%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:17:33 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 51
% Syntax : Number of formulae : 364 ( 16 unt; 17 def)
% Number of atoms : 1495 ( 359 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 2196 (1065 ~;1114 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = inverse(sk_c2)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = inverse(sk_c2)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = multiply(sk_c6,sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c7 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7
| inverse(X1) != sk_c6
| multiply(X1,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X2) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(X3,sk_c6) != sk_c5
| inverse(X3) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( multiply(sk_c6,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6)
| sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5)
| sk_c7 != multiply(sk_c6,sk_c5)
| sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c5 != inverse(sk_c6)
| sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X3] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c6 != inverse(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> sk_c5 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( sk_c5 = inverse(sk_c6)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( sk_c5 != inverse(sk_c6)
| spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl0_3
<=> ! [X2] :
( sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f78,definition,
( spl0_4
<=> sk_c7 = multiply(sk_c6,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f79,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( sk_c7 != multiply(sk_c6,sk_c5)
| spl0_4 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_5
<=> ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X1] :
( sk_c6 != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( ! [X0] :
( inverse(X0) != sk_c7
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_7
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f89,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c7) != 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,f82,f78,f75,f71,f68]) ).
fof(f93,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f95,plain,
( sk_c6 = inverse(sk_c4)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c2,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| ~ 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_c5 = multiply(sk_c4,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f62,f97,f102]) ).
fof(f106,plain,
( spl0_2
| spl0_9 ),
inference(avatar_split_clause,[],[f60,f97,f71]) ).
fof(f108,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f110,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f58,f97,f108]) ).
fof(f113,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f115,plain,
( sk_c6 = multiply(sk_c3,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f97,f113]) ).
fof(f117,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f54,f97,f78]) ).
fof(f119,definition,
( spl0_13
<=> sk_c6 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( sk_c6 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f119,f93]) ).
fof(f123,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f119,f102]) ).
fof(f124,plain,
( spl0_2
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f119,f71]) ).
fof(f125,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f119,f108]) ).
fof(f126,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f119,f113]) ).
fof(f127,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f119,f78]) ).
fof(f129,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c1,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f130,plain,
( sk_c7 != multiply(sk_c1,sk_c6)
| spl0_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( sk_c7 = multiply(sk_c1,sk_c6)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f129,f93]) ).
fof(f133,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f129,f102]) ).
fof(f134,plain,
( spl0_2
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f129,f71]) ).
fof(f135,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f129,f108]) ).
fof(f136,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f129,f113]) ).
fof(f137,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f129,f78]) ).
fof(f139,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f141,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f139,f93]) ).
fof(f143,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f139,f102]) ).
fof(f144,plain,
( spl0_2
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f139,f71]) ).
fof(f145,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f139,f108]) ).
fof(f146,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f139,f113]) ).
fof(f147,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f139,f78]) ).
fof(f148,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f88,f93]) ).
fof(f149,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f88,f102]) ).
fof(f150,plain,
( spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f88,f71]) ).
fof(f151,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f88,f108]) ).
fof(f152,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f88,f113]) ).
fof(f153,plain,
( spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f88,f78]) ).
fof(f154,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_2 ),
inference(superposition,[],[f3,f72]) ).
fof(f155,plain,
( identity = multiply(sk_c6,sk_c4)
| ~ spl0_8 ),
inference(superposition,[],[f3,f95]) ).
fof(f156,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_11 ),
inference(superposition,[],[f3,f110]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f161,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_12 ),
inference(superposition,[],[f4,f115]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f166,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_2 ),
inference(superposition,[],[f4,f154]) ).
fof(f167,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c6,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f166,f1]) ).
fof(f176,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f167,f79]) ).
fof(f177,plain,
( sk_c4 = multiply(sk_c5,identity)
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f167,f155]) ).
fof(f213,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f163,f176]) ).
fof(f214,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f163,f115]) ).
fof(f216,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f163,f104]) ).
fof(f221,plain,
( sk_c6 = multiply(sk_c6,sk_c5)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f216,f95]) ).
fof(f223,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f214,f110]) ).
fof(f224,plain,
( identity = sk_c7
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f213,f3]) ).
fof(f230,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f156,f224]) ).
fof(f233,plain,
( identity = sk_c3
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f230,f1]) ).
fof(f239,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f163,f221]) ).
fof(f241,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f239,f3]) ).
fof(f261,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f223,f224]) ).
fof(f262,plain,
( identity = sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f261,f1]) ).
fof(f265,plain,
( sk_c5 != multiply(identity,sk_c7)
| ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f90,f262]) ).
fof(f268,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f155,f262]) ).
fof(f277,plain,
( identity = sk_c4
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f268,f1]) ).
fof(f280,plain,
( sk_c7 != sk_c5
| ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f265,f1]) ).
fof(f286,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f280,f241]) ).
fof(f289,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f286,f224]) ).
fof(f290,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f291,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f83,f262]) ).
fof(f293,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f291,f241]) ).
fof(f295,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f293,f262]) ).
fof(f298,plain,
( ! [X0,X1] :
( identity != multiply(X0,multiply(X1,identity))
| identity != inverse(multiply(X0,X1)) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f295,f4]) ).
fof(f305,definition,
( spl0_16
<=> identity = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f306,plain,
( identity = sk_c4
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f309,definition,
( spl0_17
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f310,plain,
( identity = inverse(identity)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f324,plain,
( identity != multiply(sk_c6,identity)
| identity != inverse(multiply(sk_c3,sk_c7))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f298,f161]) ).
fof(f330,plain,
( identity != multiply(identity,identity)
| identity != inverse(multiply(sk_c3,sk_c7))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f324,f262]) ).
fof(f338,plain,
( identity != inverse(multiply(sk_c3,sk_c7))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f330,f1]) ).
fof(f341,plain,
( identity != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f338,f115]) ).
fof(f344,plain,
( identity != sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f341,f72]) ).
fof(f346,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f344,f241]) ).
fof(f347,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f346]) ).
fof(f348,plain,
( ! [X3] :
( sk_c5 != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f69,f262]) ).
fof(f349,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f348,f241]) ).
fof(f350,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f349,f262]) ).
fof(f351,plain,
( spl0_16
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f277,f113,f108,f93,f78,f71,f305]) ).
fof(f353,plain,
( ! [X0,X1] :
( identity != multiply(X0,multiply(X1,identity))
| identity != inverse(multiply(X0,X1)) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f350,f4]) ).
fof(f372,plain,
( identity != multiply(sk_c6,identity)
| identity != inverse(multiply(sk_c3,sk_c7))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f353,f161]) ).
fof(f378,plain,
( identity != multiply(identity,identity)
| identity != inverse(multiply(sk_c3,sk_c7))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f372,f262]) ).
fof(f386,plain,
( identity != inverse(multiply(sk_c3,sk_c7))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f378,f1]) ).
fof(f389,plain,
( identity != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f386,f115]) ).
fof(f392,plain,
( identity != sk_c5
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f389,f72]) ).
fof(f394,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f392,f241]) ).
fof(f395,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f394]) ).
fof(f400,plain,
( identity = inverse(sk_c1)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f141,f224]) ).
fof(f403,plain,
( sk_c5 = multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f89,f224]) ).
fof(f406,plain,
( sk_c5 = multiply(identity,identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f403,f262]) ).
fof(f407,plain,
( identity = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f406,f1]) ).
fof(f431,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15 ),
inference(superposition,[],[f3,f400]) ).
fof(f432,plain,
( identity = sk_c1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_15 ),
inference(forward_demodulation,[],[f431,f1]) ).
fof(f448,plain,
( sk_c7 = inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f110,f233]) ).
fof(f449,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f448,f224]) ).
fof(f453,plain,
( spl0_17
| ~ spl0_2
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f449,f108,f78,f71,f309]) ).
fof(f463,plain,
( sk_c7 = multiply(identity,sk_c6)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f131,f432]) ).
fof(f466,plain,
( sk_c6 = sk_c7
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f463,f1]) ).
fof(f467,plain,
( identity = sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f466,f224]) ).
fof(f468,plain,
( sk_c5 = inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f72,f467]) ).
fof(f469,plain,
( sk_c7 = multiply(identity,sk_c5)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f79,f467]) ).
fof(f477,plain,
( sk_c7 = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f469,f1]) ).
fof(f479,plain,
( identity = sk_c5
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f477,f224]) ).
fof(f520,plain,
( identity = inverse(sk_c2)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f121,f467]) ).
fof(f526,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f3,f520]) ).
fof(f527,plain,
( identity = sk_c2
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f526,f1]) ).
fof(f531,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f520,f527]) ).
fof(f532,plain,
( spl0_17
| ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f531,f139,f129,f119,f78,f71,f309]) ).
fof(f535,plain,
( identity = inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f468,f479]) ).
fof(f536,plain,
( spl0_17
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f535,f139,f129,f78,f71,f309]) ).
fof(f543,plain,
( ! [X3] :
( sk_c5 != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f69,f467]) ).
fof(f544,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c6 != inverse(X3) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f543,f479]) ).
fof(f545,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f544,f467]) ).
fof(f549,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f545,f3]) ).
fof(f551,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f549]) ).
fof(f554,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f551,f310]) ).
fof(f558,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f554,f310]) ).
fof(f559,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f558]) ).
fof(f562,plain,
( ! [X0] :
( identity != inverse(X0)
| sk_c7 != multiply(X0,sk_c6) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f86,f224]) ).
fof(f563,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f562,f467]) ).
fof(f564,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f563,f224]) ).
fof(f568,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f564,f3]) ).
fof(f570,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f568]) ).
fof(f573,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f570,f310]) ).
fof(f577,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f573,f310]) ).
fof(f578,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f581,plain,
( ! [X2] :
( sk_c6 != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f76,f224]) ).
fof(f582,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f581,f467]) ).
fof(f583,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f582,f224]) ).
fof(f587,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f583,f3]) ).
fof(f589,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f587]) ).
fof(f592,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f589,f310]) ).
fof(f596,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f592,f310]) ).
fof(f597,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f600,plain,
( ! [X1] :
( identity != inverse(X1)
| sk_c6 != multiply(X1,sk_c5) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f83,f467]) ).
fof(f601,plain,
( ! [X1] :
( sk_c6 != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f600,f479]) ).
fof(f602,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f601,f467]) ).
fof(f606,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f602,f3]) ).
fof(f608,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f606]) ).
fof(f611,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f608,f310]) ).
fof(f615,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f611,f310]) ).
fof(f616,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f615]) ).
fof(f620,plain,
( ! [X0] :
( identity != multiply(X0,sk_c6)
| identity != inverse(X0) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f562,f224]) ).
fof(f627,plain,
( sk_c7 != multiply(identity,sk_c6)
| ~ spl0_2
| ~ spl0_4
| spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f130,f432]) ).
fof(f628,plain,
( sk_c5 = multiply(identity,sk_c6)
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f104,f306]) ).
fof(f635,plain,
( sk_c6 != sk_c7
| ~ spl0_2
| ~ spl0_4
| spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f627,f1]) ).
fof(f636,plain,
( sk_c6 = sk_c5
| ~ spl0_10
| ~ spl0_16 ),
inference(forward_demodulation,[],[f628,f1]) ).
fof(f637,plain,
( identity != sk_c6
| ~ spl0_2
| ~ spl0_4
| spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f635,f224]) ).
fof(f652,plain,
( identity = sk_c6
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f636,f407]) ).
fof(f653,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f652,f637]) ).
fof(f654,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f653]) ).
fof(f697,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f620,f652]) ).
fof(f702,plain,
( identity != sk_c4
| identity != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(superposition,[],[f697,f177]) ).
fof(f705,plain,
( identity != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f702,f306]) ).
fof(f709,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f705,f407]) ).
fof(f712,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f709,f310]) ).
fof(f713,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f712]) ).
fof(f715,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f581,f652]) ).
fof(f717,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f715,f224]) ).
fof(f721,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(superposition,[],[f717,f3]) ).
fof(f723,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f721]) ).
fof(f726,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f723,f310]) ).
fof(f730,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f726,f310]) ).
fof(f731,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f730]) ).
fof(f737,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f141]) ).
fof(f740,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f89]) ).
fof(f742,plain,
( sk_c5 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_9 ),
inference(superposition,[],[f163,f99]) ).
fof(f744,plain,
( sk_c5 = multiply(sk_c6,sk_c6)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f742,f121]) ).
fof(f745,plain,
( sk_c6 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f163,f131]) ).
fof(f746,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c6,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f131]) ).
fof(f747,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f745,f141]) ).
fof(f753,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_15 ),
inference(superposition,[],[f163,f737]) ).
fof(f779,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c1,sk_c5)
| ~ spl0_7
| ~ spl0_14 ),
inference(superposition,[],[f746,f89]) ).
fof(f786,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f740,f747]) ).
fof(f789,plain,
( sk_c5 = multiply(sk_c5,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f786,f744]) ).
fof(f886,plain,
( sk_c7 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f163,f789]) ).
fof(f888,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f886,f3]) ).
fof(f895,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f747,f888]) ).
fof(f896,plain,
( sk_c1 = multiply(inverse(identity),identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f753,f888]) ).
fof(f898,plain,
( identity = sk_c1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f896,f3]) ).
fof(f899,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f895,f1]) ).
fof(f909,plain,
( sk_c7 = inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f141,f898]) ).
fof(f920,plain,
( sk_c5 != inverse(identity)
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f73,f899]) ).
fof(f954,plain,
( multiply(sk_c7,sk_c7) = multiply(identity,sk_c5)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f779,f898]) ).
fof(f955,plain,
( sk_c5 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f954,f1]) ).
fof(f956,plain,
( sk_c6 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f955,f747]) ).
fof(f957,plain,
( identity = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f956,f899]) ).
fof(f958,plain,
( sk_c7 != multiply(sk_c6,identity)
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f80,f957]) ).
fof(f969,plain,
( sk_c7 != multiply(identity,identity)
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f958,f899]) ).
fof(f973,plain,
( identity != sk_c7
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f969,f1]) ).
fof(f976,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f973,f888]) ).
fof(f977,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f976]) ).
fof(f1013,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f909,f888]) ).
fof(f1015,plain,
( identity != inverse(identity)
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f920,f957]) ).
fof(f1018,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1013,f139,f129,f119,f97,f88,f309]) ).
fof(f1020,plain,
( ~ spl0_17
| spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1015,f139,f129,f119,f97,f88,f71,f309]) ).
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_2
| spl0_9 ),
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f111]) ).
cnf(s6,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f116]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_2
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f132]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s16,plain,
( spl0_2
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f142]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s22,plain,
( spl0_2
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s25,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s26,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_2
| spl0_7 ),
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_4
| spl0_7 ),
inference(sat_conversion,[],[f153]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f290]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f347]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f351]) ).
cnf(s47,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f395]) ).
cnf(s53,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f453]) ).
cnf(s61,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f532]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f536]) ).
cnf(s64,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f559]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f578]) ).
cnf(s70,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f597]) ).
cnf(s73,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f616]) ).
cnf(s75,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f654]) ).
cnf(s78,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f713]) ).
cnf(s80,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f731]) ).
cnf(s83,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f977]) ).
cnf(s85,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f1018]) ).
cnf(s86,plain,
( spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f1020]) ).
cnf(s88,plain,
( ~ spl0_7
| spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(rat,[],[s85,s86]) ).
cnf(s89,plain,
spl0_2,
inference(rat,[],[s88,s4,s10,s16,s22,s28]) ).
cnf(s90,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_13
| ~ spl0_9
| ~ spl0_7
| spl0_1 ),
inference(rat,[],[s1,s67,s73,s70,s83,s85,s89]) ).
cnf(s91,plain,
( spl0_15
| ~ spl0_7
| spl0_1 ),
inference(rat,[],[s1,s78,s38,s80,s40,s53,s20,s21,s23,s24,s25,s89]) ).
cnf(s92,plain,
( spl0_14
| ~ spl0_15
| ~ spl0_7 ),
inference(rat,[],[s40,s75,s14,s15,s17,s18,s19,s89]) ).
cnf(s93,plain,
( spl0_13
| ~ spl0_7
| spl0_1 ),
inference(rat,[],[s1,s78,s38,s80,s40,s62,s8,s9,s11,s12,s13,s92,s91,s89]) ).
cnf(s94,plain,
( ~ spl0_13
| ~ spl0_15
| spl0_1
| ~ spl0_14
| ~ spl0_7 ),
inference(rat,[],[s1,s78,s38,s80,s40,s61,s2,s3,s5,s6,s7,s90,s89]) ).
cnf(s95,plain,
( ~ spl0_7
| spl0_1 ),
inference(rat,[],[s94,s93,s92,s91]) ).
cnf(s96,plain,
spl0_7,
inference(rat,[],[s32,s26,s27,s29,s30,s31,s89]) ).
cnf(s97,plain,
spl0_1,
inference(rat,[],[s95,s96]) ).
cnf(s98,plain,
( ~ spl0_9
| ~ spl0_15
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s64,s83,s85,s96,s97,s89]) ).
cnf(s99,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_13
| ~ spl0_14 ),
inference(rat,[],[s64,s61,s97,s89]) ).
cnf(s100,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s99,s7,s98]) ).
cnf(s101,plain,
spl0_15,
inference(rat,[],[s47,s20,s21,s23,s24,s25,s89,s97]) ).
cnf(s102,plain,
spl0_14,
inference(rat,[],[s92,s96,s101]) ).
cnf(s103,plain,
~ spl0_13,
inference(rat,[],[s100,s101,s102]) ).
cnf(s104,plain,
spl0_4,
inference(rat,[],[s13,s103]) ).
cnf(s109,plain,
spl0_17,
inference(rat,[],[s62,s101,s102,s89,s104]) ).
cnf(s110,plain,
$false,
inference(rat,[],[s64,s102,s97,s89,s101,s109,s104]) ).
fof(f1022,plain,
$false,
inference(avatar_sat_refutation,[],[s110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:50:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.48 % (2297044)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2297050)% WARNING: option uhcvi not known.
% 0.15/0.48 % (2297051)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2390889945:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (2297049)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3043126938_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (2297053)dis+10_1_sil=32000:sp=arity:random_seed=2113274199:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (2297050)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4180896100:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (2297055)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=508196909:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % (2297056)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1536050350:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % (2297054)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2609559559:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % (2297053) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2297044-2297053"...
% 0.15/0.48 % TRYING [5]
% 0.15/0.48 % (2297055) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2297044-2297055"...
% 0.15/0.48 % (2297053)...printing done.
% 0.15/0.48 % (2297053)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.49 % (2297053)------------------------------
% 0.15/0.49 % (2297053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.49 % (2297053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.49 % (2297053)CaDiCaL version: 2.1.3
% 0.15/0.49 % (2297053)Termination reason: Refutation
% 0.15/0.49 % (2297053)Time elapsed: 0.028 s
% 0.15/0.49 % (2297053)Peak memory usage: 12 MB
% 0.15/0.49 % (2297053)Instructions burned: 34 (million)
% 0.15/0.49 % (2297044)Success in time 0.074 s
% 0.15/0.49 % Vampire exiting
%------------------------------------------------------------------------------