%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:39 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 52
% Syntax : Number of formulae : 398 ( 24 unt; 15 def)
% Number of atoms : 1705 ( 446 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 2555 (1248 ~;1292 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 125 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f36,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c3 = inverse(sk_c2)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c8
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c8) != sk_c7
| sk_c8 != multiply(sk_c7,sk_c6)
| inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c7)
| multiply(X1,X2) != sk_c7
| inverse(X1) != X2
| sk_c7 != multiply(X2,sk_c8)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f74]) ).
fof(f77,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f78,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f81,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_3
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_3 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl0_4
<=> ! [X2,X1] :
( multiply(X1,X2) != sk_c7
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f88,plain,
( ! [X2,X1] :
( multiply(X1,X2) != sk_c7
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_5
<=> sk_c8 = multiply(sk_c7,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f91,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( sk_c8 != multiply(sk_c7,sk_c6)
| spl0_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_6
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f95,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f96,plain,
( inverse(sk_c8) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f75,f94,f90,f80,f87,f83,f80,f77]) ).
fof(f99,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f103,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f105,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f106,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f73,f103,f99]) ).
fof(f108,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f110,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f71,f103,f108]) ).
fof(f113,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f115,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f69,f103,f113]) ).
fof(f118,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f119,plain,
( sk_c8 != inverse(sk_c4)
| spl0_11 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f67,f103,f118]) ).
fof(f122,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f65,f103,f83]) ).
fof(f124,definition,
( spl0_12
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f126,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f63,f124,f99]) ).
fof(f128,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f61,f124,f108]) ).
fof(f129,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f59,f124,f113]) ).
fof(f130,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f57,f124,f118]) ).
fof(f131,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f55,f124,f83]) ).
fof(f133,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f135,plain,
( sk_c7 = multiply(sk_c2,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f53,f133,f99]) ).
fof(f137,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f51,f133,f108]) ).
fof(f138,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f49,f133,f113]) ).
fof(f139,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f47,f133,f118]) ).
fof(f140,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f45,f133,f83]) ).
fof(f142,definition,
( spl0_14
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f43,f142,f99]) ).
fof(f146,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f41,f142,f108]) ).
fof(f147,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f142,f113]) ).
fof(f148,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f142,f118]) ).
fof(f151,definition,
( spl0_15
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f153,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f33,f151,f99]) ).
fof(f155,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f31,f151,f108]) ).
fof(f156,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f29,f151,f113]) ).
fof(f157,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f151,f118]) ).
fof(f159,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f23,f90,f99]) ).
fof(f160,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f21,f90,f108]) ).
fof(f161,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f19,f90,f113]) ).
fof(f162,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f17,f90,f118]) ).
fof(f163,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f15,f90,f83]) ).
fof(f164,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f94,f99]) ).
fof(f165,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f11,f94,f108]) ).
fof(f166,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f9,f94,f113]) ).
fof(f167,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f7,f94,f118]) ).
fof(f168,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f5,f94,f83]) ).
fof(f169,plain,
( sk_c8 != multiply(sk_c7,multiply(sk_c7,sk_c8))
| ~ spl0_3
| spl0_5 ),
inference(forward_demodulation,[],[f92,f84]) ).
fof(f170,plain,
( sk_c7 = multiply(sk_c5,multiply(sk_c7,sk_c8))
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f101,f84]) ).
fof(f172,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f110]) ).
fof(f173,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f120]) ).
fof(f174,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f175,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f174,f4]) ).
fof(f179,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f172]) ).
fof(f180,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(sk_c8,X0)
| ~ spl0_10 ),
inference(superposition,[],[f4,f115]) ).
fof(f181,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(multiply(sk_c7,sk_c8),X0))
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f4,f170]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c7,multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f181,f4]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f179,f1]) ).
fof(f187,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f173]) ).
fof(f188,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f187,f1]) ).
fof(f203,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f188,f115]) ).
fof(f204,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f188,f180]) ).
fof(f210,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f175,f1]) ).
fof(f212,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f175,f3]) ).
fof(f213,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f175,f175]) ).
fof(f214,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f175,f173]) ).
fof(f216,plain,
( sk_c5 = multiply(inverse(sk_c7),identity)
| ~ spl0_9 ),
inference(superposition,[],[f175,f172]) ).
fof(f217,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_9 ),
inference(superposition,[],[f175,f183]) ).
fof(f220,plain,
( multiply(sk_c7,sk_c8) = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f175,f170]) ).
fof(f221,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(inverse(sk_c5),multiply(sk_c7,X0))
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f175,f182]) ).
fof(f224,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(inverse(sk_c5),multiply(sk_c8,multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f221,f204]) ).
fof(f225,plain,
( multiply(multiply(sk_c8,sk_c8),sk_c8) = multiply(inverse(sk_c5),multiply(sk_c8,sk_c8))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f220,f203]) ).
fof(f228,plain,
( ! [X0] : multiply(sk_c5,X0) = multiply(inverse(multiply(sk_c8,sk_c8)),X0)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f217,f203]) ).
fof(f230,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f212,f213]) ).
fof(f231,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c7,multiply(sk_c8,multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f224,f110]) ).
fof(f232,plain,
( multiply(multiply(sk_c8,sk_c8),sk_c8) = multiply(sk_c7,multiply(sk_c8,sk_c8))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f225,f110]) ).
fof(f233,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,X0))))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f231,f204]) ).
fof(f234,plain,
( multiply(multiply(sk_c8,sk_c8),sk_c8) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,sk_c8)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f232,f204]) ).
fof(f235,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,X0))) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,X0))))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f233,f204]) ).
fof(f236,plain,
( multiply(sk_c8,multiply(sk_c8,sk_c8)) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,sk_c8)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f234,f4]) ).
fof(f238,plain,
( sk_c8 != multiply(multiply(sk_c8,sk_c8),multiply(multiply(sk_c8,sk_c8),sk_c8))
| ~ spl0_3
| spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f169,f203]) ).
fof(f239,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c5,multiply(multiply(sk_c8,sk_c8),sk_c8))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f170,f203]) ).
fof(f242,plain,
( ! [X0] : multiply(multiply(sk_c8,sk_c8),X0) = multiply(sk_c5,multiply(multiply(sk_c8,sk_c8),multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f182,f203]) ).
fof(f245,plain,
( ! [X0] : multiply(multiply(sk_c8,sk_c8),X0) = multiply(inverse(multiply(sk_c8,sk_c8)),multiply(multiply(sk_c8,sk_c8),multiply(sk_c8,X0)))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f242,f228]) ).
fof(f248,plain,
( multiply(sk_c8,sk_c8) = multiply(inverse(multiply(sk_c8,sk_c8)),multiply(multiply(sk_c8,sk_c8),sk_c8))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f228]) ).
fof(f249,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,multiply(multiply(sk_c8,sk_c8),sk_c8)))
| ~ spl0_3
| spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f238,f4]) ).
fof(f252,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(multiply(sk_c8,sk_c8),X0)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f175]) ).
fof(f255,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f248,f175]) ).
fof(f256,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,sk_c8))))
| ~ spl0_3
| spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f249,f4]) ).
fof(f257,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f252,f4]) ).
fof(f258,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,sk_c8)))
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f256,f235]) ).
fof(f259,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c8,sk_c8))
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f236]) ).
fof(f260,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f259,f257]) ).
fof(f261,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f260,f255]) ).
fof(f262,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f264,plain,
( inverse(sk_c8) != multiply(sk_c8,sk_c8)
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f96,f203]) ).
fof(f266,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f264,f255]) ).
fof(f272,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f175,f255]) ).
fof(f274,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f272,f3]) ).
fof(f327,plain,
( identity != inverse(identity)
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f266,f274]) ).
fof(f347,plain,
( identity = multiply(sk_c8,multiply(inverse(sk_c8),identity))
| ~ spl0_11 ),
inference(superposition,[],[f173,f214]) ).
fof(f349,plain,
( sk_c8 = inverse(multiply(inverse(sk_c8),identity))
| ~ spl0_11 ),
inference(superposition,[],[f120,f214]) ).
fof(f350,plain,
( sk_c8 = inverse(inverse(sk_c8))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f349,f230]) ).
fof(f352,plain,
( identity = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_11 ),
inference(forward_demodulation,[],[f347,f230]) ).
fof(f355,plain,
( identity = inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f350,f274]) ).
fof(f357,plain,
( identity = multiply(identity,inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f352,f274]) ).
fof(f361,plain,
( identity = inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f357,f1]) ).
fof(f364,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f361,f327]) ).
fof(f365,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f370,plain,
( sk_c7 = multiply(sk_c2,inverse(sk_c2))
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f135,f126]) ).
fof(f383,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f153]) ).
fof(f384,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_15 ),
inference(superposition,[],[f175,f383]) ).
fof(f387,plain,
( inverse(sk_c8) = sk_c1
| ~ spl0_15 ),
inference(forward_demodulation,[],[f384,f230]) ).
fof(f464,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f216,f230]) ).
fof(f465,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f105,f126]) ).
fof(f466,plain,
( sk_c8 = multiply(sk_c1,inverse(sk_c8))
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[],[f144,f95]) ).
fof(f468,plain,
( inverse(sk_c8) = multiply(sk_c2,inverse(sk_c2))
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f370,f95]) ).
fof(f470,plain,
( inverse(sk_c8) = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f465,f95]) ).
fof(f471,plain,
( sk_c8 = multiply(inverse(sk_c8),inverse(sk_c8))
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f466,f387]) ).
fof(f486,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f175,f91]) ).
fof(f489,plain,
( sk_c6 = multiply(inverse(inverse(sk_c8)),sk_c8)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f486,f95]) ).
fof(f491,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f489,f213]) ).
fof(f512,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = multiply(sk_c2,multiply(inverse(sk_c2),X0))
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f4,f468]) ).
fof(f521,plain,
( sk_c8 = multiply(inverse(inverse(sk_c2)),inverse(sk_c8))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(superposition,[],[f175,f470]) ).
fof(f523,plain,
( sk_c8 = multiply(sk_c2,inverse(sk_c8))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f521,f213]) ).
fof(f525,plain,
( multiply(sk_c7,sk_c8) != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f85,f491]) ).
fof(f526,plain,
( multiply(sk_c8,sk_c8) != multiply(inverse(sk_c8),sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f525,f95]) ).
fof(f528,plain,
( identity != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f526,f3]) ).
fof(f529,plain,
( inverse(sk_c8) = multiply(inverse(inverse(sk_c8)),sk_c8)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f175,f471]) ).
fof(f531,plain,
( inverse(sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f529,f213]) ).
fof(f558,plain,
( multiply(inverse(sk_c8),sk_c8) = multiply(sk_c2,inverse(sk_c8))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f512,f470]) ).
fof(f571,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f558,f523]) ).
fof(f578,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f571,f3]) ).
fof(f599,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f383,f578]) ).
fof(f601,plain,
( identity = multiply(inverse(identity),inverse(identity))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f471,f578]) ).
fof(f607,plain,
( identity != multiply(identity,identity)
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f528,f578]) ).
fof(f608,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f607,f1]) ).
fof(f609,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f613,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f601,f210]) ).
fof(f615,plain,
( identity = sk_c1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f599,f1]) ).
fof(f627,plain,
( ! [X4] :
( inverse(sk_c8) != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f78,f95]) ).
fof(f628,plain,
( multiply(sk_c7,sk_c8) = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f84,f491]) ).
fof(f631,plain,
( ! [X4] :
( inverse(X4) != multiply(sk_c8,sk_c8)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f627,f531]) ).
fof(f632,plain,
( multiply(sk_c7,identity) = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f628,f578]) ).
fof(f635,plain,
( ! [X4] :
( inverse(X4) != multiply(identity,identity)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f631,f578]) ).
fof(f636,plain,
( identity = multiply(sk_c7,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f632,f1]) ).
fof(f639,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f635,f1]) ).
fof(f640,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f636,f230]) ).
fof(f643,plain,
( ! [X4] :
( sk_c7 != multiply(X4,multiply(sk_c8,sk_c8))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f639,f491]) ).
fof(f645,plain,
( ! [X4] :
( sk_c7 != multiply(X4,multiply(identity,identity))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f643,f578]) ).
fof(f647,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f645,f1]) ).
fof(f649,plain,
( ! [X4] :
( sk_c7 != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f647,f230]) ).
fof(f651,plain,
( ! [X4] :
( inverse(sk_c8) != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f649,f95]) ).
fof(f652,plain,
( ! [X4] :
( multiply(sk_c8,sk_c8) != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f651,f531]) ).
fof(f653,plain,
( ! [X4] :
( multiply(identity,identity) != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f652,f578]) ).
fof(f654,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f653,f1]) ).
fof(f658,plain,
( sk_c8 = multiply(sk_c4,identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f115,f640]) ).
fof(f661,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f658,f230]) ).
fof(f666,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f661,f578]) ).
fof(f672,plain,
( sk_c8 != inverse(identity)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f119,f666]) ).
fof(f677,plain,
( identity != sk_c8
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f672,f613]) ).
fof(f682,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f677,f578]) ).
fof(f683,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f682]) ).
fof(f703,plain,
( identity != sk_c8
| identity != sk_c1
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f654,f153]) ).
fof(f704,plain,
( identity != sk_c1
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f703,f578]) ).
fof(f705,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f704,f615]) ).
fof(f706,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f705]) ).
fof(f707,plain,
( ! [X2,X1] :
( multiply(X1,X2) != inverse(sk_c8)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f88,f95]) ).
fof(f708,plain,
( ! [X2,X1] :
( multiply(X1,X2) != multiply(sk_c8,sk_c8)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f707,f531]) ).
fof(f709,plain,
( ! [X2,X1] :
( multiply(X1,X2) != multiply(identity,identity)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f708,f578]) ).
fof(f710,plain,
( ! [X2,X1] :
( identity != multiply(X1,X2)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f709,f1]) ).
fof(f711,plain,
( ! [X2,X1] :
( sk_c7 != multiply(X2,identity)
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f710,f578]) ).
fof(f712,plain,
( ! [X2,X1] :
( sk_c7 != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f711,f230]) ).
fof(f713,plain,
( ! [X2,X1] :
( inverse(sk_c8) != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f712,f95]) ).
fof(f714,plain,
( ! [X2,X1] :
( multiply(sk_c8,sk_c8) != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f713,f531]) ).
fof(f715,plain,
( ! [X2,X1] :
( multiply(identity,identity) != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f714,f578]) ).
fof(f716,plain,
( ! [X2,X1] :
( identity != multiply(X1,X2)
| identity != X2
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f715,f1]) ).
fof(f743,plain,
( identity != identity
| identity != sk_c1
| inverse(sk_c8) != sk_c1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f716,f383]) ).
fof(f751,plain,
( identity != sk_c1
| inverse(sk_c8) != sk_c1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f743]) ).
fof(f760,plain,
( inverse(sk_c8) != sk_c1
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f751,f615]) ).
fof(f774,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f760,f387]) ).
fof(f775,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f774]) ).
fof(f797,plain,
( inverse(sk_c8) = inverse(sk_c5)
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f110,f95]) ).
fof(f798,plain,
( sk_c5 = inverse(inverse(sk_c8))
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f464,f95]) ).
fof(f910,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f81,f274]) ).
fof(f1017,plain,
( ! [X3] :
( sk_c8 != multiply(X3,inverse(sk_c8))
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f910,f95]) ).
fof(f1029,plain,
( ! [X3] :
( identity != multiply(X3,inverse(identity))
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1017,f274]) ).
fof(f1041,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1029,f361]) ).
fof(f1047,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1041,f230]) ).
fof(f1061,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f81,f578]) ).
fof(f1072,plain,
( ! [X3] :
( sk_c8 != multiply(X3,inverse(sk_c8))
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1061,f95]) ).
fof(f1083,plain,
( ! [X3] :
( identity != multiply(X3,inverse(identity))
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1072,f578]) ).
fof(f1089,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1083,f613]) ).
fof(f1091,plain,
( ! [X3] :
( identity != inverse(X3)
| identity != X3 )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f1089,f230]) ).
fof(f1164,plain,
( identity != sk_c8
| identity != sk_c1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f1091,f153]) ).
fof(f1169,plain,
( identity != sk_c1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1164,f578]) ).
fof(f1170,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f1169,f615]) ).
fof(f1171,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f1170]) ).
fof(f1243,plain,
( sk_c5 = inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f798,f274]) ).
fof(f1256,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1243,f355]) ).
fof(f1354,plain,
( identity != inverse(sk_c8)
| identity != sk_c5
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1047,f797]) ).
fof(f1355,plain,
( identity != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1354,f1256]) ).
fof(f1356,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1355,f274]) ).
fof(f1357,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1356,f361]) ).
fof(f1358,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1357]) ).
fof(f1359,plain,
( ! [X2,X1] :
( multiply(X1,X2) != inverse(sk_c8)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f88,f95]) ).
fof(f1360,plain,
( ! [X2,X1] :
( multiply(X1,X2) != inverse(identity)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1359,f274]) ).
fof(f1361,plain,
( ! [X2,X1] :
( identity != multiply(X1,X2)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1360,f361]) ).
fof(f1362,plain,
( ! [X2,X1] :
( sk_c7 != multiply(X2,identity)
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1361,f274]) ).
fof(f1363,plain,
( ! [X2,X1] :
( sk_c7 != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1362,f230]) ).
fof(f1364,plain,
( ! [X2,X1] :
( inverse(sk_c8) != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1363,f95]) ).
fof(f1365,plain,
( ! [X2,X1] :
( inverse(identity) != X2
| identity != multiply(X1,X2)
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1364,f274]) ).
fof(f1366,plain,
( ! [X2,X1] :
( identity != multiply(X1,X2)
| identity != X2
| inverse(X1) != X2 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1365,f361]) ).
fof(f1374,plain,
( ! [X0] :
( identity != X0
| identity != X0
| inverse(identity) != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1366,f1]) ).
fof(f1386,plain,
( ! [X0] :
( identity != X0
| inverse(identity) != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f1374]) ).
fof(f1391,plain,
( ! [X0] :
( identity != X0
| identity != X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1386,f361]) ).
fof(f1392,plain,
( ! [X0] : identity != X0
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(duplicate_literal_removal,[],[f1391]) ).
fof(f1403,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(equality_resolution,[],[f1392]) ).
fof(f1404,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1403]) ).
fof(f1405,plain,
( ! [X4] :
( inverse(sk_c8) != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f78,f95]) ).
fof(f1406,plain,
( ! [X4] :
( inverse(X4) != inverse(identity)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1405,f274]) ).
fof(f1407,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1406,f361]) ).
fof(f1408,plain,
( ! [X4] :
( sk_c7 != multiply(X4,multiply(sk_c8,sk_c8))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1407,f491]) ).
fof(f1409,plain,
( ! [X4] :
( sk_c7 != multiply(X4,multiply(identity,identity))
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1408,f274]) ).
fof(f1410,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1409,f1]) ).
fof(f1411,plain,
( ! [X4] :
( sk_c7 != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1410,f230]) ).
fof(f1412,plain,
( ! [X4] :
( inverse(sk_c8) != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1411,f95]) ).
fof(f1413,plain,
( ! [X4] :
( inverse(identity) != X4
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1412,f274]) ).
fof(f1414,plain,
( ! [X4] :
( identity != inverse(X4)
| identity != X4 )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1413,f361]) ).
fof(f1416,plain,
( identity != inverse(sk_c8)
| identity != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1414,f797]) ).
fof(f1417,plain,
( identity != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1416,f1256]) ).
fof(f1418,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1417,f274]) ).
fof(f1419,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1418,f361]) ).
fof(f1420,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1419]) ).
cnf(s1,plain,
( spl0_2
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f106]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f111]) ).
cnf(s5,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f116]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f121]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f122]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f129]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f130]) ).
cnf(s12,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f131]) ).
cnf(s13,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s14,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s15,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s16,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s17,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s18,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s19,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s20,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s21,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s23,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s24,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s28,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f159]) ).
cnf(s29,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f160]) ).
cnf(s30,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f161]) ).
cnf(s31,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f162]) ).
cnf(s32,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f163]) ).
cnf(s33,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f164]) ).
cnf(s34,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f165]) ).
cnf(s35,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f166]) ).
cnf(s36,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f167]) ).
cnf(s37,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f168]) ).
cnf(s38,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f262]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f365]) ).
cnf(s42,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f609]) ).
cnf(s44,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f683]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f706]) ).
cnf(s46,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f775]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f1171]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f1358]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f1404]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f1420]) ).
cnf(s60,plain,
spl0_3,
inference(rat,[],[s42,s7,s12,s17,s32,s37]) ).
cnf(s61,plain,
spl0_6,
inference(rat,[],[s39,s33,s34,s35,s36,s60]) ).
cnf(s62,plain,
spl0_5,
inference(rat,[],[s38,s28,s29,s30,s31,s60]) ).
cnf(s63,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s44,s11,s16,s21,s26,s58,s60,s62,s61]) ).
cnf(s64,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s46,s10,s15,s20,s25,s61]) ).
cnf(s65,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_4
| ~ spl0_7 ),
inference(rat,[],[s46,s9,s14,s19,s24,s63,s61]) ).
cnf(s66,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s65,s64]) ).
cnf(s67,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s58,s4,s5,s6,s66,s61,s60]) ).
cnf(s68,plain,
~ spl0_4,
inference(rat,[],[s46,s3,s8,s13,s18,s23,s67,s61]) ).
cnf(s69,plain,
( spl0_11
| ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s44,s11,s16,s21,s26,s60,s62,s61]) ).
cnf(s70,plain,
( spl0_9
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s54,s9,s14,s19,s24,s61]) ).
cnf(s71,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s57,s69,s70,s60,s61]) ).
cnf(s72,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s54,s10,s15,s20,s25,s71,s61]) ).
cnf(s73,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s57,s4,s5,s6,s72,s61,s60]) ).
cnf(s74,plain,
~ spl0_2,
inference(rat,[],[s54,s3,s8,s13,s18,s23,s73,s61]) ).
cnf(s75,plain,
spl0_1,
inference(rat,[],[s2,s61,s60,s62,s68,s74]) ).
cnf(s76,plain,
( spl0_9
| ~ spl0_8 ),
inference(rat,[],[s45,s9,s14,s19,s24,s62,s61,s75]) ).
cnf(s77,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s59,s69,s76,s60,s62,s61,s75]) ).
cnf(s78,plain,
( ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s45,s10,s15,s20,s25,s77,s75,s61,s62]) ).
cnf(s79,plain,
~ spl0_7,
inference(rat,[],[s59,s4,s5,s6,s78,s60,s62,s61,s75]) ).
cnf(s80,plain,
spl0_15,
inference(rat,[],[s23,s79]) ).
cnf(s81,plain,
spl0_14,
inference(rat,[],[s18,s79]) ).
cnf(s82,plain,
spl0_13,
inference(rat,[],[s13,s79]) ).
cnf(s83,plain,
spl0_12,
inference(rat,[],[s8,s79]) ).
cnf(s84,plain,
spl0_8,
inference(rat,[],[s3,s79]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s45,s80,s84,s75,s61,s62,s83,s81,s82]) ).
fof(f1421,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP383-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:00:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.46 % (3751931)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (3751941)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1934391908:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (3751937)% WARNING: option uhcvi not known.
% 0.11/0.46 % (3751936)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3868277500_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (3751938)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3731745588:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (3751939)dis+10_1_sil=32000:sp=arity:random_seed=3490838081:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (3751940)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3498827374:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (3751942)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1075685882:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (3751937)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2480103488:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % TRYING [1]
% 0.11/0.46 % TRYING [2]
% 0.11/0.46 % TRYING [3]
% 0.11/0.46 % (3751941) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3751931-3751941"...
% 0.11/0.46 % TRYING [4]
% 0.11/0.46 % (3751941)...printing done.
% 0.11/0.46 % (3751941)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (3751941)------------------------------
% 0.11/0.46 % (3751941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (3751941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (3751941)CaDiCaL version: 2.1.3
% 0.11/0.46 % (3751941)Termination reason: Refutation
% 0.11/0.46 % (3751941)Time elapsed: 0.015 s
% 0.11/0.46 % (3751941)Peak memory usage: 12 MB
% 0.11/0.46 % (3751941)Instructions burned: 43 (million)
% 0.11/0.46 % (3751931)Success in time 0.043 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------