%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP263-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 10:13:29 AM UTC 2026
% Result : Unsatisfiable 3.32s 1.33s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 74
% Syntax : Number of formulae : 392 ( 26 unt; 28 def)
% Number of atoms : 1183 ( 421 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1445 ( 654 ~; 763 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/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/sandbox/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(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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_c2,sk_c10) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c10 = inverse(sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c10 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c2)
| sk_c11 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c2)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c2)
| sk_c8 = inverse(sk_c6) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f82,plain,
( sk_c10 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| 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/sandbox/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_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c11 != multiply(sk_c9,sk_c10)
| 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_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c11 != multiply(sk_c9,sk_c10)
| 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_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c11 != multiply(sk_c9,sk_c10)
| 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_c11 = multiply(sk_c9,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( sk_c11 = multiply(sk_c9,sk_c10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f119,plain,
( sk_c11 != multiply(sk_c9,sk_c10)
| spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f106,f114,f111,f117,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(f127,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f129,plain,
( sk_c8 = inverse(sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f132,definition,
( spl0_7
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f134,plain,
( inverse(sk_c7) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f137,definition,
( spl0_8
<=> sk_c11 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f139,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f142,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f94,f117,f142]) ).
fof(f147,definition,
( spl0_10
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f149,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f92,f117,f147]) ).
fof(f152,definition,
( spl0_11
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f154,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f90,f117,f152]) ).
fof(f157,definition,
( spl0_12
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f159,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f88,f117,f157]) ).
fof(f162,definition,
( spl0_13
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f164,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f86,f117,f162]) ).
fof(f167,definition,
( spl0_14
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f169,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f84,f117,f167]) ).
fof(f172,definition,
( spl0_15
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f174,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( spl0_5
| spl0_15 ),
inference(avatar_split_clause,[],[f82,f172,f122]) ).
fof(f176,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f80,f172,f127]) ).
fof(f177,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f78,f172,f132]) ).
fof(f178,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f76,f172,f137]) ).
fof(f179,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f74,f172,f142]) ).
fof(f180,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f72,f172,f147]) ).
fof(f181,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f70,f172,f152]) ).
fof(f182,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f68,f172,f157]) ).
fof(f183,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f66,f172,f162]) ).
fof(f184,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f64,f172,f167]) ).
fof(f186,definition,
( spl0_16
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f188,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f189,plain,
( spl0_5
| spl0_16 ),
inference(avatar_split_clause,[],[f62,f186,f122]) ).
fof(f190,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f60,f186,f127]) ).
fof(f191,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f58,f186,f132]) ).
fof(f192,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f56,f186,f137]) ).
fof(f193,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f186,f142]) ).
fof(f194,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f186,f147]) ).
fof(f195,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f50,f186,f152]) ).
fof(f196,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f48,f186,f157]) ).
fof(f197,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f186,f162]) ).
fof(f198,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f186,f167]) ).
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_6
| spl0_17 ),
inference(avatar_split_clause,[],[f40,f200,f127]) ).
fof(f205,plain,
( spl0_7
| spl0_17 ),
inference(avatar_split_clause,[],[f38,f200,f132]) ).
fof(f206,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f36,f200,f137]) ).
fof(f207,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f200,f142]) ).
fof(f208,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f200,f147]) ).
fof(f211,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f200,f162]) ).
fof(f212,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f200,f167]) ).
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_6
| spl0_18 ),
inference(avatar_split_clause,[],[f20,f214,f127]) ).
fof(f219,plain,
( spl0_7
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f214,f132]) ).
fof(f220,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f17,f214,f137]) ).
fof(f221,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f15,f214,f142]) ).
fof(f222,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f13,f214,f147]) ).
fof(f225,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f214,f162]) ).
fof(f226,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f214,f167]) ).
fof(f227,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f3,f164]) ).
fof(f234,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f235,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c11,X0)) = multiply(sk_c10,X0)
| ~ spl0_14 ),
inference(superposition,[],[f4,f169]) ).
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_13 ),
inference(superposition,[],[f4,f227]) ).
fof(f244,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f243,f1]) ).
fof(f257,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f244,f169]) ).
fof(f266,plain,
( multiply(sk_c3,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f235,f257]) ).
fof(f268,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f266,f169]) ).
fof(f307,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f240,f257]) ).
fof(f312,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_12 ),
inference(superposition,[],[f240,f159]) ).
fof(f315,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_10 ),
inference(superposition,[],[f240,f149]) ).
fof(f332,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f315,f144]) ).
fof(f335,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f312,f154]) ).
fof(f339,plain,
( identity = sk_c10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f307,f3]) ).
fof(f353,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f240,f332]) ).
fof(f355,plain,
( identity = sk_c11
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f353,f3]) ).
fof(f358,plain,
( sk_c11 = sk_c10
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f355,f339]) ).
fof(f365,plain,
( sk_c8 = multiply(sk_c8,sk_c10)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f332,f358]) ).
fof(f366,plain,
( sk_c11 = sk_c8
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f365,f139]) ).
fof(f368,plain,
( sk_c10 = sk_c8
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f366,f358]) ).
fof(f371,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f240,f335]) ).
fof(f373,plain,
( identity = sk_c9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f371,f3]) ).
fof(f376,plain,
( sk_c10 = sk_c9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f373,f339]) ).
fof(f380,plain,
( sk_c11 != multiply(sk_c10,sk_c10)
| spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f119,f376]) ).
fof(f381,plain,
( sk_c11 != sk_c10
| spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f380,f268]) ).
fof(f382,plain,
( $false
| spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f381,f358]) ).
fof(f383,plain,
( spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f382]) ).
fof(f384,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f115,f358]) ).
fof(f386,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f384,f358]) ).
fof(f390,plain,
( sk_c10 != sk_c8
| sk_c10 != multiply(sk_c5,sk_c10)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f386,f144]) ).
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(f405,definition,
( spl0_21
<=> sk_c10 = multiply(sk_c5,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f408,plain,
( ~ spl0_21
| ~ spl0_20
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f390,f167,f162,f147,f142,f114,f399,f405]) ).
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_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f109,f358]) ).
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_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f415,f358]) ).
fof(f417,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f368,f167,f162,f147,f142,f137,f399]) ).
fof(f466,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c10 != multiply(X3,sk_c10) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f112,f376]) ).
fof(f467,plain,
( sk_c6 = multiply(sk_c7,sk_c10)
| ~ spl0_5
| ~ spl0_20 ),
inference(superposition,[],[f124,f400]) ).
fof(f469,plain,
( sk_c11 = multiply(sk_c5,sk_c10)
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f149,f400]) ).
fof(f482,plain,
( sk_c10 = multiply(sk_c5,sk_c10)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f469,f358]) ).
fof(f487,plain,
( spl0_21
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f482,f399,f167,f162,f147,f142,f405]) ).
fof(f491,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f466,f154]) ).
fof(f495,plain,
( sk_c10 != multiply(sk_c4,sk_c10)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f491]) ).
fof(f499,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f495,f159]) ).
fof(f504,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f499,f376]) ).
fof(f505,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f504]) ).
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_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f416,f164]) ).
fof(f552,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c4,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f416,f154]) ).
fof(f561,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c4,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f552,f268]) ).
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_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f551,f169]) ).
fof(f567,plain,
( ! [X0] :
( sk_c10 != sk_c9
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f561,f159]) ).
fof(f568,plain,
( ! [X0] :
( sk_c11 != sk_c10
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f562,f257]) ).
fof(f572,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f567,f376]) ).
fof(f573,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f568,f358]) ).
fof(f577,plain,
( spl0_28
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f572,f167,f162,f157,f152,f147,f142,f108,f532]) ).
fof(f578,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f573,f358]) ).
fof(f582,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f578,f358]) ).
fof(f586,plain,
( spl0_28
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f582,f167,f162,f147,f142,f108,f532]) ).
fof(f649,plain,
( sk_c10 != inverse(sk_c6)
| sk_c6 != multiply(sk_c7,sk_c10)
| ~ spl0_7
| ~ spl0_28 ),
inference(superposition,[],[f533,f134]) ).
fof(f690,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f3,f174]) ).
fof(f776,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_18 ),
inference(superposition,[],[f240,f216]) ).
fof(f777,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c11,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f216]) ).
fof(f778,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f776,f202]) ).
fof(f792,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(f812,definition,
( spl0_31
<=> sk_c11 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f813,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f822,definition,
( spl0_33
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f823,plain,
( sk_c11 = sk_c10
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f833,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(f834,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f850,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,[],[f792,f216]) ).
fof(f858,definition,
( spl0_37
<=> sk_c11 = multiply(sk_c11,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f859,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f861,plain,
( spl0_34
| ~ spl0_37
| ~ spl0_33
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f850,f214,f200,f108,f822,f858,f833]) ).
fof(f865,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c2,multiply(sk_c10,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f188]) ).
fof(f900,definition,
( spl0_39
<=> sk_c10 = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f1146,plain,
( sk_c10 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f649,f467]) ).
fof(f1162,plain,
( sk_c10 != sk_c8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_demodulation,[],[f1146,f129]) ).
fof(f1168,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1162,f400]) ).
fof(f1169,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f1168]) ).
fof(f1188,plain,
( multiply(sk_c1,sk_c11) = multiply(sk_c10,sk_c10)
| ~ spl0_18
| ~ spl0_37 ),
inference(superposition,[],[f777,f859]) ).
fof(f1190,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_37 ),
inference(superposition,[],[f240,f859]) ).
fof(f1192,plain,
( identity = sk_c10
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1190,f3]) ).
fof(f1194,plain,
( sk_c11 = multiply(sk_c1,sk_c11)
| ~ spl0_18
| ~ spl0_31
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1188,f813]) ).
fof(f1196,plain,
( sk_c11 = sk_c10
| ~ spl0_18
| ~ spl0_31
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1194,f216]) ).
fof(f1209,plain,
( spl0_33
| ~ spl0_18
| ~ spl0_31
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1196,f858,f812,f214,f822]) ).
fof(f1211,definition,
( spl0_52
<=> sk_c10 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1212,plain,
( sk_c10 = multiply(sk_c1,sk_c10)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f1225,plain,
( sk_c10 = multiply(sk_c1,sk_c10)
| ~ spl0_18
| ~ spl0_33 ),
inference(superposition,[],[f216,f823]) ).
fof(f1230,plain,
( spl0_52
| ~ spl0_18
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f1225,f822,f214,f1211]) ).
fof(f1242,plain,
( sk_c10 != inverse(sk_c1)
| sk_c11 != inverse(inverse(sk_c1))
| ~ spl0_18
| ~ spl0_34 ),
inference(superposition,[],[f834,f216]) ).
fof(f1253,plain,
( sk_c11 != sk_c10
| sk_c11 != inverse(inverse(sk_c1))
| ~ spl0_17
| ~ spl0_18
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1242,f202]) ).
fof(f1270,plain,
( spl0_37
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f778,f214,f200,f858]) ).
fof(f1271,plain,
( sk_c11 != inverse(sk_c11)
| sk_c11 != sk_c10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_34 ),
inference(forward_demodulation,[],[f1253,f202]) ).
fof(f1273,definition,
( spl0_58
<=> sk_c11 = inverse(sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f1275,plain,
( sk_c11 != inverse(sk_c11)
| spl0_58 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f1276,plain,
( ~ spl0_33
| ~ spl0_58
| ~ spl0_17
| ~ spl0_18
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f1271,f833,f214,f200,f1273,f822]) ).
fof(f1489,plain,
( sk_c10 = multiply(sk_c10,sk_c2)
| ~ spl0_15
| ~ spl0_37 ),
inference(forward_demodulation,[],[f690,f1192]) ).
fof(f1604,plain,
( multiply(sk_c2,sk_c10) = multiply(sk_c9,sk_c2)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_37 ),
inference(superposition,[],[f865,f1489]) ).
fof(f1607,plain,
( sk_c2 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_15
| ~ spl0_37 ),
inference(superposition,[],[f240,f1489]) ).
fof(f1609,plain,
( identity = sk_c2
| ~ spl0_15
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1607,f3]) ).
fof(f1613,plain,
( sk_c10 = sk_c2
| ~ spl0_15
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1609,f1192]) ).
fof(f1626,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_15
| ~ spl0_37 ),
inference(superposition,[],[f174,f1613]) ).
fof(f1638,plain,
( spl0_39
| ~ spl0_15
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1626,f858,f172,f900]) ).
fof(f1640,plain,
( multiply(sk_c9,sk_c10) = multiply(sk_c10,sk_c10)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1604,f1613]) ).
fof(f1642,plain,
( sk_c11 = multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1640,f118]) ).
fof(f1660,plain,
( spl0_31
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f1642,f858,f186,f172,f117,f812]) ).
fof(f1673,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_33
| spl0_58 ),
inference(superposition,[],[f1275,f823]) ).
fof(f1675,plain,
( ~ spl0_39
| ~ spl0_33
| spl0_58 ),
inference(avatar_split_clause,[],[f1673,f1273,f822,f900]) ).
fof(f1676,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_33 ),
inference(forward_demodulation,[],[f115,f823]) ).
fof(f1678,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_3
| ~ spl0_33 ),
inference(forward_demodulation,[],[f1676,f823]) ).
fof(f1682,plain,
( sk_c11 != sk_c10
| sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_33 ),
inference(superposition,[],[f1678,f202]) ).
fof(f1687,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f1682,f823]) ).
fof(f1688,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_33
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1687,f1212]) ).
fof(f1689,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_33
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f1688]) ).
fof(f1692,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c2,sk_c10)
| ~ spl0_2
| ~ spl0_15 ),
inference(superposition,[],[f112,f174]) ).
fof(f1693,plain,
( sk_c9 != multiply(sk_c2,sk_c10)
| ~ spl0_2
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f1692]) ).
fof(f1694,plain,
( $false
| ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1693,f188]) ).
fof(f1695,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1694]) ).
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(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f145]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f150]) ).
cnf(s9,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f155]) ).
cnf(s10,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f160]) ).
cnf(s11,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f165]) ).
cnf(s12,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f170]) ).
cnf(s13,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f175]) ).
cnf(s14,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f176]) ).
cnf(s15,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f177]) ).
cnf(s16,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f178]) ).
cnf(s17,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f179]) ).
cnf(s18,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f180]) ).
cnf(s19,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f181]) ).
cnf(s20,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f182]) ).
cnf(s21,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f183]) ).
cnf(s22,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f184]) ).
cnf(s23,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f189]) ).
cnf(s24,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f190]) ).
cnf(s25,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f191]) ).
cnf(s26,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f192]) ).
cnf(s27,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f193]) ).
cnf(s28,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f194]) ).
cnf(s29,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f195]) ).
cnf(s30,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f196]) ).
cnf(s31,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f197]) ).
cnf(s32,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f198]) ).
cnf(s33,plain,
( spl0_5
| spl0_17 ),
inference(sat_conversion,[],[f203]) ).
cnf(s34,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f204]) ).
cnf(s35,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s36,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f206]) ).
cnf(s37,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f207]) ).
cnf(s38,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f208]) ).
cnf(s41,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f211]) ).
cnf(s42,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f212]) ).
cnf(s43,plain,
( spl0_5
| spl0_18 ),
inference(sat_conversion,[],[f217]) ).
cnf(s44,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f218]) ).
cnf(s45,plain,
( spl0_7
| spl0_18 ),
inference(sat_conversion,[],[f219]) ).
cnf(s46,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f220]) ).
cnf(s47,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f221]) ).
cnf(s48,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f222]) ).
cnf(s51,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f225]) ).
cnf(s52,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f226]) ).
cnf(s53,plain,
( spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f383]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f408]) ).
cnf(s57,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f417]) ).
cnf(s63,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f487]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f505]) ).
cnf(s74,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_28 ),
inference(sat_conversion,[],[f577]) ).
cnf(s75,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_10
| ~ spl0_13
| ~ spl0_14
| spl0_28 ),
inference(sat_conversion,[],[f586]) ).
cnf(s109,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| spl0_34
| ~ spl0_37 ),
inference(sat_conversion,[],[f861]) ).
cnf(s143,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| ~ spl0_28 ),
inference(sat_conversion,[],[f1169]) ).
cnf(s152,plain,
( ~ spl0_18
| ~ spl0_31
| spl0_33
| ~ spl0_37 ),
inference(sat_conversion,[],[f1209]) ).
cnf(s157,plain,
( ~ spl0_18
| ~ spl0_33
| spl0_52 ),
inference(sat_conversion,[],[f1230]) ).
cnf(s166,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_37 ),
inference(sat_conversion,[],[f1270]) ).
cnf(s167,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_33
| ~ spl0_34
| ~ spl0_58 ),
inference(sat_conversion,[],[f1276]) ).
cnf(s249,plain,
( ~ spl0_15
| ~ spl0_37
| spl0_39 ),
inference(sat_conversion,[],[f1638]) ).
cnf(s261,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| spl0_31
| ~ spl0_37 ),
inference(sat_conversion,[],[f1660]) ).
cnf(s266,plain,
( ~ spl0_33
| ~ spl0_39
| spl0_58 ),
inference(sat_conversion,[],[f1675]) ).
cnf(s272,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_33
| ~ spl0_52 ),
inference(sat_conversion,[],[f1689]) ).
cnf(s273,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f1695]) ).
cnf(s274,plain,
spl0_4,
inference(rat,[],[s53,s7,s8,s9,s10,s11,s12]) ).
cnf(s275,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s272,s157,s152,s261,s166,s22,s32,s42,s52,s274]) ).
cnf(s276,plain,
( spl0_13
| ~ spl0_3 ),
inference(rat,[],[s272,s157,s152,s261,s166,s21,s31,s41,s51,s274]) ).
cnf(s277,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_3 ),
inference(rat,[],[s55,s63,s57,s275,s276]) ).
cnf(s278,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s272,s157,s152,s261,s166,s18,s28,s38,s48,s274]) ).
cnf(s279,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s272,s157,s152,s261,s166,s17,s27,s37,s47,s274]) ).
cnf(s280,plain,
( ~ spl0_9
| ~ spl0_3
| ~ spl0_10 ),
inference(rat,[],[s272,s157,s152,s261,s166,s16,s26,s36,s46,s277,s274]) ).
cnf(s281,plain,
~ spl0_3,
inference(rat,[],[s280,s279,s278]) ).
cnf(s282,plain,
( spl0_16
| ~ spl0_2 ),
inference(rat,[],[s66,s29,s30,s31,s32]) ).
cnf(s283,plain,
( ~ spl0_16
| ~ spl0_2 ),
inference(rat,[],[s66,s19,s20,s21,s22,s273]) ).
cnf(s284,plain,
~ spl0_2,
inference(rat,[],[s283,s282]) ).
cnf(s285,plain,
spl0_1,
inference(rat,[],[s2,s274,s281,s284]) ).
cnf(s286,plain,
( spl0_14
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s109,s167,s266,s152,s261,s249,s166,s42,s52,s285,s274]) ).
cnf(s287,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s109,s167,s266,s152,s261,s249,s166,s285,s274]) ).
cnf(s288,plain,
( spl0_18
| ~ spl0_13
| ~ spl0_10
| ~ spl0_9
| ~ spl0_14 ),
inference(rat,[],[s143,s57,s43,s44,s45,s46,s75,s285]) ).
cnf(s289,plain,
( ~ spl0_13
| ~ spl0_10
| ~ spl0_9
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s143,s57,s33,s34,s35,s36,s287,s288,s75,s286,s285]) ).
cnf(s290,plain,
( spl0_13
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s287,s41,s51]) ).
cnf(s291,plain,
( spl0_10
| ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s287,s38,s48]) ).
cnf(s292,plain,
( ~ spl0_10
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16 ),
inference(rat,[],[s287,s37,s47,s289]) ).
cnf(s293,plain,
( ~ spl0_16
| ~ spl0_15 ),
inference(rat,[],[s292,s291,s290]) ).
cnf(s294,plain,
spl0_16,
inference(rat,[],[s143,s57,s74,s23,s24,s25,s26,s27,s28,s29,s30,s31,s32,s285]) ).
cnf(s295,plain,
~ spl0_15,
inference(rat,[],[s293,s294]) ).
cnf(s296,plain,
spl0_14,
inference(rat,[],[s22,s295]) ).
cnf(s297,plain,
spl0_13,
inference(rat,[],[s21,s295]) ).
cnf(s298,plain,
spl0_12,
inference(rat,[],[s20,s295]) ).
cnf(s299,plain,
spl0_11,
inference(rat,[],[s19,s295]) ).
cnf(s300,plain,
spl0_10,
inference(rat,[],[s18,s295]) ).
cnf(s301,plain,
spl0_9,
inference(rat,[],[s17,s295]) ).
cnf(s302,plain,
spl0_8,
inference(rat,[],[s16,s295]) ).
cnf(s303,plain,
spl0_7,
inference(rat,[],[s15,s295]) ).
cnf(s304,plain,
spl0_6,
inference(rat,[],[s14,s295]) ).
cnf(s305,plain,
spl0_5,
inference(rat,[],[s13,s295]) ).
cnf(s306,plain,
spl0_28,
inference(rat,[],[s74,s296,s298,s297,s300,s301,s285,s299]) ).
cnf(s308,plain,
spl0_20,
inference(rat,[],[s57,s296,s297,s300,s301,s302]) ).
cnf(s310,plain,
$false,
inference(rat,[],[s143,s306,s304,s305,s303,s308]) ).
fof(f1698,plain,
$false,
inference(avatar_sat_refutation,[],[s310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP263-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:43:10 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.32/1.33 % (2740128)Input is clausal, will run a generic CNF schedule.
% 3.32/1.33 % (2740134)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3334115167:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.32/1.33 % (2740133)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=3794677980:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.32/1.33 % (2740139)dis-21_1_sil=8000:lcm=predicate:random_seed=1269366901: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)
% 3.32/1.33 % (2740136)lrs+10_1_sil=8000:sp=occurrence:random_seed=2488610367:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.32/1.33 % (2740137)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1774750019:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.32/1.33 % (2740135)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3452396788:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.32/1.33 % (2740138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3477621778:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.32/1.33 % (2740139)Refutation not found, incomplete strategy
% 3.32/1.33 % (2740139)------------------------------
% 3.32/1.33 % (2740139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.33 % (2740139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.33 % (2740139)CaDiCaL version: 2.1.3
% 3.32/1.33 % (2740139)Termination reason: Refutation not found, incomplete strategy
% 3.32/1.33 % (2740139)Time elapsed: 0.002 s
% 3.32/1.33 % (2740139)Peak memory usage: 88 MB
% 3.32/1.33 % (2740139)Instructions burned: 2 (million)
% 3.32/1.33 % (2740136)Refutation not found, incomplete strategy
% 3.32/1.33 % (2740136)------------------------------
% 3.32/1.33 % (2740136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.33 % (2740136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.33 % (2740136)CaDiCaL version: 2.1.3
% 3.32/1.33 % (2740136)Termination reason: Refutation not found, incomplete strategy
% 3.32/1.33 % (2740136)Time elapsed: 0.004 s
% 3.32/1.33 % (2740136)Peak memory usage: 88 MB
% 3.32/1.33 % (2740136)Instructions burned: 5 (million)
% 3.32/1.33 % (2740138)First to succeed.
% 3.32/1.33 % (2740138)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2740128"
% 3.32/1.33 % (2740137)Instruction limit reached!
% 3.32/1.33 % (2740137)------------------------------
% 3.32/1.33 % (2740137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.33 % (2740137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.33 % (2740137)CaDiCaL version: 2.1.3
% 3.32/1.33 % (2740137)Termination reason: Instruction limit
% 3.32/1.33 % (2740137)Termination phase: Saturation
% 3.32/1.33 % (2740137)Time elapsed: 0.065 s
% 3.32/1.33 % (2740137)Peak memory usage: 89 MB
% 3.32/1.33 % (2740137)Instructions burned: 114 (million)
% 3.32/1.33 % (2740147)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=1041876618:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.32/1.33 % (2740136)------------------------------
% 3.32/1.33 % (2740136)------------------------------
% 3.32/1.33 % (2740139)------------------------------
% 3.32/1.33 % (2740139)------------------------------
% 3.32/1.33 % (2740147)Refutation not found, incomplete strategy
% 3.32/1.33 % (2740147)------------------------------
% 3.32/1.33 % (2740147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.33 % (2740147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.33 % (2740147)CaDiCaL version: 2.1.3
% 3.32/1.33 % (2740147)Termination reason: Refutation not found, incomplete strategy
% 3.32/1.33 % (2740147)Time elapsed: 0.004 s
% 3.32/1.33 % (2740147)Peak memory usage: 88 MB
% 3.32/1.33 % (2740147)Instructions burned: 5 (million)
% 3.32/1.33 % (2740138)Refutation found. Thanks to Tanya!
% 3.32/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.32/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.53 % (2740138)------------------------------
% 3.91/1.53 % (2740138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.53 % (2740138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.53 % (2740138)CaDiCaL version: 2.1.3
% 3.91/1.53 % (2740138)Termination reason: Refutation
% 3.91/1.53 % (2740138)Time elapsed: 0.038 s
% 3.91/1.53 % (2740138)Peak memory usage: 90 MB
% 3.91/1.53 % (2740138)Instructions burned: 58 (million)
% 3.91/1.53 % (2740138)------------------------------
% 3.91/1.53 % (2740138)------------------------------
% 3.91/1.53 % (2740128)Success in time 0.47 s
% 3.91/1.53 % Vampire exiting
%------------------------------------------------------------------------------