%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP308-1 : 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 : n006.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 10:17:27 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 59
% Syntax : Number of formulae : 429 ( 21 unt; 20 def)
% Number of atoms : 1549 ( 422 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2188 (1068 ~;1100 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c8
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(equality_resolution,[],[f78]) ).
fof(f81,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f85,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f88,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_6
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( sk_c6 != inverse(sk_c8)
| spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_7
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f102,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f79,f101,f97,f93,f90,f87,f84,f81]) ).
fof(f106,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f112,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f110,f106]) ).
fof(f115,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f117,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f74,f110,f115]) ).
fof(f120,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f122,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f110,f120]) ).
fof(f125,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f127,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f70,f110,f125]) ).
fof(f130,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f132,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f68,f110,f130]) ).
fof(f135,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f136,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| spl0_14 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f66,f110,f135]) ).
fof(f140,definition,
( spl0_15
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f142,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f64,f140,f106]) ).
fof(f144,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f62,f140,f115]) ).
fof(f145,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f140,f120]) ).
fof(f146,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f140,f125]) ).
fof(f147,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f140,f130]) ).
fof(f148,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f140,f135]) ).
fof(f150,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f152,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f150,f106]) ).
fof(f154,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f50,f150,f115]) ).
fof(f155,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f48,f150,f120]) ).
fof(f156,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f150,f125]) ).
fof(f157,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f150,f130]) ).
fof(f158,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f150,f135]) ).
fof(f159,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f93,f106]) ).
fof(f160,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f38,f93,f115]) ).
fof(f161,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f36,f93,f120]) ).
fof(f162,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f34,f93,f125]) ).
fof(f163,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f32,f93,f130]) ).
fof(f164,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f30,f93,f135]) ).
fof(f165,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f97,f106]) ).
fof(f166,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f97,f115]) ).
fof(f167,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f97,f120]) ).
fof(f168,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f22,f97,f125]) ).
fof(f169,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f97,f130]) ).
fof(f171,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f101,f106]) ).
fof(f172,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f101,f115]) ).
fof(f173,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f101,f120]) ).
fof(f174,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f101,f125]) ).
fof(f175,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f101,f130]) ).
fof(f176,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f101,f135]) ).
fof(f177,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f117]) ).
fof(f179,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f3,f132]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_14 ),
inference(superposition,[],[f4,f137]) ).
fof(f185,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f108]) ).
fof(f186,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f182,f1]) ).
fof(f193,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f179]) ).
fof(f194,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f193,f1]) ).
fof(f195,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c3,identity)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f183,f179]) ).
fof(f207,plain,
( multiply(sk_c6,sk_c3) = multiply(sk_c5,identity)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f185,f179]) ).
fof(f224,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_13 ),
inference(superposition,[],[f186,f179]) ).
fof(f227,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f186,f177]) ).
fof(f230,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f186,f137]) ).
fof(f232,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f186,f127]) ).
fof(f241,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f232,f122]) ).
fof(f243,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f230,f132]) ).
fof(f245,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f186,f241]) ).
fof(f247,plain,
( identity = sk_c6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f3]) ).
fof(f251,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f186,f243]) ).
fof(f253,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f251,f3]) ).
fof(f260,plain,
( sk_c8 != multiply(identity,sk_c7)
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f95,f247]) ).
fof(f261,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f260,f1]) ).
fof(f299,plain,
( sk_c5 = multiply(inverse(identity),identity)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f227,f247]) ).
fof(f300,plain,
( identity = sk_c5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f299,f3]) ).
fof(f304,plain,
( sk_c6 = multiply(identity,sk_c8)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f108,f300]) ).
fof(f307,plain,
( sk_c8 = sk_c6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f304,f1]) ).
fof(f311,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f307,f247]) ).
fof(f348,plain,
( multiply(sk_c3,identity) = multiply(identity,sk_c3)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f195,f253]) ).
fof(f349,plain,
( sk_c3 = multiply(sk_c3,identity)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f348,f1]) ).
fof(f350,plain,
( identity != sk_c8
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f261,f253]) ).
fof(f351,plain,
( $false
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f350,f311]) ).
fof(f352,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f354,plain,
( identity != multiply(sk_c8,sk_c7)
| spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f103,f247]) ).
fof(f356,plain,
( identity != sk_c8
| spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f354,f243]) ).
fof(f358,plain,
( $false
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f356,f311]) ).
fof(f359,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f360,plain,
( sk_c6 != inverse(identity)
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f99,f311]) ).
fof(f362,plain,
( identity != inverse(identity)
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f360,f247]) ).
fof(f369,plain,
( multiply(sk_c6,sk_c3) = multiply(identity,identity)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f207,f300]) ).
fof(f370,plain,
( identity = multiply(sk_c6,sk_c3)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f369,f1]) ).
fof(f371,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f370,f247]) ).
fof(f372,plain,
( identity = sk_c3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f371,f1]) ).
fof(f373,plain,
( sk_c8 = inverse(identity)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f132,f372]) ).
fof(f383,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f373,f311]) ).
fof(f387,plain,
( $false
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f383,f362]) ).
fof(f388,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f389,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f85,f253]) ).
fof(f390,plain,
( sk_c6 = inverse(identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f98,f311]) ).
fof(f391,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f389,f247]) ).
fof(f392,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f390,f247]) ).
fof(f393,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f391,f253]) ).
fof(f401,plain,
( identity != sk_c3
| identity != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f393,f349]) ).
fof(f404,plain,
( identity != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f401,f372]) ).
fof(f409,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f404,f132]) ).
fof(f413,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f409,f311]) ).
fof(f414,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f418,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f82,f247]) ).
fof(f419,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f418,f311]) ).
fof(f420,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f419,f247]) ).
fof(f424,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f420,f224]) ).
fof(f429,plain,
( identity != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f424,f372]) ).
fof(f434,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f429,f311]) ).
fof(f439,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f434,f392]) ).
fof(f440,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f439,f392]) ).
fof(f441,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f442,plain,
( ! [X1] :
( sk_c7 != multiply(identity,multiply(X1,identity))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f91,f311]) ).
fof(f443,plain,
( ! [X1] :
( sk_c7 != multiply(X1,identity)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f442,f1]) ).
fof(f444,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f443,f253]) ).
fof(f445,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f444,f311]) ).
fof(f450,plain,
( identity != sk_c3
| identity != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f445,f349]) ).
fof(f453,plain,
( identity != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f450,f372]) ).
fof(f458,plain,
( identity != sk_c8
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f453,f132]) ).
fof(f462,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f458,f311]) ).
fof(f463,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f462]) ).
fof(f492,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f152,f253]) ).
fof(f495,plain,
( ! [X2] :
( identity != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f88,f253]) ).
fof(f520,plain,
( sk_c8 = sk_c6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f102,f243]) ).
fof(f524,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f98,f520]) ).
fof(f526,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f112]) ).
fof(f531,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f186,f142]) ).
fof(f533,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f531,f112]) ).
fof(f536,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f186,f492]) ).
fof(f539,plain,
( sk_c3 = sk_c2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f536,f224]) ).
fof(f552,plain,
( identity != sk_c7
| sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f495,f137]) ).
fof(f556,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f552,f253]) ).
fof(f563,definition,
( spl0_18
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f564,plain,
( identity = sk_c8
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f568,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f556,f132]) ).
fof(f569,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f578,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_9 ),
inference(superposition,[],[f186,f526]) ).
fof(f581,plain,
( sk_c3 = sk_c1
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f578,f224]) ).
fof(f614,plain,
( multiply(sk_c3,sk_c8) = sk_c2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f142,f581]) ).
fof(f616,plain,
( sk_c3 = multiply(sk_c3,sk_c8)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f614,f539]) ).
fof(f617,plain,
( sk_c7 = sk_c3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f616,f137]) ).
fof(f618,plain,
( identity = sk_c3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f617,f253]) ).
fof(f642,plain,
( ! [X1] :
( identity != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f91,f253]) ).
fof(f649,plain,
( identity != multiply(sk_c8,sk_c2)
| sk_c8 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f642,f142]) ).
fof(f650,plain,
( identity != sk_c8
| sk_c8 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f642,f194]) ).
fof(f651,plain,
( identity != sk_c8
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f650,f132]) ).
fof(f652,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f649,f492]) ).
fof(f657,plain,
( ~ spl0_18
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f651,f135,f130,f90,f563]) ).
fof(f658,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f652,f112]) ).
fof(f659,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f666,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f82,f520]) ).
fof(f667,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f666,f520]) ).
fof(f670,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[],[f179,f564]) ).
fof(f677,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_9
| ~ spl0_18 ),
inference(superposition,[],[f526,f564]) ).
fof(f681,plain,
( identity = sk_c1
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_demodulation,[],[f677,f1]) ).
fof(f688,plain,
( identity = sk_c3
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f670,f1]) ).
fof(f695,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f667,f564]) ).
fof(f696,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f695,f564]) ).
fof(f700,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(superposition,[],[f696,f224]) ).
fof(f707,plain,
( identity != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f700,f618]) ).
fof(f712,plain,
( identity != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f707,f524]) ).
fof(f717,plain,
( identity != sk_c8
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f712,f524]) ).
fof(f718,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f717,f564]) ).
fof(f719,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f718]) ).
fof(f720,plain,
( sk_c7 != multiply(sk_c3,identity)
| spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f136,f564]) ).
fof(f722,plain,
( sk_c7 = multiply(identity,sk_c2)
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f152,f564]) ).
fof(f723,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f102,f564]) ).
fof(f724,plain,
( sk_c6 = inverse(identity)
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_demodulation,[],[f98,f564]) ).
fof(f726,plain,
( sk_c7 = sk_c2
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f722,f1]) ).
fof(f727,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f723,f1]) ).
fof(f733,plain,
( sk_c2 = multiply(identity,sk_c8)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(superposition,[],[f142,f681]) ).
fof(f736,plain,
( sk_c8 = sk_c2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f733,f1]) ).
fof(f739,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f736,f564]) ).
fof(f753,plain,
( sk_c7 != multiply(identity,identity)
| ~ spl0_13
| spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f720,f688]) ).
fof(f754,plain,
( identity != sk_c7
| ~ spl0_13
| spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f753,f1]) ).
fof(f756,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f739,f726]) ).
fof(f760,plain,
( $false
| ~ spl0_9
| ~ spl0_13
| spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f756,f754]) ).
fof(f761,plain,
( ~ spl0_9
| ~ spl0_13
| spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f760]) ).
fof(f783,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_16 ),
inference(superposition,[],[f186,f152]) ).
fof(f785,plain,
( multiply(sk_c6,sk_c7) = sk_c2
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f783,f98]) ).
fof(f786,plain,
( sk_c8 = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f785,f94]) ).
fof(f791,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f85,f102]) ).
fof(f793,plain,
( sk_c7 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f791]) ).
fof(f803,plain,
( sk_c7 != sk_c6
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f793,f98]) ).
fof(f809,definition,
( spl0_25
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f810,plain,
( identity = sk_c6
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f815,definition,
( spl0_26
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f816,plain,
( sk_c7 = sk_c6
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f819,definition,
( spl0_27
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f820,plain,
( sk_c8 = sk_c7
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f823,plain,
( ~ spl0_26
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f803,f101,f97,f84,f815]) ).
fof(f827,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f533,f786]) ).
fof(f870,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f186,f827]) ).
fof(f872,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f870,f3]) ).
fof(f876,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f726,f786]) ).
fof(f879,plain,
( spl0_18
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f872,f150,f140,f110,f97,f93,f563]) ).
fof(f883,plain,
( spl0_27
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f876,f563,f150,f97,f93,f819]) ).
fof(f884,plain,
( spl0_26
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f727,f563,f101,f815]) ).
fof(f926,plain,
( identity = sk_c7
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f820,f564]) ).
fof(f928,plain,
( sk_c6 = multiply(sk_c8,identity)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_27 ),
inference(superposition,[],[f102,f926]) ).
fof(f935,plain,
( sk_c6 = multiply(identity,identity)
| ~ spl0_7
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f928,f564]) ).
fof(f940,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f935,f1]) ).
fof(f948,plain,
( spl0_25
| ~ spl0_7
| ~ spl0_18
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f940,f819,f563,f101,f809]) ).
fof(f992,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f88,f564]) ).
fof(f993,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f992,f926]) ).
fof(f994,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f993,f564]) ).
fof(f1005,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_18
| ~ spl0_27 ),
inference(superposition,[],[f994,f3]) ).
fof(f1006,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_18
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1005]) ).
fof(f1008,plain,
( identity != inverse(sk_c6)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1006,f724]) ).
fof(f1010,plain,
( identity != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1008,f816]) ).
fof(f1013,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1010,f926]) ).
fof(f1014,plain,
( identity != sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1013,f724]) ).
fof(f1015,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1014,f810]) ).
fof(f1016,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1015]) ).
fof(f1017,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_26 ),
inference(forward_demodulation,[],[f82,f816]) ).
fof(f1018,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1017,f926]) ).
fof(f1019,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1018,f564]) ).
fof(f1020,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1019,f816]) ).
fof(f1021,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1020,f926]) ).
fof(f1029,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(superposition,[],[f1021,f3]) ).
fof(f1030,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1029]) ).
fof(f1032,plain,
( identity != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1030,f724]) ).
fof(f1034,plain,
( identity != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1032,f816]) ).
fof(f1037,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1034,f926]) ).
fof(f1038,plain,
( identity != sk_c6
| ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1037,f724]) ).
fof(f1039,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1038,f810]) ).
fof(f1040,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1039]) ).
fof(f1041,plain,
( ! [X1] :
( sk_c7 != multiply(identity,multiply(X1,identity))
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f91,f564]) ).
fof(f1042,plain,
( ! [X1] :
( sk_c7 != multiply(X1,identity)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1041,f1]) ).
fof(f1043,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1042,f926]) ).
fof(f1044,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1043,f564]) ).
fof(f1047,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_18
| ~ spl0_27 ),
inference(superposition,[],[f1044,f3]) ).
fof(f1048,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_18
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f1047]) ).
fof(f1050,plain,
( identity != inverse(sk_c6)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1048,f724]) ).
fof(f1052,plain,
( identity != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1050,f816]) ).
fof(f1055,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1052,f926]) ).
fof(f1056,plain,
( identity != sk_c6
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_demodulation,[],[f1055,f724]) ).
fof(f1057,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1056,f810]) ).
fof(f1058,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1057]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f123]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s9,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s10,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s11,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s12,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s13,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s14,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f153]) ).
cnf(s15,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f154]) ).
cnf(s16,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f155]) ).
cnf(s17,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f156]) ).
cnf(s18,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f157]) ).
cnf(s19,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f158]) ).
cnf(s20,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f159]) ).
cnf(s21,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f160]) ).
cnf(s22,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f161]) ).
cnf(s23,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f162]) ).
cnf(s24,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f163]) ).
cnf(s25,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f164]) ).
cnf(s26,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f165]) ).
cnf(s27,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f166]) ).
cnf(s28,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f167]) ).
cnf(s29,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f168]) ).
cnf(s30,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s32,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f171]) ).
cnf(s33,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f172]) ).
cnf(s34,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s35,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f174]) ).
cnf(s36,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f175]) ).
cnf(s37,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f176]) ).
cnf(s38,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f352]) ).
cnf(s39,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f359]) ).
cnf(s40,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f388]) ).
cnf(s43,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f414]) ).
cnf(s48,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f441]) ).
cnf(s51,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f463]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f569]) ).
cnf(s69,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18 ),
inference(sat_conversion,[],[f657]) ).
cnf(s70,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f659]) ).
cnf(s80,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f719]) ).
cnf(s84,plain,
( ~ spl0_9
| ~ spl0_13
| spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f761]) ).
cnf(s90,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_26 ),
inference(sat_conversion,[],[f823]) ).
cnf(s98,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f879]) ).
cnf(s100,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18
| spl0_27 ),
inference(sat_conversion,[],[f883]) ).
cnf(s101,plain,
( ~ spl0_7
| ~ spl0_18
| spl0_26 ),
inference(sat_conversion,[],[f884]) ).
cnf(s104,plain,
( ~ spl0_7
| ~ spl0_18
| spl0_25
| ~ spl0_27 ),
inference(sat_conversion,[],[f948]) ).
cnf(s111,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f1016]) ).
cnf(s113,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f1040]) ).
cnf(s115,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_18
| ~ spl0_25
| ~ spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f1058]) ).
cnf(s116,plain,
spl0_5,
inference(rat,[],[s38,s20,s21,s22,s23,s24,s25]) ).
cnf(s117,plain,
spl0_6,
inference(rat,[],[s40,s26,s27,s28,s29,s30]) ).
cnf(s118,plain,
spl0_7,
inference(rat,[],[s39,s32,s33,s34,s35,s36,s37]) ).
cnf(s119,plain,
( spl0_9
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s51,s3,s4,s5,s6,s7]) ).
cnf(s120,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s84,s98,s13,s19,s51,s119,s116,s117]) ).
cnf(s121,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s115,s104,s100,s101,s98,s12,s18,s117,s118,s116]) ).
cnf(s122,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s70,s84,s98,s11,s17,s121,s116,s117]) ).
cnf(s123,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s70,s84,s98,s10,s16,s121,s116,s117]) ).
cnf(s124,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s70,s84,s98,s9,s15,s120,s123,s122,s121,s119,s117,s116]) ).
cnf(s125,plain,
~ spl0_4,
inference(rat,[],[s84,s69,s121,s98,s2,s8,s14,s124,s116,s117]) ).
cnf(s126,plain,
( ~ spl0_13
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s84,s98,s13,s19,s59,s116,s117]) ).
cnf(s127,plain,
( ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s111,s104,s100,s101,s98,s12,s18,s126,s116,s118,s117]) ).
cnf(s128,plain,
~ spl0_3,
inference(rat,[],[s59,s6,s7,s127]) ).
cnf(s129,plain,
( spl0_16
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s43,s14,s15,s16,s17,s19]) ).
cnf(s130,plain,
( ~ spl0_13
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s43,s8,s9,s10,s11,s13,s98,s129,s101,s90,s116,s117,s118]) ).
cnf(s131,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s98,s12,s18,s130,s101,s90,s116,s117,s118]) ).
cnf(s132,plain,
~ spl0_2,
inference(rat,[],[s43,s2,s3,s4,s5,s6,s7,s131]) ).
cnf(s133,plain,
spl0_1,
inference(rat,[],[s1,s117,s116,s125,s118,s128,s132]) ).
cnf(s134,plain,
( ~ spl0_16
| ~ spl0_18
| ~ spl0_13
| ~ spl0_9
| ~ spl0_15 ),
inference(rat,[],[s84,s80,s133,s118,s117]) ).
cnf(s135,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_13
| ~ spl0_9 ),
inference(rat,[],[s134,s98,s116,s117]) ).
cnf(s136,plain,
( spl0_16
| ~ spl0_13 ),
inference(rat,[],[s48,s14,s15,s16,s17,s117,s133]) ).
cnf(s137,plain,
( ~ spl0_16
| ~ spl0_13
| ~ spl0_9 ),
inference(rat,[],[s48,s8,s9,s10,s11,s135,s133,s117]) ).
cnf(s138,plain,
( ~ spl0_13
| ~ spl0_9 ),
inference(rat,[],[s137,s136]) ).
cnf(s139,plain,
( ~ spl0_18
| ~ spl0_27
| ~ spl0_26 ),
inference(rat,[],[s104,s113,s133,s117,s118]) ).
cnf(s140,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_9 ),
inference(rat,[],[s139,s100,s101,s98,s118,s117,s116]) ).
cnf(s141,plain,
~ spl0_9,
inference(rat,[],[s140,s12,s18,s138]) ).
cnf(s143,plain,
spl0_13,
inference(rat,[],[s6,s141]) ).
cnf(s144,plain,
spl0_12,
inference(rat,[],[s5,s141]) ).
cnf(s145,plain,
spl0_11,
inference(rat,[],[s4,s141]) ).
cnf(s146,plain,
spl0_10,
inference(rat,[],[s3,s141]) ).
cnf(s147,plain,
spl0_8,
inference(rat,[],[s2,s141]) ).
cnf(s150,plain,
$false,
inference(rat,[],[s48,s145,s146,s133,s117,s143,s147,s144]) ).
fof(f1059,plain,
$false,
inference(avatar_sat_refutation,[],[s150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP308-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:49:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.15/0.46 % (2743591)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2743599)dis+10_1_sil=32000:sp=arity:random_seed=2140162420:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (2743597)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2743596)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=871254935_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (2743598)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1167878286:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (2743597)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=868696720:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (2743600)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3574145582:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (2743601)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1449918655:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (2743602)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1910364907:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (2743599) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2743591-2743599"...
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % (2743599)...printing done.
% 0.15/0.46 % (2743599)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2743599)------------------------------
% 0.15/0.46 % (2743599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2743599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2743599)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2743599)Termination reason: Refutation
% 0.15/0.46 % (2743599)Time elapsed: 0.013 s
% 0.15/0.46 % (2743599)Peak memory usage: 12 MB
% 0.15/0.46 % (2743599)Instructions burned: 34 (million)
% 0.15/0.46 % (2743591)Success in time 0.044 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------