TSTP Solution File: GRP194+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n023.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 15:39:32 EDT 2023
% Result : Theorem 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 50
% Syntax : Number of formulae : 246 ( 9 unt; 0 def)
% Number of atoms : 741 ( 142 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 903 ( 408 ~; 417 |; 25 &)
% ( 43 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 45 ( 43 usr; 42 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 99 (; 91 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f855,plain,
$false,
inference(avatar_smt_refutation,[],[f46,f51,f57,f65,f77,f80,f84,f96,f101,f160,f176,f180,f192,f210,f211,f212,f248,f254,f277,f297,f303,f309,f349,f356,f363,f411,f421,f425,f481,f488,f489,f490,f499,f522,f528,f534,f540,f552,f591,f597,f641,f679,f685,f686,f703,f734,f740,f757,f839,f854]) ).
fof(f854,plain,
( spl2_2
| ~ spl2_6
| ~ spl2_41 ),
inference(avatar_contradiction_clause,[],[f853]) ).
fof(f853,plain,
( $false
| spl2_2
| ~ spl2_6
| ~ spl2_41 ),
inference(subsumption_resolution,[],[f852,f76]) ).
fof(f76,plain,
( group_member(phi(f_left_zero),h)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f74,plain,
( spl2_6
<=> group_member(phi(f_left_zero),h) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f852,plain,
( ~ group_member(phi(f_left_zero),h)
| spl2_2
| ~ spl2_41 ),
inference(subsumption_resolution,[],[f851,f50]) ).
fof(f50,plain,
( ~ left_zero(h,phi(f_left_zero))
| spl2_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl2_2
<=> left_zero(h,phi(f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f851,plain,
( left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h)
| ~ spl2_41 ),
inference(trivial_inequality_removal,[],[f849]) ).
fof(f849,plain,
( phi(f_left_zero) != phi(f_left_zero)
| left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h)
| ~ spl2_41 ),
inference(superposition,[],[f39,f838]) ).
fof(f838,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero)))
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f836,plain,
( spl2_41
<=> phi(f_left_zero) = multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
fof(f39,plain,
! [X0,X1] :
( multiply(X0,X1,sK1(X0,X1)) != X1
| left_zero(X0,X1)
| ~ group_member(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ( multiply(X0,X1,sK1(X0,X1)) != X1
& group_member(sK1(X0,X1),X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X3] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
=> ( multiply(X0,X1,sK1(X0,X1)) != X1
& group_member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X3] :
( multiply(X0,X1,X3) = X1
| ~ group_member(X3,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) )
| ~ left_zero(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( ! [X2] :
( group_member(X2,X0)
=> multiply(X0,X1,X2) = X1 )
& group_member(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',left_zero) ).
fof(f839,plain,
( spl2_41
| ~ spl2_3
| ~ spl2_9
| ~ spl2_10
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f831,f207,f169,f157,f54,f836]) ).
fof(f54,plain,
( spl2_3
<=> group_member(f_left_zero,f) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f157,plain,
( spl2_9
<=> sK1(h,phi(f_left_zero)) = phi(sK0(sK1(h,phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f169,plain,
( spl2_10
<=> group_member(sK0(sK1(h,phi(f_left_zero))),f) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f207,plain,
( spl2_12
<=> f_left_zero = multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f831,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero)))
| ~ spl2_3
| ~ spl2_9
| ~ spl2_10
| ~ spl2_12 ),
inference(forward_demodulation,[],[f824,f209]) ).
fof(f209,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero))))
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f824,plain,
( multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) = phi(multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero)))))
| ~ spl2_3
| ~ spl2_9
| ~ spl2_10 ),
inference(resolution,[],[f199,f56]) ).
fof(f56,plain,
( group_member(f_left_zero,f)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f199,plain,
( ! [X0] :
( ~ group_member(X0,f)
| phi(multiply(f,X0,sK0(sK1(h,phi(f_left_zero))))) = multiply(h,phi(X0),sK1(h,phi(f_left_zero))) )
| ~ spl2_9
| ~ spl2_10 ),
inference(forward_demodulation,[],[f193,f159]) ).
fof(f159,plain,
( sK1(h,phi(f_left_zero)) = phi(sK0(sK1(h,phi(f_left_zero))))
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f193,plain,
( ! [X0] :
( multiply(h,phi(X0),phi(sK0(sK1(h,phi(f_left_zero))))) = phi(multiply(f,X0,sK0(sK1(h,phi(f_left_zero)))))
| ~ group_member(X0,f) )
| ~ spl2_10 ),
inference(resolution,[],[f170,f35]) ).
fof(f35,plain,
! [X0,X1] :
( ~ group_member(X1,f)
| multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ( group_member(X1,f)
& group_member(X0,f) )
=> multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2] :
( ( group_member(X2,f)
& group_member(X1,f) )
=> multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',homomorphism2) ).
fof(f170,plain,
( group_member(sK0(sK1(h,phi(f_left_zero))),f)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f757,plain,
( spl2_40
| ~ spl2_6
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f748,f173,f74,f754]) ).
fof(f754,plain,
( spl2_40
<=> multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) = phi(sK0(multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
fof(f173,plain,
( spl2_11
<=> group_member(sK1(h,phi(f_left_zero)),h) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f748,plain,
( multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))) = phi(sK0(multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero)))))
| ~ spl2_6
| ~ spl2_11 ),
inference(resolution,[],[f269,f175]) ).
fof(f175,plain,
( group_member(sK1(h,phi(f_left_zero)),h)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f269,plain,
( ! [X2] :
( ~ group_member(X2,h)
| multiply(h,phi(f_left_zero),X2) = phi(sK0(multiply(h,phi(f_left_zero),X2))) )
| ~ spl2_6 ),
inference(resolution,[],[f102,f76]) ).
fof(f102,plain,
! [X0,X1] :
( ~ group_member(X1,h)
| ~ group_member(X0,h)
| multiply(h,X1,X0) = phi(sK0(multiply(h,X1,X0))) ),
inference(resolution,[],[f40,f33]) ).
fof(f33,plain,
! [X0] :
( ~ group_member(X0,h)
| phi(sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ( phi(sK0(X0)) = X0
& group_member(sK0(X0),f) )
| ~ group_member(X0,h) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f23]) ).
fof(f23,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
=> ( phi(sK0(X0)) = X0
& group_member(sK0(X0),f) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
| ~ group_member(X0,h) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0] :
( group_member(X0,h)
=> ? [X1] :
( phi(X1) = X0
& group_member(X1,f) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1] :
( group_member(X1,h)
=> ? [X2] :
( phi(X2) = X1
& group_member(X2,f) ) ),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',surjective) ).
fof(f40,plain,
! [X2,X0,X1] :
( group_member(multiply(X0,X1,X2),X0)
| ~ group_member(X2,X0)
| ~ group_member(X1,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( group_member(multiply(X0,X1,X2),X0)
| ~ group_member(X2,X0)
| ~ group_member(X1,X0) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( group_member(multiply(X0,X1,X2),X0)
| ~ group_member(X2,X0)
| ~ group_member(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( ( group_member(X2,X0)
& group_member(X1,X0) )
=> group_member(multiply(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',total_function) ).
fof(f740,plain,
( spl2_39
| ~ spl2_1
| ~ spl2_5
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f725,f418,f70,f43,f737]) ).
fof(f737,plain,
( spl2_39
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))),sK0(phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
fof(f43,plain,
( spl2_1
<=> left_zero(f,f_left_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f70,plain,
( spl2_5
<=> group_member(sK0(phi(f_left_zero)),f) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f418,plain,
( spl2_24
<=> group_member(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),h) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f725,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))),sK0(phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_5
| ~ spl2_24 ),
inference(resolution,[],[f720,f71]) ).
fof(f71,plain,
( group_member(sK0(phi(f_left_zero)),f)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f720,plain,
( ! [X4] :
( ~ group_member(X4,f)
| f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))),X4)) )
| ~ spl2_1
| ~ spl2_24 ),
inference(resolution,[],[f224,f420]) ).
fof(f420,plain,
( group_member(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),h)
| ~ spl2_24 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f224,plain,
( ! [X2,X1] :
( ~ group_member(X2,h)
| f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(X2),X1))
| ~ group_member(X1,f) )
| ~ spl2_1 ),
inference(resolution,[],[f103,f32]) ).
fof(f32,plain,
! [X0] :
( group_member(sK0(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f24]) ).
fof(f103,plain,
( ! [X2,X3] :
( ~ group_member(X3,f)
| ~ group_member(X2,f)
| f_left_zero = multiply(f,f_left_zero,multiply(f,X3,X2)) )
| ~ spl2_1 ),
inference(resolution,[],[f40,f87]) ).
fof(f87,plain,
( ! [X0] :
( ~ group_member(X0,f)
| f_left_zero = multiply(f,f_left_zero,X0) )
| ~ spl2_1 ),
inference(resolution,[],[f37,f45]) ).
fof(f45,plain,
( left_zero(f,f_left_zero)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f37,plain,
! [X3,X0,X1] :
( ~ left_zero(X0,X1)
| ~ group_member(X3,X0)
| multiply(X0,X1,X3) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f734,plain,
( spl2_38
| ~ spl2_1
| ~ spl2_3
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f723,f418,f54,f43,f731]) ).
fof(f731,plain,
( spl2_38
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))),f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
fof(f723,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))),f_left_zero))
| ~ spl2_1
| ~ spl2_3
| ~ spl2_24 ),
inference(resolution,[],[f720,f56]) ).
fof(f703,plain,
( spl2_37
| ~ spl2_1
| ~ spl2_11
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f671,f418,f173,f43,f700]) ).
fof(f700,plain,
( spl2_37
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
fof(f671,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_11
| ~ spl2_24 ),
inference(resolution,[],[f578,f175]) ).
fof(f578,plain,
( ! [X4] :
( ~ group_member(X4,h)
| f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,X4,multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))) )
| ~ spl2_1
| ~ spl2_24 ),
inference(resolution,[],[f111,f420]) ).
fof(f111,plain,
( ! [X2,X3] :
( ~ group_member(X3,h)
| f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,X2,X3)))
| ~ group_member(X2,h) )
| ~ spl2_1 ),
inference(resolution,[],[f89,f40]) ).
fof(f89,plain,
( ! [X0] :
( ~ group_member(X0,h)
| f_left_zero = multiply(f,f_left_zero,sK0(X0)) )
| ~ spl2_1 ),
inference(resolution,[],[f87,f32]) ).
fof(f686,plain,
( spl2_36
| ~ spl2_1
| ~ spl2_11
| ~ spl2_20
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f608,f414,f353,f173,f43,f682]) ).
fof(f682,plain,
( spl2_36
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
fof(f353,plain,
( spl2_20
<=> phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)) = multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f414,plain,
( spl2_23
<=> group_member(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),f) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f608,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_11
| ~ spl2_20
| ~ spl2_23 ),
inference(forward_demodulation,[],[f603,f355]) ).
fof(f355,plain,
( phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)) = multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f603,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)),sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_11
| ~ spl2_23 ),
inference(resolution,[],[f581,f415]) ).
fof(f415,plain,
( group_member(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),f)
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f581,plain,
( ! [X0] :
( ~ group_member(X0,f)
| f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,phi(X0),sK1(h,phi(f_left_zero))))) )
| ~ spl2_1
| ~ spl2_11 ),
inference(resolution,[],[f577,f34]) ).
fof(f34,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( group_member(X0,f)
=> group_member(phi(X0),h) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1] :
( group_member(X1,f)
=> group_member(phi(X1),h) ),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',homomorphism1) ).
fof(f577,plain,
( ! [X3] :
( ~ group_member(X3,h)
| f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,X3,sK1(h,phi(f_left_zero))))) )
| ~ spl2_1
| ~ spl2_11 ),
inference(resolution,[],[f111,f175]) ).
fof(f685,plain,
( spl2_36
| ~ spl2_1
| ~ spl2_11
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f584,f418,f173,f43,f682]) ).
fof(f584,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_11
| ~ spl2_24 ),
inference(resolution,[],[f577,f420]) ).
fof(f679,plain,
( spl2_35
| ~ spl2_1
| ~ spl2_6
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f670,f418,f74,f43,f676]) ).
fof(f676,plain,
( spl2_35
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,phi(f_left_zero),multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
fof(f670,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,phi(f_left_zero),multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_6
| ~ spl2_24 ),
inference(resolution,[],[f578,f76]) ).
fof(f641,plain,
( spl2_34
| ~ spl2_1
| ~ spl2_6
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f633,f418,f74,f43,f638]) ).
fof(f638,plain,
( spl2_34
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f633,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_6
| ~ spl2_24 ),
inference(resolution,[],[f576,f420]) ).
fof(f576,plain,
( ! [X2] :
( ~ group_member(X2,h)
| f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,X2,phi(f_left_zero)))) )
| ~ spl2_1
| ~ spl2_6 ),
inference(resolution,[],[f111,f76]) ).
fof(f597,plain,
( spl2_33
| ~ spl2_1
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f583,f173,f43,f594]) ).
fof(f594,plain,
( spl2_33
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f583,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_11 ),
inference(resolution,[],[f577,f175]) ).
fof(f591,plain,
( spl2_32
| ~ spl2_1
| ~ spl2_6
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f582,f173,f74,f43,f588]) ).
fof(f588,plain,
( spl2_32
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f582,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,phi(f_left_zero),sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_6
| ~ spl2_11 ),
inference(resolution,[],[f577,f76]) ).
fof(f552,plain,
( spl2_31
| ~ spl2_1
| ~ spl2_10
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f514,f414,f169,f43,f549]) ).
fof(f549,plain,
( spl2_31
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),sK0(sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f514,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),sK0(sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_10
| ~ spl2_23 ),
inference(resolution,[],[f429,f170]) ).
fof(f429,plain,
( ! [X1] :
( ~ group_member(X1,f)
| f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),X1)) )
| ~ spl2_1
| ~ spl2_23 ),
inference(resolution,[],[f415,f103]) ).
fof(f540,plain,
( spl2_30
| ~ spl2_1
| ~ spl2_10
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f438,f414,f169,f43,f537]) ).
fof(f537,plain,
( spl2_30
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f438,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)))
| ~ spl2_1
| ~ spl2_10
| ~ spl2_23 ),
inference(resolution,[],[f415,f226]) ).
fof(f226,plain,
( ! [X4] :
( ~ group_member(X4,f)
| f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),X4)) )
| ~ spl2_1
| ~ spl2_10 ),
inference(resolution,[],[f103,f170]) ).
fof(f534,plain,
( spl2_29
| ~ spl2_1
| ~ spl2_5
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f467,f418,f70,f43,f531]) ).
fof(f531,plain,
( spl2_29
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
fof(f467,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_5
| ~ spl2_24 ),
inference(resolution,[],[f420,f288]) ).
fof(f288,plain,
( ! [X0] :
( ~ group_member(X0,h)
| f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(X0))) )
| ~ spl2_1
| ~ spl2_5 ),
inference(resolution,[],[f225,f32]) ).
fof(f225,plain,
( ! [X3] :
( ~ group_member(X3,f)
| f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),X3)) )
| ~ spl2_1
| ~ spl2_5 ),
inference(resolution,[],[f103,f71]) ).
fof(f528,plain,
( spl2_28
| ~ spl2_1
| ~ spl2_5
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f513,f414,f70,f43,f525]) ).
fof(f525,plain,
( spl2_28
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),sK0(phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
fof(f513,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),sK0(phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_5
| ~ spl2_23 ),
inference(resolution,[],[f429,f71]) ).
fof(f522,plain,
( spl2_27
| ~ spl2_1
| ~ spl2_3
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f511,f414,f54,f43,f519]) ).
fof(f519,plain,
( spl2_27
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
fof(f511,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),f_left_zero))
| ~ spl2_1
| ~ spl2_3
| ~ spl2_23 ),
inference(resolution,[],[f429,f56]) ).
fof(f499,plain,
( spl2_26
| ~ spl2_1
| ~ spl2_5
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f437,f414,f70,f43,f496]) ).
fof(f496,plain,
( spl2_26
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
fof(f437,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)))
| ~ spl2_1
| ~ spl2_5
| ~ spl2_23 ),
inference(resolution,[],[f415,f225]) ).
fof(f490,plain,
( spl2_25
| ~ spl2_1
| ~ spl2_22
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f471,f418,f408,f43,f478]) ).
fof(f478,plain,
( spl2_25
<=> f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
fof(f408,plain,
( spl2_22
<=> multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)) = phi(sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f471,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_22
| ~ spl2_24 ),
inference(forward_demodulation,[],[f460,f410]) ).
fof(f410,plain,
( multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)) = phi(sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f460,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(phi(sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))))
| ~ spl2_1
| ~ spl2_24 ),
inference(resolution,[],[f420,f113]) ).
fof(f113,plain,
( ! [X0] :
( ~ group_member(X0,h)
| f_left_zero = multiply(f,f_left_zero,sK0(phi(sK0(X0)))) )
| ~ spl2_1 ),
inference(resolution,[],[f108,f32]) ).
fof(f108,plain,
( ! [X0] :
( ~ group_member(X0,f)
| f_left_zero = multiply(f,f_left_zero,sK0(phi(X0))) )
| ~ spl2_1 ),
inference(resolution,[],[f89,f34]) ).
fof(f489,plain,
( spl2_25
| ~ spl2_1
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f458,f418,f43,f478]) ).
fof(f458,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_24 ),
inference(resolution,[],[f420,f89]) ).
fof(f488,plain,
( spl2_25
| ~ spl2_1
| ~ spl2_20
| ~ spl2_22
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f448,f414,f408,f353,f43,f478]) ).
fof(f448,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_20
| ~ spl2_22
| ~ spl2_23 ),
inference(forward_demodulation,[],[f447,f410]) ).
fof(f447,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(phi(sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))))
| ~ spl2_1
| ~ spl2_20
| ~ spl2_23 ),
inference(forward_demodulation,[],[f432,f355]) ).
fof(f432,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(phi(sK0(phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero))))))
| ~ spl2_1
| ~ spl2_23 ),
inference(resolution,[],[f415,f123]) ).
fof(f123,plain,
( ! [X0] :
( ~ group_member(X0,f)
| f_left_zero = multiply(f,f_left_zero,sK0(phi(sK0(phi(X0))))) )
| ~ spl2_1 ),
inference(resolution,[],[f113,f34]) ).
fof(f481,plain,
( spl2_25
| ~ spl2_1
| ~ spl2_20
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f444,f414,f353,f43,f478]) ).
fof(f444,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_20
| ~ spl2_23 ),
inference(forward_demodulation,[],[f430,f355]) ).
fof(f430,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero))))
| ~ spl2_1
| ~ spl2_23 ),
inference(resolution,[],[f415,f108]) ).
fof(f425,plain,
( ~ spl2_3
| ~ spl2_10
| spl2_23 ),
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f424,plain,
( $false
| ~ spl2_3
| ~ spl2_10
| spl2_23 ),
inference(subsumption_resolution,[],[f423,f170]) ).
fof(f423,plain,
( ~ group_member(sK0(sK1(h,phi(f_left_zero))),f)
| ~ spl2_3
| spl2_23 ),
inference(subsumption_resolution,[],[f422,f56]) ).
fof(f422,plain,
( ~ group_member(f_left_zero,f)
| ~ group_member(sK0(sK1(h,phi(f_left_zero))),f)
| spl2_23 ),
inference(resolution,[],[f416,f40]) ).
fof(f416,plain,
( ~ group_member(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),f)
| spl2_23 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f421,plain,
( ~ spl2_23
| spl2_24
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f357,f353,f418,f414]) ).
fof(f357,plain,
( group_member(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)),h)
| ~ group_member(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero),f)
| ~ spl2_20 ),
inference(superposition,[],[f34,f355]) ).
fof(f411,plain,
( spl2_22
| ~ spl2_6
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f403,f173,f74,f408]) ).
fof(f403,plain,
( multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero)) = phi(sK0(multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))))
| ~ spl2_6
| ~ spl2_11 ),
inference(resolution,[],[f270,f76]) ).
fof(f270,plain,
( ! [X3] :
( ~ group_member(X3,h)
| multiply(h,sK1(h,phi(f_left_zero)),X3) = phi(sK0(multiply(h,sK1(h,phi(f_left_zero)),X3))) )
| ~ spl2_11 ),
inference(resolution,[],[f102,f175]) ).
fof(f363,plain,
( spl2_21
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_19 ),
inference(avatar_split_clause,[],[f358,f346,f70,f62,f54,f360]) ).
fof(f360,plain,
( spl2_21
<=> phi(f_left_zero) = phi(multiply(f,sK0(phi(f_left_zero)),f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f62,plain,
( spl2_4
<=> phi(f_left_zero) = phi(sK0(phi(f_left_zero))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f346,plain,
( spl2_19
<=> phi(f_left_zero) = multiply(h,phi(f_left_zero),phi(f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f358,plain,
( phi(f_left_zero) = phi(multiply(f,sK0(phi(f_left_zero)),f_left_zero))
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5
| ~ spl2_19 ),
inference(forward_demodulation,[],[f343,f348]) ).
fof(f348,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),phi(f_left_zero))
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f343,plain,
( multiply(h,phi(f_left_zero),phi(f_left_zero)) = phi(multiply(f,sK0(phi(f_left_zero)),f_left_zero))
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(forward_demodulation,[],[f338,f64]) ).
fof(f64,plain,
( phi(f_left_zero) = phi(sK0(phi(f_left_zero)))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f338,plain,
( multiply(h,phi(sK0(phi(f_left_zero))),phi(f_left_zero)) = phi(multiply(f,sK0(phi(f_left_zero)),f_left_zero))
| ~ spl2_3
| ~ spl2_5 ),
inference(resolution,[],[f161,f71]) ).
fof(f161,plain,
( ! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),phi(f_left_zero)) = phi(multiply(f,X0,f_left_zero)) )
| ~ spl2_3 ),
inference(resolution,[],[f35,f56]) ).
fof(f356,plain,
( spl2_20
| ~ spl2_3
| ~ spl2_9
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f344,f169,f157,f54,f353]) ).
fof(f344,plain,
( phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)) = multiply(h,sK1(h,phi(f_left_zero)),phi(f_left_zero))
| ~ spl2_3
| ~ spl2_9
| ~ spl2_10 ),
inference(forward_demodulation,[],[f339,f159]) ).
fof(f339,plain,
( multiply(h,phi(sK0(sK1(h,phi(f_left_zero)))),phi(f_left_zero)) = phi(multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero))
| ~ spl2_3
| ~ spl2_10 ),
inference(resolution,[],[f161,f170]) ).
fof(f349,plain,
( spl2_19
| ~ spl2_3
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f342,f93,f54,f346]) ).
fof(f93,plain,
( spl2_7
<=> f_left_zero = multiply(f,f_left_zero,f_left_zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f342,plain,
( phi(f_left_zero) = multiply(h,phi(f_left_zero),phi(f_left_zero))
| ~ spl2_3
| ~ spl2_7 ),
inference(forward_demodulation,[],[f336,f95]) ).
fof(f95,plain,
( f_left_zero = multiply(f,f_left_zero,f_left_zero)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f336,plain,
( multiply(h,phi(f_left_zero),phi(f_left_zero)) = phi(multiply(f,f_left_zero,f_left_zero))
| ~ spl2_3 ),
inference(resolution,[],[f161,f56]) ).
fof(f309,plain,
( spl2_18
| ~ spl2_1
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f289,f70,f43,f306]) ).
fof(f306,plain,
( spl2_18
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f289,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_5 ),
inference(resolution,[],[f225,f71]) ).
fof(f303,plain,
( spl2_17
| ~ spl2_1
| ~ spl2_5
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f290,f169,f70,f43,f300]) ).
fof(f300,plain,
( spl2_17
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f290,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),sK0(sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_5
| ~ spl2_10 ),
inference(resolution,[],[f225,f170]) ).
fof(f297,plain,
( spl2_16
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f287,f70,f54,f43,f294]) ).
fof(f294,plain,
( spl2_16
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f287,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(phi(f_left_zero)),f_left_zero))
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(resolution,[],[f225,f56]) ).
fof(f277,plain,
( spl2_15
| ~ spl2_1
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f241,f169,f43,f274]) ).
fof(f274,plain,
( spl2_15
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),sK0(sK1(h,phi(f_left_zero))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f241,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),sK0(sK1(h,phi(f_left_zero)))))
| ~ spl2_1
| ~ spl2_10 ),
inference(resolution,[],[f226,f170]) ).
fof(f254,plain,
( spl2_14
| ~ spl2_1
| ~ spl2_5
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f240,f169,f70,f43,f251]) ).
fof(f251,plain,
( spl2_14
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),sK0(phi(f_left_zero)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f240,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),sK0(phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_5
| ~ spl2_10 ),
inference(resolution,[],[f226,f71]) ).
fof(f248,plain,
( spl2_13
| ~ spl2_1
| ~ spl2_3
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f238,f169,f54,f43,f245]) ).
fof(f245,plain,
( spl2_13
<=> f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f238,plain,
( f_left_zero = multiply(f,f_left_zero,multiply(f,sK0(sK1(h,phi(f_left_zero))),f_left_zero))
| ~ spl2_1
| ~ spl2_3
| ~ spl2_10 ),
inference(resolution,[],[f226,f56]) ).
fof(f212,plain,
( spl2_12
| ~ spl2_1
| ~ spl2_9
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f204,f169,f157,f43,f207]) ).
fof(f204,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_9
| ~ spl2_10 ),
inference(forward_demodulation,[],[f196,f159]) ).
fof(f196,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(phi(sK0(sK1(h,phi(f_left_zero))))))
| ~ spl2_1
| ~ spl2_10 ),
inference(resolution,[],[f170,f108]) ).
fof(f211,plain,
( spl2_12
| ~ spl2_1
| ~ spl2_10 ),
inference(avatar_split_clause,[],[f197,f169,f43,f207]) ).
fof(f197,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_10 ),
inference(resolution,[],[f170,f87]) ).
fof(f210,plain,
( spl2_12
| ~ spl2_1
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f184,f173,f43,f207]) ).
fof(f184,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(sK1(h,phi(f_left_zero))))
| ~ spl2_1
| ~ spl2_11 ),
inference(resolution,[],[f175,f89]) ).
fof(f192,plain,
( spl2_10
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f191,plain,
( $false
| spl2_10
| ~ spl2_11 ),
inference(subsumption_resolution,[],[f190,f175]) ).
fof(f190,plain,
( ~ group_member(sK1(h,phi(f_left_zero)),h)
| spl2_10 ),
inference(resolution,[],[f171,f32]) ).
fof(f171,plain,
( ~ group_member(sK0(sK1(h,phi(f_left_zero))),f)
| spl2_10 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f180,plain,
( spl2_2
| ~ spl2_6
| spl2_11 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f179,plain,
( $false
| spl2_2
| ~ spl2_6
| spl2_11 ),
inference(subsumption_resolution,[],[f178,f76]) ).
fof(f178,plain,
( ~ group_member(phi(f_left_zero),h)
| spl2_2
| spl2_11 ),
inference(subsumption_resolution,[],[f177,f50]) ).
fof(f177,plain,
( left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h)
| spl2_11 ),
inference(resolution,[],[f174,f38]) ).
fof(f38,plain,
! [X0,X1] :
( group_member(sK1(X0,X1),X0)
| left_zero(X0,X1)
| ~ group_member(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f174,plain,
( ~ group_member(sK1(h,phi(f_left_zero)),h)
| spl2_11 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( ~ spl2_10
| spl2_11
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f167,f157,f173,f169]) ).
fof(f167,plain,
( group_member(sK1(h,phi(f_left_zero)),h)
| ~ group_member(sK0(sK1(h,phi(f_left_zero))),f)
| ~ spl2_9 ),
inference(superposition,[],[f34,f159]) ).
fof(f160,plain,
( spl2_9
| spl2_2
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f155,f74,f48,f157]) ).
fof(f155,plain,
( sK1(h,phi(f_left_zero)) = phi(sK0(sK1(h,phi(f_left_zero))))
| spl2_2
| ~ spl2_6 ),
inference(subsumption_resolution,[],[f152,f76]) ).
fof(f152,plain,
( ~ group_member(phi(f_left_zero),h)
| sK1(h,phi(f_left_zero)) = phi(sK0(sK1(h,phi(f_left_zero))))
| spl2_2 ),
inference(resolution,[],[f67,f50]) ).
fof(f67,plain,
! [X0] :
( left_zero(h,X0)
| ~ group_member(X0,h)
| sK1(h,X0) = phi(sK0(sK1(h,X0))) ),
inference(resolution,[],[f38,f33]) ).
fof(f101,plain,
( spl2_8
| ~ spl2_1
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f90,f70,f43,f98]) ).
fof(f98,plain,
( spl2_8
<=> f_left_zero = multiply(f,f_left_zero,sK0(phi(f_left_zero))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f90,plain,
( f_left_zero = multiply(f,f_left_zero,sK0(phi(f_left_zero)))
| ~ spl2_1
| ~ spl2_5 ),
inference(resolution,[],[f87,f71]) ).
fof(f96,plain,
( spl2_7
| ~ spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f88,f54,f43,f93]) ).
fof(f88,plain,
( f_left_zero = multiply(f,f_left_zero,f_left_zero)
| ~ spl2_1
| ~ spl2_3 ),
inference(resolution,[],[f87,f56]) ).
fof(f84,plain,
( spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f83]) ).
fof(f83,plain,
( $false
| spl2_5
| ~ spl2_6 ),
inference(subsumption_resolution,[],[f82,f76]) ).
fof(f82,plain,
( ~ group_member(phi(f_left_zero),h)
| spl2_5 ),
inference(resolution,[],[f72,f32]) ).
fof(f72,plain,
( ~ group_member(sK0(phi(f_left_zero)),f)
| spl2_5 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f80,plain,
( ~ spl2_3
| spl2_6 ),
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f79,plain,
( $false
| ~ spl2_3
| spl2_6 ),
inference(subsumption_resolution,[],[f78,f56]) ).
fof(f78,plain,
( ~ group_member(f_left_zero,f)
| spl2_6 ),
inference(resolution,[],[f75,f34]) ).
fof(f75,plain,
( ~ group_member(phi(f_left_zero),h)
| spl2_6 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( ~ spl2_5
| spl2_6
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f66,f62,f74,f70]) ).
fof(f66,plain,
( group_member(phi(f_left_zero),h)
| ~ group_member(sK0(phi(f_left_zero)),f)
| ~ spl2_4 ),
inference(superposition,[],[f34,f64]) ).
fof(f65,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f59,f54,f62]) ).
fof(f59,plain,
( phi(f_left_zero) = phi(sK0(phi(f_left_zero)))
| ~ spl2_3 ),
inference(resolution,[],[f58,f56]) ).
fof(f58,plain,
! [X0] :
( ~ group_member(X0,f)
| phi(X0) = phi(sK0(phi(X0))) ),
inference(resolution,[],[f33,f34]) ).
fof(f57,plain,
( spl2_3
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f52,f43,f54]) ).
fof(f52,plain,
( group_member(f_left_zero,f)
| ~ spl2_1 ),
inference(resolution,[],[f36,f45]) ).
fof(f36,plain,
! [X0,X1] :
( ~ left_zero(X0,X1)
| group_member(X1,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f30,f48]) ).
fof(f30,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
~ left_zero(h,phi(f_left_zero)),
inference(flattening,[],[f9]) ).
fof(f9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',prove_left_zero_h) ).
fof(f46,plain,
spl2_1,
inference(avatar_split_clause,[],[f31,f43]) ).
fof(f31,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/tmp/tmp.wcOoho7h7U/Vampire---4.8_4635',left_zero_for_f) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 17:41:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.41 % (4783)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (4807)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)
% 0.20/0.42 % (4803)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.20/0.42 % (4806)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.42 % (4805)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)
% 0.20/0.42 % (4804)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.20/0.42 % (4808)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)
% 0.20/0.42 % (4809)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)
% 0.20/0.42 TRYING [1]
% 0.20/0.42 TRYING [1]
% 0.20/0.42 TRYING [2]
% 0.20/0.42 TRYING [2]
% 0.20/0.42 TRYING [3]
% 0.20/0.42 TRYING [3]
% 0.20/0.43 TRYING [4]
% 0.20/0.43 TRYING [4]
% 0.20/0.46 TRYING [5]
% 0.20/0.46 TRYING [5]
% 0.20/0.53 TRYING [6]
% 0.20/0.54 TRYING [1]
% 0.20/0.54 TRYING [2]
% 0.20/0.54 TRYING [3]
% 0.20/0.54 % (4805)First to succeed.
% 0.20/0.55 % (4805)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Theorem for Vampire---4
% 0.20/0.55 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.55 % (4805)------------------------------
% 0.20/0.55 % (4805)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.55 % (4805)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.55 % (4805)Termination reason: Refutation
% 0.20/0.55
% 0.20/0.55 % (4805)Memory used [KB]: 6140
% 0.20/0.55 % (4805)Time elapsed: 0.130 s
% 0.20/0.55 % (4805)------------------------------
% 0.20/0.55 % (4805)------------------------------
% 0.20/0.55 % (4783)Success in time 0.19 s
% 0.20/0.55 % Vampire---4.8 exiting
%------------------------------------------------------------------------------