%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP271-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:30 AM UTC 2026
% Result : Unsatisfiable 3.31s 1.33s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 74
% Syntax : Number of formulae : 397 ( 23 unt; 24 def)
% Number of atoms : 1195 ( 425 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1443 ( 645 ~; 774 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f20,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f22,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c11 = inverse(sk_c1)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c11 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f36,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f38,plain,
( sk_c11 = inverse(sk_c1)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f40,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f42,plain,
( sk_c11 = inverse(sk_c1)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_40) ).
fof(f82,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c10 = inverse(sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).
fof(f96,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f95]) ).
fof(f97,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_48) ).
fof(f98,plain,
( sk_c10 = inverse(sk_c2)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).
fof(f100,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f99]) ).
fof(f101,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_50) ).
fof(f102,plain,
( sk_c10 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f105]) ).
fof(f108,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f109,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_2
| ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f106,f114,f117,f111,f114,f111,f108]) ).
fof(f122,definition,
( spl0_5
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f124,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl0_6
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f128,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f102,f126,f122]) ).
fof(f131,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f133,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f100,f126,f131]) ).
fof(f136,definition,
( spl0_8
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f138,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f98,f126,f136]) ).
fof(f141,definition,
( spl0_9
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f143,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f96,f126,f141]) ).
fof(f146,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f148,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f94,f126,f146]) ).
fof(f151,definition,
( spl0_11
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f153,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f92,f126,f151]) ).
fof(f156,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f158,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f90,f126,f156]) ).
fof(f161,definition,
( spl0_13
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f163,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f88,f126,f161]) ).
fof(f166,definition,
( spl0_14
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f168,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f86,f126,f166]) ).
fof(f171,definition,
( spl0_15
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f173,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f84,f126,f171]) ).
fof(f176,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f178,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f179,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f82,f176,f122]) ).
fof(f180,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f80,f176,f131]) ).
fof(f181,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f78,f176,f136]) ).
fof(f182,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f76,f176,f141]) ).
fof(f183,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f74,f176,f146]) ).
fof(f184,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f72,f176,f151]) ).
fof(f185,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f70,f176,f156]) ).
fof(f186,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f68,f176,f161]) ).
fof(f187,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f66,f176,f166]) ).
fof(f188,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f64,f176,f171]) ).
fof(f193,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f54,f117,f146]) ).
fof(f194,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f52,f117,f151]) ).
fof(f195,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f50,f117,f156]) ).
fof(f196,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f48,f117,f161]) ).
fof(f197,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f46,f117,f166]) ).
fof(f198,plain,
( spl0_15
| spl0_4 ),
inference(avatar_split_clause,[],[f44,f117,f171]) ).
fof(f200,definition,
( spl0_17
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f202,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f203,plain,
( spl0_5
| spl0_17 ),
inference(avatar_split_clause,[],[f42,f200,f122]) ).
fof(f204,plain,
( spl0_7
| spl0_17 ),
inference(avatar_split_clause,[],[f40,f200,f131]) ).
fof(f205,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f38,f200,f136]) ).
fof(f206,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f36,f200,f141]) ).
fof(f207,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f200,f146]) ).
fof(f208,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f200,f151]) ).
fof(f209,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f200,f156]) ).
fof(f210,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f200,f161]) ).
fof(f211,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f200,f166]) ).
fof(f212,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f200,f171]) ).
fof(f214,definition,
( spl0_18
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f216,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( spl0_5
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f214,f122]) ).
fof(f218,plain,
( spl0_7
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f214,f131]) ).
fof(f219,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f214,f136]) ).
fof(f220,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f17,f214,f141]) ).
fof(f221,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f15,f214,f146]) ).
fof(f222,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f13,f214,f151]) ).
fof(f223,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f11,f214,f156]) ).
fof(f224,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f9,f214,f161]) ).
fof(f225,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f214,f166]) ).
fof(f226,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f214,f171]) ).
fof(f227,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f168]) ).
fof(f230,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f3,f138]) ).
fof(f234,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f240,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f234,f1]) ).
fof(f243,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f227]) ).
fof(f244,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f243,f1]) ).
fof(f257,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f244,f173]) ).
fof(f306,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f240,f257]) ).
fof(f311,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_13 ),
inference(superposition,[],[f240,f163]) ).
fof(f314,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_11 ),
inference(superposition,[],[f240,f153]) ).
fof(f323,plain,
( sk_c7 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f240,f230]) ).
fof(f326,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f323,f133]) ).
fof(f331,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f314,f148]) ).
fof(f334,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f311,f158]) ).
fof(f338,plain,
( identity = sk_c10
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f306,f3]) ).
fof(f340,plain,
( multiply(sk_c8,sk_c10) = sk_c7
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f326,f338]) ).
fof(f341,plain,
( sk_c11 = sk_c7
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f340,f143]) ).
fof(f352,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f240,f331]) ).
fof(f354,plain,
( identity = sk_c11
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f352,f3]) ).
fof(f357,plain,
( sk_c11 = sk_c10
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f354,f338]) ).
fof(f365,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f331,f357]) ).
fof(f366,plain,
( sk_c11 = sk_c8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f365,f143]) ).
fof(f368,plain,
( sk_c10 = sk_c8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f366,f357]) ).
fof(f371,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f240,f334]) ).
fof(f373,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f371,f3]) ).
fof(f376,plain,
( sk_c10 = sk_c9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f373,f338]) ).
fof(f380,plain,
( sk_c10 != multiply(sk_c11,sk_c10)
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f119,f376]) ).
fof(f381,plain,
( sk_c11 != sk_c10
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f380,f257]) ).
fof(f382,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f381,f357]) ).
fof(f383,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f384,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f115,f357]) ).
fof(f386,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f384,f357]) ).
fof(f389,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f386,f158]) ).
fof(f393,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f389]) ).
fof(f399,definition,
( spl0_20
<=> sk_c10 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f400,plain,
( sk_c10 = sk_c8
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f409,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f393,f163]) ).
fof(f412,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f409,f376]) ).
fof(f413,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f412]) ).
fof(f415,plain,
( ! [X6,X4] :
( sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f109,f357]) ).
fof(f416,plain,
( ! [X6,X4] :
( sk_c10 != multiply(inverse(X4),sk_c10)
| sk_c10 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f415,f357]) ).
fof(f417,plain,
( spl0_20
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f368,f171,f166,f151,f146,f141,f399]) ).
fof(f467,plain,
( sk_c6 = multiply(sk_c7,sk_c10)
| ~ spl0_5
| ~ spl0_20 ),
inference(superposition,[],[f124,f400]) ).
fof(f484,plain,
( sk_c6 = multiply(sk_c11,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f467,f341]) ).
fof(f488,plain,
( sk_c11 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f484,f257]) ).
fof(f489,plain,
( sk_c10 = sk_c6
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f488,f357]) ).
fof(f532,definition,
( spl0_28
<=> ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f533,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f551,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c11,sk_c10)
| sk_c10 != multiply(sk_c3,sk_c11)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f416,f168]) ).
fof(f562,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c11,sk_c10)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f551,f173]) ).
fof(f568,plain,
( ! [X0] :
( sk_c11 != sk_c10
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f562,f257]) ).
fof(f573,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f568,f357]) ).
fof(f578,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f573,f357]) ).
fof(f582,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f578,f357]) ).
fof(f586,plain,
( spl0_28
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f582,f171,f166,f151,f146,f108,f532]) ).
fof(f649,plain,
( sk_c10 != inverse(sk_c6)
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_8
| ~ spl0_28 ),
inference(superposition,[],[f533,f138]) ).
fof(f652,plain,
( sk_c10 != sk_c8
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_28 ),
inference(forward_demodulation,[],[f649,f133]) ).
fof(f658,plain,
( sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f652,f400]) ).
fof(f665,plain,
( sk_c6 != multiply(sk_c11,sk_c10)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f658,f341]) ).
fof(f671,plain,
( sk_c11 != sk_c6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f665,f257]) ).
fof(f676,plain,
( sk_c11 != sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f671,f489]) ).
fof(f677,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f676,f357]) ).
fof(f678,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f688,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_6 ),
inference(superposition,[],[f3,f128]) ).
fof(f776,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f240,f216]) ).
fof(f778,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f776,f202]) ).
fof(f785,plain,
( ! [X0] :
( sk_c11 != multiply(sk_c11,sk_c10)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0))
| sk_c11 != multiply(sk_c1,sk_c11) )
| ~ spl0_1
| ~ spl0_17 ),
inference(superposition,[],[f109,f202]) ).
fof(f798,plain,
( ! [X0] :
( sk_c11 != sk_c10
| sk_c11 != multiply(sk_c11,sk_c10)
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f785,f216]) ).
fof(f815,definition,
( spl0_33
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f816,plain,
( sk_c11 = sk_c10
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f822,definition,
( spl0_34
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f823,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f825,definition,
( spl0_35
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f826,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f828,plain,
( spl0_34
| ~ spl0_35
| ~ spl0_33
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f798,f214,f200,f108,f815,f825,f822]) ).
fof(f862,plain,
( sk_c10 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_16 ),
inference(superposition,[],[f240,f178]) ).
fof(f864,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f862,f128]) ).
fof(f1114,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_35 ),
inference(superposition,[],[f240,f826]) ).
fof(f1115,plain,
( ! [X0] : multiply(sk_c11,X0) = multiply(sk_c11,multiply(sk_c10,X0))
| ~ spl0_35 ),
inference(superposition,[],[f4,f826]) ).
fof(f1116,plain,
( identity = sk_c10
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1114,f3]) ).
fof(f1127,plain,
( sk_c10 != inverse(sk_c1)
| sk_c11 != inverse(inverse(sk_c1))
| ~ spl0_18
| ~ spl0_34 ),
inference(superposition,[],[f823,f216]) ).
fof(f1138,plain,
( sk_c11 != sk_c10
| sk_c11 != inverse(inverse(sk_c1))
| ~ spl0_17
| ~ spl0_18
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1127,f202]) ).
fof(f1188,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c11),multiply(sk_c11,X0))
| ~ spl0_35 ),
inference(superposition,[],[f240,f1115]) ).
fof(f1191,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1188,f240]) ).
fof(f1294,plain,
( multiply(sk_c11,sk_c9) = multiply(sk_c11,sk_c10)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_35 ),
inference(superposition,[],[f1115,f864]) ).
fof(f1297,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_6
| ~ spl0_16 ),
inference(superposition,[],[f240,f864]) ).
fof(f1299,plain,
( identity = sk_c9
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1297,f3]) ).
fof(f1301,plain,
( sk_c11 = multiply(sk_c11,sk_c9)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1294,f826]) ).
fof(f1303,plain,
( sk_c11 = sk_c10
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1301,f118]) ).
fof(f1308,plain,
( spl0_35
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f778,f214,f200,f825]) ).
fof(f1324,plain,
( spl0_33
| ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1303,f825,f176,f126,f117,f815]) ).
fof(f1325,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != sk_c10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1138,f202]) ).
fof(f1382,plain,
( sk_c10 != sk_c10
| multiply(sk_c4,sk_c10) != sk_c9
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[],[f112,f158]) ).
fof(f1385,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c2,sk_c10)
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f112,f128]) ).
fof(f1386,plain,
( sk_c9 != multiply(sk_c2,sk_c10)
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f1385]) ).
fof(f1387,plain,
( multiply(sk_c4,sk_c10) != sk_c9
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f1382]) ).
fof(f1388,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1386,f178]) ).
fof(f1389,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1388]) ).
fof(f1392,plain,
( ~ spl0_13
| ~ spl0_2
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f1387,f156,f111,f161]) ).
fof(f1403,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_33 ),
inference(forward_demodulation,[],[f115,f816]) ).
fof(f1404,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1403,f816]) ).
fof(f1422,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_33 ),
inference(superposition,[],[f1404,f128]) ).
fof(f1423,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_33 ),
inference(trivial_inequality_removal,[],[f1422]) ).
fof(f1425,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1423,f178]) ).
fof(f1439,plain,
( sk_c10 = sk_c9
| ~ spl0_6
| ~ spl0_16
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1299,f1116]) ).
fof(f1440,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_33
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f1439,f1425]) ).
fof(f1441,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_33
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f1440]) ).
fof(f1453,definition,
( spl0_54
<=> sk_c10 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f1455,plain,
( sk_c10 != inverse(sk_c10)
| spl0_54 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f1461,plain,
( sk_c11 != inverse(sk_c11)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[],[f1325,f816]) ).
fof(f1476,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1461,f816]) ).
fof(f1487,plain,
( ~ spl0_54
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1476,f822,f815,f214,f200,f1453]) ).
fof(f1663,plain,
( identity = sk_c2
| ~ spl0_6
| ~ spl0_35 ),
inference(superposition,[],[f688,f1191]) ).
fof(f1666,plain,
( sk_c10 = sk_c2
| ~ spl0_6
| ~ spl0_35 ),
inference(forward_demodulation,[],[f1663,f1116]) ).
fof(f1681,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_6
| ~ spl0_35 ),
inference(superposition,[],[f128,f1666]) ).
fof(f1690,plain,
( $false
| ~ spl0_6
| ~ spl0_35
| spl0_54 ),
inference(forward_subsumption_resolution,[],[f1681,f1455]) ).
fof(f1691,plain,
( ~ spl0_6
| ~ spl0_35
| spl0_54 ),
inference(avatar_contradiction_clause,[],[f1690]) ).
cnf(s1,plain,
( spl0_2
| spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f120]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s4,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f134]) ).
cnf(s5,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f139]) ).
cnf(s6,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f144]) ).
cnf(s7,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f149]) ).
cnf(s8,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f159]) ).
cnf(s10,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f164]) ).
cnf(s11,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f169]) ).
cnf(s12,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f174]) ).
cnf(s13,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f179]) ).
cnf(s14,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f180]) ).
cnf(s15,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f181]) ).
cnf(s16,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f182]) ).
cnf(s17,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f183]) ).
cnf(s18,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f184]) ).
cnf(s19,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f185]) ).
cnf(s20,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f186]) ).
cnf(s21,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f187]) ).
cnf(s22,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f188]) ).
cnf(s27,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f193]) ).
cnf(s28,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f194]) ).
cnf(s29,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f195]) ).
cnf(s30,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f196]) ).
cnf(s31,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f197]) ).
cnf(s32,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f198]) ).
cnf(s33,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s34,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s35,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s36,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s37,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s38,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s39,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f209]) ).
cnf(s40,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f210]) ).
cnf(s41,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f211]) ).
cnf(s42,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f212]) ).
cnf(s43,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f217]) ).
cnf(s44,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f218]) ).
cnf(s45,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f219]) ).
cnf(s46,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f220]) ).
cnf(s47,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s48,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s49,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f223]) ).
cnf(s50,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f224]) ).
cnf(s51,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f225]) ).
cnf(s52,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f226]) ).
cnf(s53,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f383]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f413]) ).
cnf(s57,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| spl0_20 ),
inference(sat_conversion,[],[f417]) ).
cnf(s75,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| spl0_28 ),
inference(sat_conversion,[],[f586]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(sat_conversion,[],[f678]) ).
cnf(s102,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| spl0_34
| ~ spl0_35 ),
inference(sat_conversion,[],[f828]) ).
cnf(s135,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_35 ),
inference(sat_conversion,[],[f1308]) ).
cnf(s138,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_16
| spl0_33
| ~ spl0_35 ),
inference(sat_conversion,[],[f1324]) ).
cnf(s145,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_16 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s146,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1392]) ).
cnf(s153,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_16
| ~ spl0_33
| ~ spl0_35 ),
inference(sat_conversion,[],[f1441]) ).
cnf(s157,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| ~ spl0_34
| ~ spl0_54 ),
inference(sat_conversion,[],[f1487]) ).
cnf(s171,plain,
( ~ spl0_6
| ~ spl0_35
| spl0_54 ),
inference(sat_conversion,[],[f1691]) ).
cnf(s172,plain,
spl0_4,
inference(rat,[],[s53,s27,s28,s29,s30,s31,s32]) ).
cnf(s173,plain,
( spl0_6
| ~ spl0_3 ),
inference(rat,[],[s56,s7,s8,s9,s10,s11,s12]) ).
cnf(s174,plain,
( ~ spl0_16
| ~ spl0_35
| ~ spl0_3
| ~ spl0_6 ),
inference(rat,[],[s138,s153,s172]) ).
cnf(s175,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s174,s135,s22,s42,s52,s173]) ).
cnf(s176,plain,
( spl0_14
| spl0_35 ),
inference(rat,[],[s135,s41,s51]) ).
cnf(s177,plain,
( spl0_13
| spl0_35 ),
inference(rat,[],[s135,s40,s50]) ).
cnf(s178,plain,
( spl0_12
| spl0_35 ),
inference(rat,[],[s135,s39,s49]) ).
cnf(s179,plain,
( spl0_11
| spl0_35 ),
inference(rat,[],[s135,s38,s48]) ).
cnf(s180,plain,
( spl0_35
| ~ spl0_3 ),
inference(rat,[],[s135,s37,s47,s56,s179,s178,s177,s176,s175]) ).
cnf(s181,plain,
~ spl0_3,
inference(rat,[],[s56,s17,s18,s19,s20,s21,s174,s180,s175,s173]) ).
cnf(s182,plain,
( spl0_16
| ~ spl0_2 ),
inference(rat,[],[s146,s19,s20]) ).
cnf(s183,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s146,s9,s10,s145]) ).
cnf(s184,plain,
~ spl0_2,
inference(rat,[],[s183,s182]) ).
cnf(s185,plain,
spl0_1,
inference(rat,[],[s2,s172,s181,s184]) ).
cnf(s186,plain,
( spl0_18
| ~ spl0_15
| ~ spl0_10
| spl0_35 ),
inference(rat,[],[s91,s57,s43,s44,s45,s46,s75,s176,s179,s185]) ).
cnf(s187,plain,
( ~ spl0_15
| ~ spl0_10
| spl0_35 ),
inference(rat,[],[s91,s57,s33,s34,s35,s36,s135,s186,s75,s176,s179,s185]) ).
cnf(s188,plain,
( spl0_15
| spl0_35 ),
inference(rat,[],[s135,s42,s52]) ).
cnf(s189,plain,
( ~ spl0_15
| spl0_35 ),
inference(rat,[],[s135,s37,s47,s187]) ).
cnf(s190,plain,
spl0_35,
inference(rat,[],[s189,s188]) ).
cnf(s191,plain,
( spl0_18
| ~ spl0_15
| ~ spl0_10 ),
inference(rat,[],[s91,s57,s75,s43,s44,s45,s46,s48,s51,s185]) ).
cnf(s192,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_54
| ~ spl0_33 ),
inference(rat,[],[s102,s157,s190,s185]) ).
cnf(s193,plain,
( ~ spl0_15
| ~ spl0_10
| ~ spl0_33
| ~ spl0_54 ),
inference(rat,[],[s91,s57,s75,s33,s34,s35,s36,s38,s41,s192,s191,s185]) ).
cnf(s194,plain,
( spl0_15
| ~ spl0_33
| ~ spl0_54 ),
inference(rat,[],[s192,s42,s52]) ).
cnf(s195,plain,
( ~ spl0_15
| ~ spl0_33
| ~ spl0_54 ),
inference(rat,[],[s192,s37,s47,s193]) ).
cnf(s196,plain,
( ~ spl0_33
| ~ spl0_54 ),
inference(rat,[],[s195,s194]) ).
cnf(s197,plain,
spl0_16,
inference(rat,[],[s91,s57,s75,s13,s14,s15,s16,s17,s18,s21,s22,s185]) ).
cnf(s198,plain,
~ spl0_6,
inference(rat,[],[s196,s138,s171,s172,s197,s190]) ).
cnf(s199,plain,
spl0_14,
inference(rat,[],[s11,s198]) ).
cnf(s202,plain,
spl0_11,
inference(rat,[],[s8,s198]) ).
cnf(s203,plain,
spl0_10,
inference(rat,[],[s7,s198]) ).
cnf(s204,plain,
spl0_9,
inference(rat,[],[s6,s198]) ).
cnf(s205,plain,
spl0_8,
inference(rat,[],[s5,s198]) ).
cnf(s206,plain,
spl0_7,
inference(rat,[],[s4,s198]) ).
cnf(s207,plain,
spl0_5,
inference(rat,[],[s3,s198]) ).
cnf(s208,plain,
~ spl0_15,
inference(rat,[],[s91,s57,s75,s207,s204,s203,s202,s199,s206,s205,s185]) ).
cnf(s209,plain,
$false,
inference(rat,[],[s12,s208,s198]) ).
fof(f1692,plain,
$false,
inference(avatar_sat_refutation,[],[s209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP271-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:43:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.31/1.33 % (3256811)Input is clausal, will run a generic CNF schedule.
% 3.31/1.33 % (3256818)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1220533522:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.31/1.33 % (3256820)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2913022677:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.31/1.33 % (3256819)lrs+10_1_sil=8000:sp=occurrence:random_seed=217461379:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.31/1.33 % (3256821)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=515561996:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.31/1.33 % (3256817)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1136000342:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.31/1.33 % (3256822)dis-21_1_sil=8000:lcm=predicate:random_seed=1634918743:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.31/1.33 % (3256816)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3697116735:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.31/1.33 % (3256822)Refutation not found, incomplete strategy
% 3.31/1.33 % (3256822)------------------------------
% 3.31/1.33 % (3256822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.33 % (3256822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.33 % (3256822)CaDiCaL version: 2.1.3
% 3.31/1.33 % (3256822)Termination reason: Refutation not found, incomplete strategy
% 3.31/1.33 % (3256822)Time elapsed: 0.002 s
% 3.31/1.33 % (3256822)Peak memory usage: 88 MB
% 3.31/1.33 % (3256822)Instructions burned: 2 (million)
% 3.31/1.33 % (3256819)Refutation not found, incomplete strategy
% 3.31/1.33 % (3256819)------------------------------
% 3.31/1.33 % (3256819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.33 % (3256819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.33 % (3256819)CaDiCaL version: 2.1.3
% 3.31/1.33 % (3256819)Termination reason: Refutation not found, incomplete strategy
% 3.31/1.33 % (3256819)Time elapsed: 0.004 s
% 3.31/1.33 % (3256819)Peak memory usage: 88 MB
% 3.31/1.33 % (3256819)Instructions burned: 5 (million)
% 3.31/1.33 % (3256821)First to succeed.
% 3.31/1.33 % (3256821)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3256811"
% 3.31/1.33 % (3256820)Instruction limit reached!
% 3.31/1.33 % (3256820)------------------------------
% 3.31/1.33 % (3256820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.33 % (3256820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.33 % (3256820)CaDiCaL version: 2.1.3
% 3.31/1.33 % (3256820)Termination reason: Instruction limit
% 3.31/1.33 % (3256820)Termination phase: Saturation
% 3.31/1.33 % (3256820)Time elapsed: 0.065 s
% 3.31/1.33 % (3256820)Peak memory usage: 89 MB
% 3.31/1.33 % (3256820)Instructions burned: 115 (million)
% 3.31/1.33 % (3256830)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2261382170:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.31/1.33 % (3256830)Refutation not found, incomplete strategy
% 3.31/1.33 % (3256830)------------------------------
% 3.31/1.33 % (3256830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.31/1.33 % (3256830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.31/1.33 % (3256830)CaDiCaL version: 2.1.3
% 3.31/1.33 % (3256830)Termination reason: Refutation not found, incomplete strategy
% 3.31/1.33 % (3256830)Time elapsed: 0.004 s
% 3.31/1.33 % (3256830)Peak memory usage: 88 MB
% 3.31/1.33 % (3256830)Instructions burned: 5 (million)
% 3.31/1.33 % (3256819)------------------------------
% 3.31/1.33 % (3256819)------------------------------
% 3.31/1.33 % (3256822)------------------------------
% 3.31/1.33 % (3256822)------------------------------
% 3.31/1.33 % (3256821)Refutation found. Thanks to Tanya!
% 3.31/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.31/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.53 % (3256821)------------------------------
% 3.91/1.53 % (3256821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.53 % (3256821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.53 % (3256821)CaDiCaL version: 2.1.3
% 3.91/1.53 % (3256821)Termination reason: Refutation
% 3.91/1.53 % (3256821)Time elapsed: 0.035 s
% 3.91/1.53 % (3256821)Peak memory usage: 90 MB
% 3.91/1.53 % (3256821)Instructions burned: 56 (million)
% 3.91/1.53 % (3256821)------------------------------
% 3.91/1.53 % (3256821)------------------------------
% 3.91/1.53 % (3256811)Success in time 0.466 s
% 3.91/1.53 % Vampire exiting
%------------------------------------------------------------------------------