 : Fri Sep 1 21:57:40 EDT 2023
% Result : Unsatisfiable 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 55
% Syntax : Number of formulae : 130 ( 49 unt; 0 def)
% Number of atoms : 276 ( 95 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 261 ( 115 ~; 114 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 34 ( 32 usr; 33 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 166 (; 166 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f747,plain,
$false,
inference(avatar_sat_refutation,[],[f30,f34,f38,f42,f46,f50,f54,f58,f68,f84,f88,f92,f111,f133,f137,f141,f241,f288,f303,f379,f383,f509,f513,f573,f630,f719,f723,f727,f731,f735,f739,f743,f746]) ).
fof(f746,plain,
( spl0_1
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f745]) ).
fof(f745,plain,
( $false
| spl0_1
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f744]) ).
fof(f744,plain,
( additive_identity != additive_identity
| spl0_1
| ~ spl0_31 ),
inference(superposition,[],[f29,f738]) ).
fof(f738,plain,
( ! [X2,X3] : additive_identity = associator(X2,X2,X3)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f737,plain,
( spl0_31
<=> ! [X2,X3] : additive_identity = associator(X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f29,plain,
( additive_identity != associator(x,x,y)
| spl0_1 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f27,plain,
( spl0_1
<=> additive_identity = associator(x,x,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f743,plain,
( spl0_32
| ~ spl0_5
| ~ spl0_8
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f681,f628,f56,f44,f741]) ).
fof(f741,plain,
( spl0_32
<=> ! [X4,X5] : additive_identity = associator(X4,X5,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f44,plain,
( spl0_5
<=> ! [X0] : additive_identity = multiply(X0,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f56,plain,
( spl0_8
<=> ! [X0] : additive_identity = add(X0,additive_inverse(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f628,plain,
( spl0_25
<=> ! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f681,plain,
( ! [X4,X5] : additive_identity = associator(X4,X5,additive_identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f680,f57]) ).
fof(f57,plain,
( ! [X0] : additive_identity = add(X0,additive_inverse(X0))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f680,plain,
( ! [X4,X5] : add(additive_identity,additive_inverse(additive_identity)) = associator(X4,X5,additive_identity)
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f679,f45]) ).
fof(f45,plain,
( ! [X0] : additive_identity = multiply(X0,additive_identity)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f679,plain,
( ! [X4,X5] : associator(X4,X5,additive_identity) = add(additive_identity,additive_inverse(multiply(X4,additive_identity)))
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f640,f45]) ).
fof(f640,plain,
( ! [X4,X5] : associator(X4,X5,additive_identity) = add(additive_identity,additive_inverse(multiply(X4,multiply(X5,additive_identity))))
| ~ spl0_5
| ~ spl0_25 ),
inference(superposition,[],[f629,f45]) ).
fof(f629,plain,
( ! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2))))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f739,plain,
( spl0_31
| ~ spl0_8
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f678,f628,f139,f56,f737]) ).
fof(f139,plain,
( spl0_16
<=> ! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f678,plain,
( ! [X2,X3] : additive_identity = associator(X2,X2,X3)
| ~ spl0_8
| ~ spl0_16
| ~ spl0_25 ),
inference(forward_demodulation,[],[f639,f57]) ).
fof(f639,plain,
( ! [X2,X3] : associator(X2,X2,X3) = add(multiply(X2,multiply(X2,X3)),additive_inverse(multiply(X2,multiply(X2,X3))))
| ~ spl0_16
| ~ spl0_25 ),
inference(superposition,[],[f629,f140]) ).
fof(f140,plain,
( ! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f735,plain,
( spl0_30
| ~ spl0_8
| ~ spl0_15
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f677,f628,f135,f56,f733]) ).
fof(f733,plain,
( spl0_30
<=> ! [X0,X1] : additive_identity = associator(X0,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f135,plain,
( spl0_15
<=> ! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f677,plain,
( ! [X0,X1] : additive_identity = associator(X0,X1,X1)
| ~ spl0_8
| ~ spl0_15
| ~ spl0_25 ),
inference(forward_demodulation,[],[f638,f57]) ).
fof(f638,plain,
( ! [X0,X1] : associator(X0,X1,X1) = add(multiply(X0,multiply(X1,X1)),additive_inverse(multiply(X0,multiply(X1,X1))))
| ~ spl0_15
| ~ spl0_25 ),
inference(superposition,[],[f629,f136]) ).
fof(f136,plain,
( ! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f731,plain,
( spl0_29
| ~ spl0_3
| ~ spl0_4
| ~ spl0_13
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f666,f628,f108,f40,f36,f729]) ).
fof(f729,plain,
( spl0_29
<=> ! [X6,X5] : additive_identity = associator(additive_identity,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f36,plain,
( spl0_3
<=> ! [X0] : add(X0,additive_identity) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f40,plain,
( spl0_4
<=> ! [X0] : additive_identity = multiply(additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f108,plain,
( spl0_13
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f666,plain,
( ! [X6,X5] : additive_identity = associator(additive_identity,X5,X6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f665,f41]) ).
fof(f41,plain,
( ! [X0] : additive_identity = multiply(additive_identity,X0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f665,plain,
( ! [X6,X5] : multiply(additive_identity,X6) = associator(additive_identity,X5,X6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f664,f37]) ).
fof(f37,plain,
( ! [X0] : add(X0,additive_identity) = X0
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f664,plain,
( ! [X6,X5] : add(multiply(additive_identity,X6),additive_identity) = associator(additive_identity,X5,X6)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_25 ),
inference(forward_demodulation,[],[f663,f110]) ).
fof(f110,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f663,plain,
( ! [X6,X5] : add(multiply(additive_identity,X6),additive_inverse(additive_identity)) = associator(additive_identity,X5,X6)
| ~ spl0_4
| ~ spl0_25 ),
inference(forward_demodulation,[],[f633,f41]) ).
fof(f633,plain,
( ! [X6,X5] : associator(additive_identity,X5,X6) = add(multiply(additive_identity,X6),additive_inverse(multiply(additive_identity,multiply(X5,X6))))
| ~ spl0_4
| ~ spl0_25 ),
inference(superposition,[],[f629,f41]) ).
fof(f727,plain,
( spl0_28
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f658,f628,f56,f44,f40,f725]) ).
fof(f725,plain,
( spl0_28
<=> ! [X0,X1] : additive_identity = associator(X0,additive_identity,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f658,plain,
( ! [X0,X1] : additive_identity = associator(X0,additive_identity,X1)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f657,f57]) ).
fof(f657,plain,
( ! [X0,X1] : add(additive_identity,additive_inverse(additive_identity)) = associator(X0,additive_identity,X1)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f656,f45]) ).
fof(f656,plain,
( ! [X0,X1] : associator(X0,additive_identity,X1) = add(additive_identity,additive_inverse(multiply(X0,additive_identity)))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_demodulation,[],[f631,f41]) ).
fof(f631,plain,
( ! [X0,X1] : associator(X0,additive_identity,X1) = add(multiply(additive_identity,X1),additive_inverse(multiply(X0,multiply(additive_identity,X1))))
| ~ spl0_5
| ~ spl0_25 ),
inference(superposition,[],[f629,f45]) ).
fof(f723,plain,
( spl0_27
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f264,f239,f56,f44,f40,f721]) ).
fof(f721,plain,
( spl0_27
<=> ! [X3] : additive_identity = commutator(X3,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f239,plain,
( spl0_17
<=> ! [X0,X1] : commutator(X0,X1) = add(multiply(X1,X0),additive_inverse(multiply(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f264,plain,
( ! [X3] : additive_identity = commutator(X3,additive_identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f263,f57]) ).
fof(f263,plain,
( ! [X3] : add(additive_identity,additive_inverse(additive_identity)) = commutator(X3,additive_identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f244,f45]) ).
fof(f244,plain,
( ! [X3] : commutator(X3,additive_identity) = add(additive_identity,additive_inverse(multiply(X3,additive_identity)))
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f240,f41]) ).
fof(f240,plain,
( ! [X0,X1] : commutator(X0,X1) = add(multiply(X1,X0),additive_inverse(multiply(X0,X1)))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f719,plain,
( spl0_26
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f260,f239,f56,f44,f40,f717]) ).
fof(f717,plain,
( spl0_26
<=> ! [X0] : additive_identity = commutator(additive_identity,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f260,plain,
( ! [X0] : additive_identity = commutator(additive_identity,X0)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[],[f259,f57]) ).
fof(f259,plain,
( ! [X0] : add(additive_identity,additive_inverse(additive_identity)) = commutator(additive_identity,X0)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f242,f41]) ).
fof(f242,plain,
( ! [X0] : commutator(additive_identity,X0) = add(additive_identity,additive_inverse(multiply(additive_identity,X0)))
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f240,f45]) ).
fof(f630,plain,
spl0_25,
inference(avatar_split_clause,[],[f14,f628]) ).
fof(f14,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',associator) ).
fof(f573,plain,
( spl0_24
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f256,f239,f56,f571]) ).
fof(f571,plain,
( spl0_24
<=> ! [X2] : additive_identity = commutator(X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f256,plain,
( ! [X2] : additive_identity = commutator(X2,X2)
| ~ spl0_8
| ~ spl0_17 ),
inference(superposition,[],[f240,f57]) ).
fof(f513,plain,
spl0_23,
inference(avatar_split_clause,[],[f25,f511]) ).
fof(f511,plain,
( spl0_23
<=> ! [X2,X0,X1] : add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X1,X2))) = additive_inverse(multiply(add(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f25,plain,
! [X2,X0,X1] : add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X1,X2))) = additive_inverse(multiply(add(X0,X1),X2)),
inference(forward_demodulation,[],[f22,f18]) ).
fof(f18,axiom,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',inverse_product2) ).
fof(f22,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),additive_inverse(X2)) = add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X1,X2))),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',distributivity_of_difference4) ).
fof(f509,plain,
spl0_22,
inference(avatar_split_clause,[],[f24,f507]) ).
fof(f507,plain,
( spl0_22
<=> ! [X2,X0,X1] : add(additive_inverse(multiply(X0,X1)),additive_inverse(multiply(X0,X2))) = additive_inverse(multiply(X0,add(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f24,plain,
! [X2,X0,X1] : add(additive_inverse(multiply(X0,X1)),additive_inverse(multiply(X0,X2))) = additive_inverse(multiply(X0,add(X1,X2))),
inference(forward_demodulation,[],[f21,f17]) ).
fof(f17,axiom,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',inverse_product1) ).
fof(f21,axiom,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X1)),additive_inverse(multiply(X0,X2))),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',distributivity_of_difference3) ).
fof(f383,plain,
spl0_21,
inference(avatar_split_clause,[],[f20,f381]) ).
fof(f381,plain,
( spl0_21
<=> ! [X2,X0,X1] : multiply(add(X0,additive_inverse(X1)),X2) = add(multiply(X0,X2),additive_inverse(multiply(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f20,axiom,
! [X2,X0,X1] : multiply(add(X0,additive_inverse(X1)),X2) = add(multiply(X0,X2),additive_inverse(multiply(X1,X2))),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',distributivity_of_difference2) ).
fof(f379,plain,
spl0_20,
inference(avatar_split_clause,[],[f19,f377]) ).
fof(f377,plain,
( spl0_20
<=> ! [X2,X0,X1] : multiply(X0,add(X1,additive_inverse(X2))) = add(multiply(X0,X1),additive_inverse(multiply(X0,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f19,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,additive_inverse(X2))) = add(multiply(X0,X1),additive_inverse(multiply(X0,X2))),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',distributivity_of_difference1) ).
fof(f303,plain,
spl0_19,
inference(avatar_split_clause,[],[f9,f301]) ).
fof(f301,plain,
( spl0_19
<=> ! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f9,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',distribute2) ).
fof(f288,plain,
spl0_18,
inference(avatar_split_clause,[],[f8,f286]) ).
fof(f286,plain,
( spl0_18
<=> ! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f8,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',distribute1) ).
fof(f241,plain,
spl0_17,
inference(avatar_split_clause,[],[f15,f239]) ).
fof(f15,axiom,
! [X0,X1] : commutator(X0,X1) = add(multiply(X1,X0),additive_inverse(multiply(X0,X1))),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',commutator) ).
fof(f141,plain,
spl0_16,
inference(avatar_split_clause,[],[f13,f139]) ).
fof(f13,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',left_alternative) ).
fof(f137,plain,
spl0_15,
inference(avatar_split_clause,[],[f12,f135]) ).
fof(f12,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',right_alternative) ).
fof(f133,plain,
spl0_14,
inference(avatar_split_clause,[],[f11,f131]) ).
fof(f131,plain,
( spl0_14
<=> ! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f11,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',associativity_for_addition) ).
fof(f111,plain,
( spl0_13
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f60,f52,f36,f108]) ).
fof(f52,plain,
( spl0_7
<=> ! [X0] : additive_identity = add(additive_inverse(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f60,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f53,f37]) ).
fof(f53,plain,
( ! [X0] : additive_identity = add(additive_inverse(X0),X0)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f92,plain,
spl0_12,
inference(avatar_split_clause,[],[f18,f90]) ).
fof(f90,plain,
( spl0_12
<=> ! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f88,plain,
spl0_11,
inference(avatar_split_clause,[],[f17,f86]) ).
fof(f86,plain,
( spl0_11
<=> ! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f84,plain,
spl0_10,
inference(avatar_split_clause,[],[f16,f82]) ).
fof(f82,plain,
( spl0_10
<=> ! [X0,X1] : multiply(X0,X1) = multiply(additive_inverse(X0),additive_inverse(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f16,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(additive_inverse(X0),additive_inverse(X1)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',product_of_inverses) ).
fof(f68,plain,
spl0_9,
inference(avatar_split_clause,[],[f10,f66]) ).
fof(f66,plain,
( spl0_9
<=> ! [X0,X1] : add(X0,X1) = add(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f10,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',commutativity_for_addition) ).
fof(f58,plain,
spl0_8,
inference(avatar_split_clause,[],[f6,f56]) ).
fof(f6,axiom,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',right_additive_inverse) ).
fof(f54,plain,
spl0_7,
inference(avatar_split_clause,[],[f5,f52]) ).
fof(f5,axiom,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',left_additive_inverse) ).
fof(f50,plain,
spl0_6,
inference(avatar_split_clause,[],[f7,f48]) ).
fof(f48,plain,
( spl0_6
<=> ! [X0] : additive_inverse(additive_inverse(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f7,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',additive_inverse_additive_inverse) ).
fof(f46,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f44]) ).
fof(f4,axiom,
! [X0] : additive_identity = multiply(X0,additive_identity),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',right_multiplicative_zero) ).
fof(f42,plain,
spl0_4,
inference(avatar_split_clause,[],[f3,f40]) ).
fof(f3,axiom,
! [X0] : additive_identity = multiply(additive_identity,X0),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',left_multiplicative_zero) ).
fof(f38,plain,
spl0_3,
inference(avatar_split_clause,[],[f2,f36]) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',right_additive_identity) ).
fof(f34,plain,
spl0_2,
inference(avatar_split_clause,[],[f1,f32]) ).
fof(f32,plain,
( spl0_2
<=> ! [X0] : add(additive_identity,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',left_additive_identity) ).
fof(f30,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f23,f27]) ).
fof(f23,axiom,
additive_identity != associator(x,x,y),
file('/export/starexec/sandbox2/tmp/tmp.MUj0J2QIaN/Vampire---4.8_2448',prove_left_alternative) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG023-7 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % 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 : Wed Aug 30 16:32:42 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.46 % (2587)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.46 % (2591)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.46 % (2589)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.46 % (2592)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 Vampire---4 for (531ds/0Mi)
% 0.22/0.46 % (2594)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.46 % (2588)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.47 TRYING [1]
% 0.22/0.47 % (2590)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.47 TRYING [2]
% 0.22/0.47 TRYING [3]
% 0.22/0.48 % (2593)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.48 % (2592)First to succeed.
% 0.22/0.48 % (2592)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Unsatisfiable for Vampire---4
% 0.22/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.48 % (2592)------------------------------
% 0.22/0.48 % (2592)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.48 % (2592)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.48 % (2592)Termination reason: Refutation
% 0.22/0.48
% 0.22/0.48 % (2592)Memory used [KB]: 6012
% 0.22/0.48 % (2592)Time elapsed: 0.018 s
% 0.22/0.48 % (2592)------------------------------
% 0.22/0.48 % (2592)------------------------------
% 0.22/0.48 % (2587)Success in time 0.112 s
% 0.22/0.48 % Vampire---4.8 exiting
%------------------------------------------------------------------------------