%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP322-1 : 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 : n003.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 10:13:38 AM UTC 2026
% Result : Unsatisfiable 2.95s 1.28s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 55
% Syntax : Number of formulae : 316 ( 23 unt; 17 def)
% Number of atoms : 954 ( 321 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1155 ( 517 ~; 621 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/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_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c8
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(sk_c9,X4) != sk_c8
| multiply(X5,sk_c9) != X4
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c7 != multiply(sk_c9,sk_c8)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c7 != multiply(sk_c9,sk_c8)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c7 != multiply(sk_c9,sk_c8)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f79]) ).
fof(f82,definition,
( spl0_1
<=> ! [X5] :
( sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f83,plain,
( ! [X5] :
( sk_c9 != inverse(X5)
| sk_c8 != multiply(sk_c9,multiply(X5,sk_c9)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c8 != multiply(X3,sk_c9) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_3
<=> sk_c7 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( sk_c7 = multiply(sk_c9,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( sk_c7 != multiply(sk_c9,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_4
<=> ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c9 != multiply(X0,sk_c8) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,definition,
( spl0_5
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f96,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( multiply(sk_c8,sk_c9) != sk_c7
| spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_1
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f80,f95,f92,f82,f88,f85,f82]) ).
fof(f100,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f102,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f104,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f106,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f104,f100]) ).
fof(f109,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f111,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f74,f104,f109]) ).
fof(f114,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c9,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = multiply(sk_c9,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f72,f104,f114]) ).
fof(f119,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f121,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f70,f104,f119]) ).
fof(f124,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f126,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f68,f104,f124]) ).
fof(f128,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f66,f104,f88]) ).
fof(f130,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f132,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f64,f130,f100]) ).
fof(f134,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f62,f130,f109]) ).
fof(f135,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f60,f130,f114]) ).
fof(f136,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f58,f130,f119]) ).
fof(f137,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f56,f130,f124]) ).
fof(f138,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f130,f88]) ).
fof(f140,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f142,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f140,f100]) ).
fof(f144,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f140,f109]) ).
fof(f145,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f140,f114]) ).
fof(f146,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f140,f119]) ).
fof(f147,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f140,f124]) ).
fof(f148,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f140,f88]) ).
fof(f150,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f152,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f150,f100]) ).
fof(f154,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f150,f109]) ).
fof(f155,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f150,f114]) ).
fof(f156,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f150,f119]) ).
fof(f157,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f150,f124]) ).
fof(f160,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f160,f100]) ).
fof(f164,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f160,f109]) ).
fof(f165,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f160,f114]) ).
fof(f166,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f160,f119]) ).
fof(f167,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f160,f124]) ).
fof(f169,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f95,f100]) ).
fof(f170,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f95,f109]) ).
fof(f171,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f95,f114]) ).
fof(f172,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f95,f119]) ).
fof(f173,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f95,f124]) ).
fof(f174,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f95,f88]) ).
fof(f175,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f102]) ).
fof(f176,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f121]) ).
fof(f179,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f181,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f116]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f126]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c9,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f111]) ).
fof(f184,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f179,f1]) ).
fof(f187,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f175]) ).
fof(f188,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f187,f1]) ).
fof(f189,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f176]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c4,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f189,f1]) ).
fof(f191,plain,
( sk_c9 = multiply(sk_c9,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f188,f111]) ).
fof(f197,plain,
( sk_c8 = sk_c9
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f191,f116]) ).
fof(f206,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f182,f197]) ).
fof(f210,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f183,f89]) ).
fof(f220,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f210,f197]) ).
fof(f232,plain,
( identity = multiply(sk_c4,identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f176]) ).
fof(f245,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f184,f3]) ).
fof(f246,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f184,f184]) ).
fof(f249,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c9),multiply(sk_c8,X0))
| ~ spl0_9 ),
inference(superposition,[],[f184,f181]) ).
fof(f251,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_10 ),
inference(superposition,[],[f184,f176]) ).
fof(f253,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_9 ),
inference(superposition,[],[f184,f116]) ).
fof(f254,plain,
( sk_c5 = multiply(inverse(sk_c9),identity)
| ~ spl0_6 ),
inference(superposition,[],[f184,f175]) ).
fof(f255,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_11 ),
inference(superposition,[],[f184,f126]) ).
fof(f256,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c4),multiply(sk_c9,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(superposition,[],[f184,f206]) ).
fof(f267,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c9,multiply(sk_c9,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f256,f121]) ).
fof(f268,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f255,f197]) ).
fof(f269,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f253,f197]) ).
fof(f272,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(inverse(sk_c9),multiply(sk_c9,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f249,f197]) ).
fof(f274,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f268,f121]) ).
fof(f275,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f269,f3]) ).
fof(f276,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f272,f184]) ).
fof(f278,plain,
( sk_c6 = multiply(sk_c4,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f232,f275]) ).
fof(f287,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f274]) ).
fof(f289,plain,
( identity = sk_c9
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f287,f3]) ).
fof(f297,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f278]) ).
fof(f300,plain,
( sk_c6 = multiply(sk_c9,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f297,f121]) ).
fof(f301,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f300,f116]) ).
fof(f302,plain,
( sk_c9 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f301,f197]) ).
fof(f311,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f251,f275]) ).
fof(f312,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f311,f302]) ).
fof(f313,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f312,f3]) ).
fof(f314,plain,
( sk_c9 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f313,f289]) ).
fof(f315,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f121,f314]) ).
fof(f326,plain,
( sk_c5 = multiply(inverse(sk_c9),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f254,f275]) ).
fof(f327,plain,
( sk_c5 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f326,f302]) ).
fof(f328,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f327,f3]) ).
fof(f329,plain,
( sk_c6 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f328,f275]) ).
fof(f330,plain,
( sk_c9 = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f329,f302]) ).
fof(f341,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c9,X0)) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f190,f314]) ).
fof(f356,plain,
( sk_c9 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f220,f276]) ).
fof(f357,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f356,f330]) ).
fof(f360,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f357]) ).
fof(f362,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f360,f3]) ).
fof(f364,plain,
( sk_c9 = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f362,f289]) ).
fof(f407,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f267,f341]) ).
fof(f467,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c6) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f245,f275]) ).
fof(f468,plain,
( ! [X0] : multiply(inverse(inverse(X0)),sk_c9) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f467,f302]) ).
fof(f483,plain,
( ! [X0] : multiply(X0,sk_c9) = X0
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f246,f468]) ).
fof(f515,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f97,f483]) ).
fof(f532,plain,
( sk_c8 != sk_c9
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f515,f364]) ).
fof(f540,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f532,f197]) ).
fof(f541,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f542,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c9)
| inverse(X0) != sk_c8 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f93,f197]) ).
fof(f544,plain,
( ! [X0] :
( sk_c9 != X0
| inverse(X0) != sk_c8 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f542,f483]) ).
fof(f546,plain,
( ! [X0] :
( sk_c9 != X0
| inverse(X0) != sk_c9 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f544,f197]) ).
fof(f547,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(equality_resolution,[],[f546]) ).
fof(f548,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f547,f315]) ).
fof(f549,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f550,plain,
( ! [X5] :
( sk_c8 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f83,f407]) ).
fof(f551,plain,
( ! [X5] :
( sk_c8 != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f550,f483]) ).
fof(f552,plain,
( ! [X5] :
( sk_c9 != X5
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f551,f197]) ).
fof(f553,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(equality_resolution,[],[f552]) ).
fof(f554,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f553,f315]) ).
fof(f555,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f554]) ).
fof(f572,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f184,f132]) ).
fof(f574,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f572,f106]) ).
fof(f582,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f83,f106]) ).
fof(f584,plain,
( sk_c8 != multiply(sk_c9,multiply(sk_c2,sk_c9))
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f582]) ).
fof(f591,definition,
( spl0_17
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f592,plain,
( sk_c8 = sk_c9
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f595,plain,
( sk_c8 != multiply(sk_c9,sk_c3)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f584,f132]) ).
fof(f597,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f595,f142]) ).
fof(f598,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f597]) ).
fof(f604,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f86,f121]) ).
fof(f610,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f612,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| spl0_18 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f623,plain,
( sk_c8 != sk_c8
| sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f93,f152]) ).
fof(f624,plain,
( sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_4
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f623]) ).
fof(f625,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f624,f162]) ).
fof(f626,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f625]) ).
fof(f637,plain,
( sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f604]) ).
fof(f639,plain,
( ~ spl0_11
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f637,f119,f85,f124]) ).
fof(f645,plain,
( sk_c8 != sk_c9
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f86,f152]) ).
fof(f650,plain,
( sk_c8 = sk_c9
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f142,f574]) ).
fof(f660,plain,
( ~ spl0_18
| ~ spl0_17
| ~ spl0_2
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f645,f150,f85,f591,f610]) ).
fof(f661,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f650,f140,f130,f104,f591]) ).
fof(f663,plain,
( sk_c9 = multiply(sk_c1,sk_c9)
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f162,f592]) ).
fof(f664,plain,
( sk_c7 = multiply(sk_c9,sk_c9)
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f96,f592]) ).
fof(f668,plain,
( sk_c9 != multiply(sk_c1,sk_c9)
| ~ spl0_17
| spl0_18 ),
inference(forward_demodulation,[],[f612,f592]) ).
fof(f669,plain,
( $false
| ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f663,f668]) ).
fof(f670,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f671,plain,
( sk_c7 != multiply(sk_c9,sk_c9)
| spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f90,f592]) ).
fof(f677,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f664,f671]) ).
fof(f678,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f677]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f98]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f107]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f112]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f122]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f127]) ).
cnf(s8,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f128]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s10,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s11,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s12,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f136]) ).
cnf(s13,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s14,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s15,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s16,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s17,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f145]) ).
cnf(s18,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s19,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f147]) ).
cnf(s20,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s21,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s22,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s23,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s24,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s25,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s27,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f163]) ).
cnf(s28,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s29,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s30,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s31,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s33,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f169]) ).
cnf(s34,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f171]) ).
cnf(s36,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f172]) ).
cnf(s37,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s38,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f174]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f541]) ).
cnf(s40,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f549]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f555]) ).
cnf(s44,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f598]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f626]) ).
cnf(s50,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f639]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f660]) ).
cnf(s56,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f661]) ).
cnf(s58,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f670]) ).
cnf(s59,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_17 ),
inference(sat_conversion,[],[f678]) ).
cnf(s60,plain,
spl0_3,
inference(rat,[],[s56,s59,s8,s14,s20,s38]) ).
cnf(s61,plain,
spl0_5,
inference(rat,[],[s39,s33,s34,s35,s36,s37,s60]) ).
cnf(s62,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s47,s25,s31]) ).
cnf(s63,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s47,s24,s30]) ).
cnf(s64,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s47,s23,s29]) ).
cnf(s65,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s47,s22,s28]) ).
cnf(s66,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(rat,[],[s47,s21,s27,s40]) ).
cnf(s67,plain,
~ spl0_4,
inference(rat,[],[s66,s65,s64,s63,s62]) ).
cnf(s68,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s55,s58,s56,s7,s13,s19,s25,s31]) ).
cnf(s69,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s55,s58,s56,s6,s12,s18,s24,s30,s50]) ).
cnf(s70,plain,
~ spl0_2,
inference(rat,[],[s69,s68]) ).
cnf(s71,plain,
spl0_1,
inference(rat,[],[s2,s60,s61,s67,s70]) ).
cnf(s72,plain,
spl0_11,
inference(rat,[],[s44,s7,s13,s19,s71]) ).
cnf(s73,plain,
spl0_9,
inference(rat,[],[s44,s5,s11,s17,s71]) ).
cnf(s74,plain,
spl0_8,
inference(rat,[],[s44,s4,s10,s16,s71]) ).
cnf(s75,plain,
spl0_6,
inference(rat,[],[s44,s3,s9,s15,s71]) ).
cnf(s76,plain,
~ spl0_10,
inference(rat,[],[s41,s73,s72,s74,s71,s75]) ).
cnf(s79,plain,
spl0_13,
inference(rat,[],[s18,s76]) ).
cnf(s80,plain,
spl0_12,
inference(rat,[],[s12,s76]) ).
cnf(s81,plain,
spl0_7,
inference(rat,[],[s6,s76]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s44,s79,s71,s81,s80]) ).
fof(f679,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP322-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 09:51:56 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.95/1.28 % (261582)Input is clausal, will run a generic CNF schedule.
% 2.95/1.28 % (261591)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3298857373:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.95/1.28 % (261591)Instruction limit reached!
% 2.95/1.28 % (261591)------------------------------
% 2.95/1.28 % (261591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (261591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (261591)CaDiCaL version: 2.1.3
% 2.95/1.28 % (261591)Termination reason: Instruction limit
% 2.95/1.28 % (261591)Termination phase: Saturation
% 2.95/1.28 % (261591)Time elapsed: 0.036 s
% 2.95/1.28 % (261591)Peak memory usage: 89 MB
% 2.95/1.28 % (261591)Instructions burned: 115 (million)
% 2.95/1.28 % (261592)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1806362764:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.95/1.28 % (261588)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=194084821:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.95/1.28 % (261590)lrs+10_1_sil=8000:sp=occurrence:random_seed=2474110912:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.95/1.28 % (261589)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3847384290:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.95/1.28 % (261587)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=1082595743:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.95/1.28 % (261593)dis-21_1_sil=8000:lcm=predicate:random_seed=3480206522: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)
% 2.95/1.28 % (261590)Refutation not found, incomplete strategy
% 2.95/1.28 % (261590)------------------------------
% 2.95/1.28 % (261590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (261590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (261590)CaDiCaL version: 2.1.3
% 2.95/1.28 % (261590)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (261590)Time elapsed: 0.004 s
% 2.95/1.28 % (261590)Peak memory usage: 88 MB
% 2.95/1.28 % (261590)Instructions burned: 5 (million)
% 2.95/1.28 % (261593)Refutation not found, incomplete strategy
% 2.95/1.28 % (261593)------------------------------
% 2.95/1.28 % (261593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (261593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (261593)CaDiCaL version: 2.1.3
% 2.95/1.28 % (261593)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (261593)Time elapsed: 0.002 s
% 2.95/1.28 % (261593)Peak memory usage: 88 MB
% 2.95/1.28 % (261593)Instructions burned: 2 (million)
% 2.95/1.28 % (261592)First to succeed.
% 2.95/1.28 % (261592)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-261582"
% 2.95/1.28 % (261595)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=2179295884:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.95/1.28 % (261595)Refutation not found, incomplete strategy
% 2.95/1.28 % (261595)------------------------------
% 2.95/1.28 % (261595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (261595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (261595)CaDiCaL version: 2.1.3
% 2.95/1.28 % (261595)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (261595)Time elapsed: 0.002 s
% 2.95/1.28 % (261595)Peak memory usage: 88 MB
% 2.95/1.28 % (261595)Instructions burned: 5 (million)
% 2.95/1.28 % (261595)------------------------------
% 2.95/1.28 % (261595)------------------------------
% 2.95/1.28 % (261590)------------------------------
% 2.95/1.28 % (261590)------------------------------
% 2.95/1.28 % (261593)------------------------------
% 2.95/1.28 % (261593)------------------------------
% 2.95/1.28 % (261592)Refutation found. Thanks to Tanya!
% 2.95/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.95/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.48 % (261592)------------------------------
% 3.66/1.48 % (261592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.48 % (261592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.48 % (261592)CaDiCaL version: 2.1.3
% 3.66/1.48 % (261592)Termination reason: Refutation
% 3.66/1.48 % (261592)Time elapsed: 0.020 s
% 3.66/1.48 % (261592)Peak memory usage: 89 MB
% 3.66/1.48 % (261592)Instructions burned: 24 (million)
% 3.66/1.48 % (261592)------------------------------
% 3.66/1.48 % (261592)------------------------------
% 3.66/1.48 % (261582)Success in time 0.441 s
% 3.66/1.48 % Vampire exiting
%------------------------------------------------------------------------------