%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP374-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:47 AM UTC 2026
% Result : Unsatisfiable 2.10s 1.31s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 55
% Syntax : Number of formulae : 370 ( 19 unt; 15 def)
% Number of atoms : 1442 ( 368 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2051 ( 979 ~;1057 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c8) = sk_c7
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c8 = inverse(sk_c1)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c6 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c8,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c6 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(sk_c8,X3) != sk_c7
| multiply(X4,sk_c8) != X3
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,X3)
| multiply(X4,sk_c8) != X3
| sk_c8 != inverse(X4) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,sk_c6)
| sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1)
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ),
inference(equality_resolution,[],[f77]) ).
fof(f80,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f81,plain,
( ! [X4] :
( sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f84,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_3
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f87,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c6)
| sk_c6 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( sk_c7 != multiply(sk_c8,sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_6
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( inverse(sk_c8) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_2
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f78,f97,f83,f93,f90,f86,f83,f80]) ).
fof(f102,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f104,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f75,f106,f102]) ).
fof(f111,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f113,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f73,f106,f111]) ).
fof(f116,definition,
( spl0_10
<=> sk_c7 = multiply(sk_c8,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f118,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f71,f106,f116]) ).
fof(f121,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f123,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f69,f106,f121]) ).
fof(f126,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f67,f106,f126]) ).
fof(f130,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f65,f106,f86]) ).
fof(f132,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f134,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f63,f132,f102]) ).
fof(f136,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f61,f132,f111]) ).
fof(f137,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f59,f132,f116]) ).
fof(f138,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f57,f132,f121]) ).
fof(f139,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f55,f132,f126]) ).
fof(f140,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f53,f132,f86]) ).
fof(f141,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f51,f93,f102]) ).
fof(f142,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f49,f93,f111]) ).
fof(f143,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f47,f93,f116]) ).
fof(f144,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f45,f93,f121]) ).
fof(f145,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f43,f93,f126]) ).
fof(f146,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f41,f93,f86]) ).
fof(f148,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f148,f102]) ).
fof(f152,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f148,f111]) ).
fof(f153,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f148,f116]) ).
fof(f154,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f148,f121]) ).
fof(f155,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f31,f148,f126]) ).
fof(f156,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f29,f148,f86]) ).
fof(f158,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f160,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f158,f102]) ).
fof(f162,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f158,f111]) ).
fof(f163,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f23,f158,f116]) ).
fof(f164,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f158,f121]) ).
fof(f165,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f158,f126]) ).
fof(f166,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f17,f158,f86]) ).
fof(f167,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f97,f102]) ).
fof(f168,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f97,f111]) ).
fof(f169,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f11,f97,f116]) ).
fof(f170,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f9,f97,f121]) ).
fof(f171,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f7,f97,f126]) ).
fof(f172,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f5,f97,f86]) ).
fof(f173,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_7 ),
inference(superposition,[],[f3,f104]) ).
fof(f174,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f123]) ).
fof(f177,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f179,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f118]) ).
fof(f180,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f128]) ).
fof(f181,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c8,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f113]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f177,f1]) ).
fof(f185,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f173]) ).
fof(f186,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f185,f1]) ).
fof(f189,plain,
( sk_c8 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f186,f113]) ).
fof(f195,plain,
( sk_c8 = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f189,f118]) ).
fof(f203,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c8,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f180,f195]) ).
fof(f207,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f181,f87]) ).
fof(f217,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f207,f195]) ).
fof(f229,plain,
( identity = multiply(sk_c3,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f203,f174]) ).
fof(f246,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_10 ),
inference(superposition,[],[f182,f179]) ).
fof(f248,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f182,f174]) ).
fof(f250,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_10 ),
inference(superposition,[],[f182,f118]) ).
fof(f251,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_7 ),
inference(superposition,[],[f182,f173]) ).
fof(f252,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f182,f128]) ).
fof(f265,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[],[f252,f195]) ).
fof(f266,plain,
( sk_c5 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f250,f195]) ).
fof(f269,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f246,f195]) ).
fof(f271,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f265,f123]) ).
fof(f272,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f266,f3]) ).
fof(f273,plain,
( ! [X0] : multiply(sk_c5,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f269,f182]) ).
fof(f275,plain,
( sk_c5 = multiply(sk_c3,sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f229,f272]) ).
fof(f284,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f182,f271]) ).
fof(f286,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f284,f3]) ).
fof(f294,plain,
( sk_c5 = multiply(inverse(sk_c3),sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f182,f275]) ).
fof(f297,plain,
( sk_c5 = multiply(sk_c8,sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f294,f123]) ).
fof(f298,plain,
( sk_c7 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f297,f118]) ).
fof(f299,plain,
( sk_c8 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f298,f195]) ).
fof(f308,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f272]) ).
fof(f309,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f308,f299]) ).
fof(f310,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f309,f3]) ).
fof(f311,plain,
( sk_c8 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f310,f286]) ).
fof(f312,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f123,f311]) ).
fof(f323,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f251,f272]) ).
fof(f324,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f323,f299]) ).
fof(f325,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f324,f3]) ).
fof(f326,plain,
( sk_c5 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f325,f272]) ).
fof(f327,plain,
( sk_c8 = sk_c4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f326,f299]) ).
fof(f353,plain,
( sk_c8 = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f217,f273]) ).
fof(f354,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f353,f327]) ).
fof(f355,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f95,f354]) ).
fof(f362,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f355,f195]) ).
fof(f363,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f368,plain,
( sk_c8 != inverse(sk_c8)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f99,f195]) ).
fof(f369,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f368,f312]) ).
fof(f370,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f372,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f98,f195]) ).
fof(f375,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f94,f195]) ).
fof(f378,plain,
( identity = multiply(sk_c6,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f108]) ).
fof(f393,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f182,f375]) ).
fof(f395,plain,
( identity = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f393,f3]) ).
fof(f397,plain,
( sk_c8 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f395,f286]) ).
fof(f406,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_6 ),
inference(superposition,[],[f3,f98]) ).
fof(f407,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_5 ),
inference(superposition,[],[f182,f94]) ).
fof(f408,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c6,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f94]) ).
fof(f409,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f407,f98]) ).
fof(f410,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f182,f134]) ).
fof(f412,plain,
( sk_c6 = multiply(sk_c6,sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f410,f108]) ).
fof(f413,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f182,f160]) ).
fof(f415,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f413,f150]) ).
fof(f416,plain,
( sk_c2 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f182,f378]) ).
fof(f423,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_6 ),
inference(superposition,[],[f182,f406]) ).
fof(f492,plain,
( multiply(sk_c8,sk_c6) = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f408,f412]) ).
fof(f493,plain,
( sk_c7 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f182,f412]) ).
fof(f495,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f493,f3]) ).
fof(f496,plain,
( sk_c6 = multiply(sk_c8,sk_c6)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f492,f409]) ).
fof(f498,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f496,f94]) ).
fof(f500,plain,
( sk_c8 != sk_c6
| spl0_3
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f88,f415]) ).
fof(f522,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f251,f495]) ).
fof(f523,plain,
( sk_c4 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f522,f98]) ).
fof(f524,plain,
( sk_c6 = sk_c4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f523,f409]) ).
fof(f533,plain,
( sk_c7 = multiply(sk_c8,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f94,f498]) ).
fof(f540,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f533,f415]) ).
fof(f541,plain,
( sk_c2 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f416,f495]) ).
fof(f542,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f541,f498]) ).
fof(f543,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f542,f3]) ).
fof(f544,plain,
( sk_c7 = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f543,f495]) ).
fof(f554,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f423,f495]) ).
fof(f555,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f554,f3]) ).
fof(f563,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f500,f498]) ).
fof(f591,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f540,f563]) ).
fof(f592,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f591]) ).
fof(f593,plain,
( sk_c7 = multiply(sk_c8,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f87,f498]) ).
fof(f594,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f593,f415]) ).
fof(f607,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f84,f594]) ).
fof(f611,plain,
( sk_c8 != sk_c6
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f607,f108]) ).
fof(f614,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f611,f498]) ).
fof(f618,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f614,f594]) ).
fof(f622,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f618,f544]) ).
fof(f624,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f622,f406]) ).
fof(f627,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f624,f555]) ).
fof(f628,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f627]) ).
fof(f629,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f81,f594]) ).
fof(f633,plain,
( sk_c8 != sk_c6
| sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f629,f108]) ).
fof(f636,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f633,f498]) ).
fof(f641,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c2,sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f636,f594]) ).
fof(f644,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c7,sk_c8))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f641,f544]) ).
fof(f645,plain,
( sk_c8 != multiply(sk_c8,identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f644,f406]) ).
fof(f646,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f645,f495]) ).
fof(f647,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f646,f415]) ).
fof(f648,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f647]) ).
fof(f649,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f91,f498]) ).
fof(f650,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c6 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f649,f594]) ).
fof(f651,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c8) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f650,f498]) ).
fof(f652,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(X1,sk_c8) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f651,f594]) ).
fof(f658,plain,
( sk_c8 != sk_c6
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f652,f108]) ).
fof(f661,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f658,f498]) ).
fof(f665,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f661,f594]) ).
fof(f669,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f665,f544]) ).
fof(f671,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f669,f406]) ).
fof(f674,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f671,f555]) ).
fof(f675,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f674]) ).
fof(f749,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f372,f98]) ).
fof(f792,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c8 != multiply(X2,sk_c8) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f84,f749]) ).
fof(f793,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f792,f372]) ).
fof(f795,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f792,f104]) ).
fof(f797,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f795]) ).
fof(f798,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f793]) ).
fof(f800,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f797,f524]) ).
fof(f805,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f800,f498]) ).
fof(f809,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_demodulation,[],[f805,f406]) ).
fof(f812,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f809,f555]) ).
fof(f813,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f812]) ).
fof(f828,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f375,f397]) ).
fof(f893,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f798,f828]) ).
fof(f894,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f893]) ).
fof(f895,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c8,multiply(X4,sk_c8)) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f81,f749]) ).
fof(f898,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f895,f98]) ).
fof(f899,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f895,f104]) ).
fof(f900,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c4,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f899]) ).
fof(f902,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f900,f186]) ).
fof(f903,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f902]) ).
fof(f904,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f898,f749]) ).
fof(f906,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f904,f828]) ).
fof(f909,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f906,f828]) ).
fof(f910,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f911,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f91,f397]) ).
fof(f912,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c6 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f911,f749]) ).
fof(f913,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(X1,sk_c8) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f912,f397]) ).
fof(f915,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f913,f98]) ).
fof(f920,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f915,f749]) ).
fof(f925,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f920,f828]) ).
fof(f926,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f925]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f100]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f109]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f114]) ).
cnf(s5,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f119]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f124]) ).
cnf(s7,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s8,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s10,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s11,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s12,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s13,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s14,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s15,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f141]) ).
cnf(s16,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f142]) ).
cnf(s17,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f144]) ).
cnf(s19,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f145]) ).
cnf(s20,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f146]) ).
cnf(s21,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s22,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s23,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s24,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s25,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s26,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s27,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s28,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f162]) ).
cnf(s29,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s30,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s31,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s32,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s33,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f167]) ).
cnf(s34,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f168]) ).
cnf(s35,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f169]) ).
cnf(s36,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f170]) ).
cnf(s37,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f171]) ).
cnf(s38,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f172]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f363]) ).
cnf(s40,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f370]) ).
cnf(s44,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f592]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f628]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f648]) ).
cnf(s53,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f675]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13 ),
inference(sat_conversion,[],[f813]) ).
cnf(s58,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f894]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f903]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f910]) ).
cnf(s64,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f926]) ).
cnf(s65,plain,
spl0_3,
inference(rat,[],[s44,s8,s14,s20,s26,s32,s38]) ).
cnf(s66,plain,
spl0_6,
inference(rat,[],[s40,s33,s34,s35,s36,s37]) ).
cnf(s67,plain,
spl0_5,
inference(rat,[],[s39,s15,s16,s17,s18,s19,s65]) ).
cnf(s68,plain,
( spl0_12
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s13,s25,s31,s65,s67,s66]) ).
cnf(s69,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s12,s24,s30,s65,s67,s66]) ).
cnf(s70,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s11,s23,s29,s65,s67,s66]) ).
cnf(s71,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s53,s10,s22,s28,s64,s70,s69,s68,s65,s67,s66]) ).
cnf(s72,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s64,s4,s5,s6,s7,s71,s66,s67]) ).
cnf(s73,plain,
~ spl0_4,
inference(rat,[],[s53,s3,s9,s21,s27,s72,s65,s67,s66]) ).
cnf(s74,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_2
| ~ spl0_7 ),
inference(rat,[],[s58,s12,s13,s57,s66,s67]) ).
cnf(s75,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s47,s11,s23,s29,s65,s67,s66]) ).
cnf(s76,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s47,s10,s22,s28,s74,s66,s67,s65]) ).
cnf(s77,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s76,s75]) ).
cnf(s78,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s58,s4,s5,s6,s7,s77,s66,s67]) ).
cnf(s79,plain,
~ spl0_2,
inference(rat,[],[s47,s3,s9,s21,s27,s78,s65,s67,s66]) ).
cnf(s80,plain,
spl0_1,
inference(rat,[],[s2,s66,s65,s67,s73,s79]) ).
cnf(s81,plain,
( spl0_9
| ~ spl0_8 ),
inference(rat,[],[s50,s10,s22,s28,s65,s67,s66,s80]) ).
cnf(s82,plain,
( ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s50,s11,s23,s29,s59,s81,s65,s67,s66,s80]) ).
cnf(s83,plain,
~ spl0_7,
inference(rat,[],[s61,s4,s5,s6,s7,s82,s67,s66,s80]) ).
cnf(s84,plain,
spl0_15,
inference(rat,[],[s27,s83]) ).
cnf(s85,plain,
spl0_14,
inference(rat,[],[s21,s83]) ).
cnf(s86,plain,
spl0_13,
inference(rat,[],[s9,s83]) ).
cnf(s87,plain,
spl0_8,
inference(rat,[],[s3,s83]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s50,s87,s80,s66,s67,s65,s86,s84,s85]) ).
fof(f927,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP374-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:59:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.10/1.31 % (3750707)Input is clausal, will run a generic CNF schedule.
% 2.10/1.31 % (3750713)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3687764848:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.10/1.31 % (3750718)dis-21_1_sil=8000:lcm=predicate:random_seed=861092255:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.10/1.31 % (3750712)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3224791288:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.10/1.31 % (3750715)lrs+10_1_sil=8000:sp=occurrence:random_seed=2850236690:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.10/1.31 % (3750716)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1865710389:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.10/1.31 % (3750714)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1717271524:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.10/1.31 % (3750717)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=864596915:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.10/1.31 % (3750718)Refutation not found, incomplete strategy
% 2.10/1.31 % (3750718)------------------------------
% 2.10/1.31 % (3750718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/1.31 % (3750718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/1.31 % (3750718)CaDiCaL version: 2.1.3
% 2.10/1.31 % (3750718)Termination reason: Refutation not found, incomplete strategy
% 2.10/1.31 % (3750718)Time elapsed: 0.002 s
% 2.10/1.31 % (3750718)Peak memory usage: 88 MB
% 2.10/1.31 % (3750718)Instructions burned: 2 (million)
% 2.10/1.31 % (3750715)Refutation not found, incomplete strategy
% 2.10/1.31 % (3750715)------------------------------
% 2.10/1.31 % (3750715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/1.31 % (3750715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/1.31 % (3750715)CaDiCaL version: 2.1.3
% 2.10/1.31 % (3750715)Termination reason: Refutation not found, incomplete strategy
% 2.10/1.31 % (3750715)Time elapsed: 0.004 s
% 2.10/1.31 % (3750715)Peak memory usage: 88 MB
% 2.10/1.31 % (3750715)Instructions burned: 5 (million)
% 2.10/1.31 % (3750717)First to succeed.
% 2.10/1.31 % (3750717)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3750707"
% 2.10/1.31 % (3750716)Instruction limit reached!
% 2.10/1.31 % (3750716)------------------------------
% 2.10/1.31 % (3750716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/1.31 % (3750716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/1.31 % (3750716)CaDiCaL version: 2.1.3
% 2.10/1.31 % (3750716)Termination reason: Instruction limit
% 2.10/1.31 % (3750716)Termination phase: Saturation
% 2.10/1.31 % (3750716)Time elapsed: 0.066 s
% 2.10/1.31 % (3750716)Peak memory usage: 89 MB
% 2.10/1.31 % (3750716)Instructions burned: 115 (million)
% 2.10/1.31 % (3750715)------------------------------
% 2.10/1.31 % (3750715)------------------------------
% 2.10/1.31 % (3750718)------------------------------
% 2.10/1.31 % (3750718)------------------------------
% 2.10/1.31 % (3750726)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1299436366:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.10/1.31 % (3750726)Refutation not found, incomplete strategy
% 2.10/1.31 % (3750726)------------------------------
% 2.10/1.31 % (3750726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.10/1.31 % (3750726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/1.31 % (3750726)CaDiCaL version: 2.1.3
% 2.10/1.31 % (3750726)Termination reason: Refutation not found, incomplete strategy
% 2.10/1.31 % (3750726)Time elapsed: 0.004 s
% 2.10/1.31 % (3750726)Peak memory usage: 88 MB
% 2.10/1.31 % (3750726)Instructions burned: 5 (million)
% 2.10/1.31 % (3750717)Refutation found. Thanks to Tanya!
% 2.10/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.10/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.41 % (3750717)------------------------------
% 3.77/1.41 % (3750717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.41 % (3750717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.41 % (3750717)CaDiCaL version: 2.1.3
% 3.77/1.41 % (3750717)Termination reason: Refutation
% 3.77/1.41 % (3750717)Time elapsed: 0.021 s
% 3.77/1.41 % (3750717)Peak memory usage: 89 MB
% 3.77/1.41 % (3750717)Instructions burned: 33 (million)
% 3.77/1.41 % (3750717)------------------------------
% 3.77/1.41 % (3750717)------------------------------
% 3.77/1.41 % (3750707)Success in time 0.455 s
% 3.77/1.41 % Vampire exiting
%------------------------------------------------------------------------------