%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP295-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 10:17:24 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.69s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 49
% Syntax : Number of formulae : 404 ( 22 unt; 15 def)
% Number of atoms : 1681 ( 419 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 2509 (1232 ~;1262 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| multiply(X0,sk_c7) != sk_c6
| inverse(X0) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(X1,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c5) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c7,sk_c6) != sk_c5
| sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(sk_c7,sk_c5)
| sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c6 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> sk_c5 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( sk_c5 != multiply(sk_c6,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_4
<=> ! [X1] :
( sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( ! [X1] :
( sk_c5 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c7,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f82,plain,
( sk_c6 = multiply(sk_c7,sk_c5)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( sk_c6 != multiply(sk_c7,sk_c5)
| spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl0_6
<=> ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( ! [X0] :
( sk_c6 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_7
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f89,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( multiply(sk_c7,sk_c6) != sk_c5
| spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f66,f88,f85,f81,f78,f74,f71,f68]) ).
fof(f93,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f64,f97,f93]) ).
fof(f102,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f62,f97,f102]) ).
fof(f107,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f108,plain,
( sk_c7 != multiply(sk_c3,sk_c6)
| spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f97,f107]) ).
fof(f112,definition,
( spl0_12
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f58,f97,f112]) ).
fof(f116,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f97,f74]) ).
fof(f118,definition,
( spl0_13
<=> sk_c5 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f120,plain,
( sk_c5 = multiply(sk_c2,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f118,f93]) ).
fof(f122,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f118,f102]) ).
fof(f123,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f118,f107]) ).
fof(f124,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f118,f112]) ).
fof(f125,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f118,f74]) ).
fof(f126,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f81,f93]) ).
fof(f127,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f42,f81,f102]) ).
fof(f128,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f81,f107]) ).
fof(f129,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f38,f81,f112]) ).
fof(f130,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f36,f81,f74]) ).
fof(f132,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f134,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f132,f93]) ).
fof(f136,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f132,f102]) ).
fof(f137,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f132,f107]) ).
fof(f138,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f132,f112]) ).
fof(f139,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f132,f74]) ).
fof(f141,definition,
( spl0_15
<=> sk_c6 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f143,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f141,f93]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f141,f102]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f141,f107]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f141,f112]) ).
fof(f148,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f141,f74]) ).
fof(f149,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f88,f93]) ).
fof(f150,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f88,f102]) ).
fof(f151,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f88,f107]) ).
fof(f152,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f88,f112]) ).
fof(f153,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f88,f74]) ).
fof(f154,plain,
( sk_c6 != multiply(sk_c7,multiply(sk_c6,sk_c7))
| ~ spl0_3
| spl0_5 ),
inference(forward_demodulation,[],[f83,f75]) ).
fof(f155,plain,
( sk_c6 = multiply(sk_c4,multiply(sk_c6,sk_c7))
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f95,f75]) ).
fof(f157,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f104]) ).
fof(f158,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f114]) ).
fof(f159,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f160,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f4]) ).
fof(f164,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f157]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(sk_c7,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f109]) ).
fof(f166,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(multiply(sk_c6,sk_c7),X0))
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f4,f155]) ).
fof(f167,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c6,multiply(sk_c7,X0)))
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f166,f4]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c4,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f164,f1]) ).
fof(f172,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f158]) ).
fof(f173,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c3,X0)) = X0
| ~ spl0_12 ),
inference(forward_demodulation,[],[f172,f1]) ).
fof(f188,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f173,f109]) ).
fof(f189,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f173,f165]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c3,X0)) = multiply(sk_c4,multiply(sk_c6,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f167,f173]) ).
fof(f197,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f160,f3]) ).
fof(f198,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f160,f160]) ).
fof(f200,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_12 ),
inference(superposition,[],[f160,f173]) ).
fof(f201,plain,
( sk_c4 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f160,f157]) ).
fof(f202,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c6),X0)
| ~ spl0_10 ),
inference(superposition,[],[f160,f168]) ).
fof(f205,plain,
( multiply(sk_c6,sk_c7) = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f160,f155]) ).
fof(f210,plain,
( multiply(multiply(sk_c7,sk_c7),sk_c7) = multiply(inverse(sk_c4),multiply(sk_c7,sk_c7))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f205,f188]) ).
fof(f213,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(multiply(sk_c7,sk_c7)),X0)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f202,f188]) ).
fof(f214,plain,
( sk_c4 = multiply(inverse(multiply(sk_c7,sk_c7)),identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f201,f188]) ).
fof(f215,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f197,f198]) ).
fof(f217,plain,
( multiply(multiply(sk_c7,sk_c7),sk_c7) = multiply(sk_c6,multiply(sk_c7,sk_c7))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f210,f104]) ).
fof(f219,plain,
( multiply(multiply(sk_c7,sk_c7),sk_c7) = multiply(sk_c7,multiply(sk_c7,multiply(sk_c7,sk_c7)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f217,f189]) ).
fof(f221,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c7)) = multiply(sk_c7,multiply(sk_c7,multiply(sk_c7,sk_c7)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f219,f4]) ).
fof(f223,plain,
( multiply(sk_c7,sk_c7) != multiply(sk_c7,multiply(multiply(sk_c7,sk_c7),sk_c7))
| ~ spl0_3
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f154,f188]) ).
fof(f224,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c4,multiply(multiply(sk_c7,sk_c7),sk_c7))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f155,f188]) ).
fof(f227,plain,
( ! [X0] : multiply(multiply(sk_c7,sk_c7),X0) = multiply(sk_c4,multiply(multiply(sk_c7,sk_c7),multiply(sk_c7,X0)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f167,f188]) ).
fof(f230,plain,
( ! [X0] : multiply(multiply(sk_c7,sk_c7),X0) = multiply(inverse(multiply(sk_c7,sk_c7)),multiply(multiply(sk_c7,sk_c7),multiply(sk_c7,X0)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f227,f213]) ).
fof(f233,plain,
( multiply(sk_c7,sk_c7) = multiply(inverse(multiply(sk_c7,sk_c7)),multiply(multiply(sk_c7,sk_c7),sk_c7))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f224,f213]) ).
fof(f234,plain,
( multiply(sk_c7,sk_c7) != multiply(sk_c7,multiply(sk_c7,multiply(sk_c7,sk_c7)))
| ~ spl0_3
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f223,f4]) ).
fof(f237,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(multiply(sk_c7,sk_c7),X0)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f230,f160]) ).
fof(f240,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f233,f160]) ).
fof(f241,plain,
( multiply(sk_c7,sk_c7) != multiply(sk_c7,multiply(sk_c7,sk_c7))
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f234,f221]) ).
fof(f242,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f237,f4]) ).
fof(f243,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f241,f240]) ).
fof(f244,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f243,f240]) ).
fof(f245,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f247,plain,
( multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7)
| ~ spl0_3
| spl0_7 ),
inference(forward_demodulation,[],[f90,f75]) ).
fof(f249,plain,
( multiply(sk_c7,sk_c6) != multiply(sk_c7,multiply(sk_c7,sk_c7))
| ~ spl0_3
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f247,f189]) ).
fof(f251,plain,
( multiply(sk_c7,sk_c6) != multiply(sk_c7,sk_c7)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f242]) ).
fof(f253,plain,
( sk_c7 != multiply(sk_c7,sk_c6)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f251,f240]) ).
fof(f254,plain,
( sk_c7 != multiply(sk_c7,multiply(sk_c7,sk_c7))
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f253,f188]) ).
fof(f255,plain,
( sk_c7 != multiply(sk_c7,sk_c7)
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f254,f242]) ).
fof(f256,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f255,f240]) ).
fof(f257,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f258,plain,
( ! [X0] :
( multiply(X0,sk_c7) != multiply(sk_c7,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f86,f188]) ).
fof(f260,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f258,f240]) ).
fof(f270,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f160,f240]) ).
fof(f272,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f270,f3]) ).
fof(f279,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f260,f240]) ).
fof(f280,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f279]) ).
fof(f282,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f280,f272]) ).
fof(f289,plain,
( sk_c6 = multiply(sk_c4,multiply(sk_c6,identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f155,f272]) ).
fof(f290,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f158,f272]) ).
fof(f298,plain,
( identity = sk_c3
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f290,f1]) ).
fof(f299,plain,
( sk_c6 = multiply(sk_c6,multiply(sk_c3,identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f289,f190]) ).
fof(f302,plain,
( sk_c6 = multiply(sk_c7,multiply(sk_c7,multiply(sk_c3,identity)))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f299,f189]) ).
fof(f305,plain,
( sk_c6 = multiply(sk_c7,multiply(sk_c3,identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f302,f242]) ).
fof(f308,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f173]) ).
fof(f318,plain,
( sk_c7 = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f114,f298]) ).
fof(f319,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f318,f272]) ).
fof(f324,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f319,f282]) ).
fof(f325,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f332,plain,
( ! [X3] :
( inverse(X3) != multiply(sk_c7,sk_c7)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f69,f188]) ).
fof(f333,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f332,f240]) ).
fof(f334,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f333,f272]) ).
fof(f335,plain,
( ! [X3] :
( sk_c6 != multiply(X3,multiply(sk_c6,sk_c7))
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f334,f75]) ).
fof(f336,plain,
( ! [X3] :
( sk_c6 != multiply(X3,multiply(sk_c7,multiply(sk_c7,sk_c7)))
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f335,f189]) ).
fof(f337,plain,
( ! [X3] :
( sk_c6 != multiply(X3,multiply(sk_c7,sk_c7))
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f336,f242]) ).
fof(f338,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f337,f240]) ).
fof(f339,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f338,f272]) ).
fof(f340,plain,
( ! [X3] :
( sk_c6 != X3
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f339,f215]) ).
fof(f341,plain,
( ! [X3] :
( multiply(sk_c7,sk_c7) != X3
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f340,f188]) ).
fof(f342,plain,
( ! [X3] :
( sk_c7 != X3
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f341,f240]) ).
fof(f343,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f342,f272]) ).
fof(f345,plain,
( identity != sk_c6
| identity != sk_c4
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f343,f104]) ).
fof(f348,plain,
( identity != sk_c4
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f345,f308]) ).
fof(f351,plain,
( identity != multiply(inverse(multiply(sk_c7,sk_c7)),identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f348,f214]) ).
fof(f352,plain,
( identity != inverse(multiply(sk_c7,sk_c7))
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f351,f215]) ).
fof(f353,plain,
( identity != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f352,f240]) ).
fof(f354,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f353,f272]) ).
fof(f355,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f354,f319]) ).
fof(f356,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f357,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f72,f272]) ).
fof(f358,plain,
( ! [X2] :
( sk_c7 != multiply(X2,multiply(sk_c7,sk_c7))
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f357,f188]) ).
fof(f359,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c7)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f358,f240]) ).
fof(f360,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f359,f272]) ).
fof(f361,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f360,f215]) ).
fof(f365,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f157,f308]) ).
fof(f374,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f365,f1]) ).
fof(f397,plain,
( identity != sk_c6
| identity != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f361,f104]) ).
fof(f400,plain,
( identity != sk_c4
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f397,f308]) ).
fof(f403,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f400,f374]) ).
fof(f404,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f405,plain,
( ! [X1] :
( sk_c5 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f79,f272]) ).
fof(f406,plain,
( ! [X1] :
( sk_c5 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f405,f215]) ).
fof(f407,plain,
( ! [X1] :
( multiply(sk_c6,sk_c7) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f406,f75]) ).
fof(f408,plain,
( ! [X1] :
( multiply(sk_c7,multiply(sk_c7,sk_c7)) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f407,f189]) ).
fof(f409,plain,
( ! [X1] :
( multiply(sk_c7,sk_c7) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f408,f242]) ).
fof(f410,plain,
( ! [X1] :
( sk_c7 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f409,f240]) ).
fof(f411,plain,
( ! [X1] :
( identity != X1
| sk_c7 != inverse(X1) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f410,f272]) ).
fof(f412,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f411,f272]) ).
fof(f433,plain,
( identity != sk_c6
| identity != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f412,f104]) ).
fof(f436,plain,
( identity != sk_c4
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f433,f308]) ).
fof(f439,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f436,f374]) ).
fof(f440,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f450,plain,
( sk_c7 != multiply(inverse(sk_c7),sk_c6)
| spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f108,f200]) ).
fof(f452,plain,
( multiply(sk_c7,sk_c6) != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f76,f89]) ).
fof(f454,plain,
( sk_c6 = multiply(sk_c7,multiply(sk_c7,sk_c6))
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f82,f89]) ).
fof(f457,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f99]) ).
fof(f459,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f134]) ).
fof(f464,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(sk_c5,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f120]) ).
fof(f465,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(multiply(sk_c7,sk_c6),X0)
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f464,f89]) ).
fof(f467,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(sk_c7,multiply(sk_c6,X0))
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f465,f4]) ).
fof(f469,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c6)
| ~ spl0_15 ),
inference(superposition,[],[f160,f143]) ).
fof(f470,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f143]) ).
fof(f471,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f469,f134]) ).
fof(f472,plain,
( sk_c2 = multiply(inverse(sk_c7),identity)
| ~ spl0_9 ),
inference(superposition,[],[f160,f457]) ).
fof(f475,plain,
( sk_c2 = inverse(sk_c7)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f472,f215]) ).
fof(f482,plain,
( multiply(sk_c7,sk_c6) = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f160,f454]) ).
fof(f485,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f482,f471]) ).
fof(f486,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f485,f450]) ).
fof(f487,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f488,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_14 ),
inference(superposition,[],[f160,f459]) ).
fof(f491,plain,
( sk_c1 = inverse(sk_c7)
| ~ spl0_14 ),
inference(forward_demodulation,[],[f488,f215]) ).
fof(f498,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f143,f491]) ).
fof(f500,plain,
( identity = sk_c6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f498,f3]) ).
fof(f503,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c6)) = multiply(sk_c1,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15 ),
inference(superposition,[],[f470,f454]) ).
fof(f510,plain,
( multiply(sk_c1,identity) = multiply(identity,multiply(sk_c7,identity))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f503,f500]) ).
fof(f516,plain,
( multiply(sk_c7,identity) = multiply(sk_c1,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f510,f1]) ).
fof(f520,plain,
( sk_c1 = multiply(sk_c7,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f516,f215]) ).
fof(f522,plain,
( sk_c7 = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f520,f215]) ).
fof(f525,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f470,f522]) ).
fof(f529,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f134,f522]) ).
fof(f531,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c7,X0))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f525,f500]) ).
fof(f532,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c7,X0)) = X0
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f531,f1]) ).
fof(f533,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(inverse(sk_c7),multiply(sk_c7,X0))
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f467,f475]) ).
fof(f535,plain,
( multiply(sk_c7,multiply(sk_c6,multiply(sk_c7,sk_c6))) = multiply(sk_c2,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f467,f454]) ).
fof(f536,plain,
( multiply(sk_c2,identity) = multiply(sk_c7,multiply(sk_c6,sk_c1))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f467,f459]) ).
fof(f541,plain,
( multiply(sk_c2,identity) = multiply(sk_c7,multiply(sk_c6,inverse(sk_c7)))
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f536,f491]) ).
fof(f542,plain,
( multiply(sk_c2,identity) = multiply(sk_c7,multiply(identity,multiply(sk_c7,identity)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f535,f500]) ).
fof(f544,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f533,f160]) ).
fof(f547,plain,
( multiply(sk_c7,multiply(sk_c6,sk_c7)) = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f541,f529]) ).
fof(f548,plain,
( multiply(sk_c7,multiply(sk_c7,identity)) = multiply(sk_c2,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f542,f1]) ).
fof(f550,plain,
( ! [X0] : multiply(sk_c7,multiply(identity,X0)) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f544,f500]) ).
fof(f553,plain,
( sk_c2 = multiply(sk_c7,multiply(sk_c6,sk_c7))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f547,f215]) ).
fof(f554,plain,
( sk_c2 = multiply(sk_c7,multiply(sk_c7,identity))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f548,f215]) ).
fof(f556,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f550,f1]) ).
fof(f559,plain,
( sk_c2 = multiply(sk_c7,multiply(identity,sk_c7))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f553,f500]) ).
fof(f560,plain,
( identity = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f554,f532]) ).
fof(f563,plain,
( sk_c2 = multiply(identity,sk_c7)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f559,f556]) ).
fof(f566,plain,
( sk_c7 = sk_c2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f563,f1]) ).
fof(f568,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f566,f560]) ).
fof(f609,plain,
( multiply(sk_c6,identity) != multiply(identity,sk_c6)
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f452,f568]) ).
fof(f613,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f459,f568]) ).
fof(f620,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f613,f1]) ).
fof(f624,plain,
( sk_c6 != multiply(sk_c6,identity)
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f609,f1]) ).
fof(f630,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f624,f215]) ).
fof(f631,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f646,plain,
( ! [X1] :
( sk_c5 != multiply(X1,identity)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f79,f568]) ).
fof(f648,plain,
( ! [X1] :
( sk_c5 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f646,f215]) ).
fof(f650,plain,
( ! [X1] :
( multiply(sk_c7,sk_c6) != X1
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f648,f89]) ).
fof(f651,plain,
( ! [X1] :
( sk_c7 != X1
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f650,f471]) ).
fof(f652,plain,
( ! [X1] :
( identity != X1
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f651,f568]) ).
fof(f653,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f652,f568]) ).
fof(f656,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f653,f134]) ).
fof(f659,plain,
( identity != sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f656,f568]) ).
fof(f663,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f659,f620]) ).
fof(f664,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f663]) ).
fof(f669,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f72,f568]) ).
fof(f670,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f669,f500]) ).
fof(f671,plain,
( ! [X2] :
( sk_c7 != X2
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f670,f215]) ).
fof(f672,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != X2 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f671,f568]) ).
fof(f688,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f672,f134]) ).
fof(f691,plain,
( identity != sk_c1
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f688,f568]) ).
fof(f695,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f691,f620]) ).
fof(f696,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f695]) ).
fof(f699,plain,
( ! [X0] :
( sk_c6 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f86,f568]) ).
fof(f700,plain,
( ! [X0] :
( sk_c6 != X0
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f699,f215]) ).
fof(f701,plain,
( ! [X0] :
( identity != X0
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f700,f500]) ).
fof(f702,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f701,f568]) ).
fof(f721,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f702,f134]) ).
fof(f724,plain,
( identity != sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f721,f568]) ).
fof(f728,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f724,f620]) ).
fof(f729,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f732,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c6 != multiply(X3,sk_c5) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f69,f500]) ).
fof(f733,plain,
( ! [X3] :
( sk_c6 != multiply(X3,multiply(sk_c7,sk_c6))
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f732,f89]) ).
fof(f734,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f733,f471]) ).
fof(f735,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f734,f568]) ).
fof(f736,plain,
( ! [X3] :
( sk_c6 != X3
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f735,f215]) ).
fof(f737,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f736,f500]) ).
fof(f751,plain,
( identity != sk_c7
| identity != sk_c1
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f737,f134]) ).
fof(f754,plain,
( identity != sk_c1
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f751,f568]) ).
fof(f758,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f754,f620]) ).
fof(f759,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f758]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f91]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f100]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f121]) ).
cnf(s8,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f128]) ).
cnf(s15,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s17,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s20,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s22,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s24,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s25,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f151]) ).
cnf(s30,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f152]) ).
cnf(s31,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f245]) ).
cnf(s33,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f257]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f325]) ).
cnf(s36,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f356]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f404]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f440]) ).
cnf(s42,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f487]) ).
cnf(s43,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f631]) ).
cnf(s45,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f664]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f696]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f729]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f759]) ).
cnf(s56,plain,
spl0_3,
inference(rat,[],[s43,s6,s11,s16,s21,s26,s31]) ).
cnf(s57,plain,
spl0_7,
inference(rat,[],[s33,s27,s28,s29,s30,s56]) ).
cnf(s58,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s51,s10,s20,s25,s57]) ).
cnf(s59,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_5 ),
inference(rat,[],[s42,s19,s24,s57]) ).
cnf(s60,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s51,s8,s18,s23,s34,s59,s58,s57,s56]) ).
cnf(s61,plain,
( ~ spl0_8
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s34,s3,s4,s5,s60,s56]) ).
cnf(s62,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s51,s2,s7,s17,s22,s61,s57]) ).
cnf(s63,plain,
( ~ spl0_5
| spl0_4
| spl0_1
| spl0_2 ),
inference(rat,[],[s62,s1,s57,s56]) ).
cnf(s64,plain,
spl0_5,
inference(rat,[],[s32,s12,s13,s14,s15,s56]) ).
cnf(s66,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s40,s8,s9,s10,s56]) ).
cnf(s67,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s40,s23,s24,s25,s56]) ).
cnf(s68,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s40,s18,s19,s20,s56]) ).
cnf(s69,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s40,s3,s4,s5,s45,s68,s67,s66,s57,s64,s56]) ).
cnf(s70,plain,
~ spl0_4,
inference(rat,[],[s45,s2,s7,s17,s22,s69,s64,s57]) ).
cnf(s71,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s38,s8,s9,s10,s56]) ).
cnf(s72,plain,
( spl0_15
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s38,s23,s24,s25,s56]) ).
cnf(s73,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s38,s18,s19,s20,s56]) ).
cnf(s74,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s38,s3,s4,s5,s48,s73,s72,s71,s57,s64,s56]) ).
cnf(s75,plain,
~ spl0_2,
inference(rat,[],[s48,s2,s7,s17,s22,s74,s64,s57]) ).
cnf(s76,plain,
spl0_1,
inference(rat,[],[s63,s64,s70,s75]) ).
cnf(s77,plain,
( spl0_13
| ~ spl0_8 ),
inference(rat,[],[s36,s8,s9,s10,s56,s76]) ).
cnf(s78,plain,
( spl0_15
| ~ spl0_8 ),
inference(rat,[],[s36,s23,s24,s25,s56,s76]) ).
cnf(s79,plain,
( spl0_14
| ~ spl0_8 ),
inference(rat,[],[s36,s18,s19,s20,s56,s76]) ).
cnf(s80,plain,
~ spl0_8,
inference(rat,[],[s36,s3,s4,s5,s54,s79,s78,s77,s56,s76,s64,s57]) ).
cnf(s81,plain,
spl0_15,
inference(rat,[],[s22,s80]) ).
cnf(s82,plain,
spl0_14,
inference(rat,[],[s17,s80]) ).
cnf(s83,plain,
spl0_13,
inference(rat,[],[s7,s80]) ).
cnf(s84,plain,
spl0_9,
inference(rat,[],[s2,s80]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s54,s81,s76,s57,s64,s83,s84,s82]) ).
fof(f762,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP295-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.58 % Computer : n017.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Sun Sep 27 09:43:53 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.62 Running first-order model finding
% 0.11/0.62 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.69 % (2293075)Will run a generic schedule for satisfiability detection.
% 0.15/0.69 % (2293080)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4254459243_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.69 % TRYING [1]
% 0.15/0.69 % TRYING [2]
% 0.15/0.69 % TRYING [3]
% 0.15/0.69 % (2293081)% WARNING: option uhcvi not known.
% 0.15/0.69 % TRYING [4]
% 0.15/0.69 % (2293081)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2438512628:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.69 % (2293082)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2018152030:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.69 % (2293083)dis+10_1_sil=32000:sp=arity:random_seed=2582414615:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.69 % (2293084)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1857064929:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.69 % (2293085)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3184409324:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.69 % (2293086)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3445242575:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.69 % TRYING [5]
% 0.15/0.69 % (2293085) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2293075-2293085"...
% 0.15/0.69 % TRYING [6]
% 0.15/0.69 % (2293084) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2293075-2293084"...
% 0.15/0.69 % (2293085)...printing done.
% 0.15/0.69 % (2293085)Refutation found. Thanks to Tanya!
% 0.15/0.69 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.69 % (2293085)------------------------------
% 0.15/0.69 % (2293085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.69 % (2293085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.69 % (2293085)CaDiCaL version: 2.1.3
% 0.15/0.69 % (2293085)Termination reason: Refutation
% 0.15/0.69 % (2293085)Time elapsed: 0.016 s
% 0.15/0.69 % (2293085)Peak memory usage: 12 MB
% 0.15/0.69 % (2293085)Instructions burned: 26 (million)
% 0.15/0.69 % (2293075)Success in time 0.06 s
% 0.15/0.69 % Vampire exiting
%------------------------------------------------------------------------------