%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 10:13:28 AM UTC 2026
% Result : Unsatisfiable 2.62s 1.29s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 57
% Syntax : Number of formulae : 381 ( 19 unt; 18 def)
% Number of atoms : 1410 ( 348 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1978 ( 949 ~;1011 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = inverse(sk_c2)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c8) = 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_c6,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c8) = 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_c6,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c6,sk_c8) = 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_c6,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c6 = inverse(sk_c3)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c6 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(X2,sk_c6) != sk_c8
| inverse(X2) != sk_c6
| 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] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2)
| 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] :
( sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f88,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c6)
| sk_c6 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_5
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f91,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_5 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_6
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f95,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_7
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f98,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f75,f97,f94,f90,f87,f83,f80,f77]) ).
fof(f101,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f103,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f107,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f73,f105,f101]) ).
fof(f110,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f71,f105,f110]) ).
fof(f115,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f117,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f69,f105,f115]) ).
fof(f120,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f122,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f67,f105,f120]) ).
fof(f124,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f65,f105,f83]) ).
fof(f126,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c3,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f128,plain,
( sk_c8 = multiply(sk_c3,sk_c6)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f63,f126,f101]) ).
fof(f130,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f61,f126,f110]) ).
fof(f131,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f59,f126,f115]) ).
fof(f132,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f57,f126,f120]) ).
fof(f133,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f55,f126,f83]) ).
fof(f134,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f53,f90,f101]) ).
fof(f135,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f51,f90,f110]) ).
fof(f136,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f49,f90,f115]) ).
fof(f137,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f47,f90,f120]) ).
fof(f138,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f45,f90,f83]) ).
fof(f140,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f142,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f43,f140,f101]) ).
fof(f144,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f41,f140,f110]) ).
fof(f145,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f140,f115]) ).
fof(f146,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f140,f120]) ).
fof(f147,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f140,f83]) ).
fof(f149,definition,
( spl0_15
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f151,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f33,f149,f101]) ).
fof(f153,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f31,f149,f110]) ).
fof(f154,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f29,f149,f115]) ).
fof(f155,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f149,f120]) ).
fof(f156,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f149,f83]) ).
fof(f158,definition,
( spl0_16
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f160,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f23,f158,f101]) ).
fof(f162,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f21,f158,f110]) ).
fof(f163,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f19,f158,f115]) ).
fof(f164,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f17,f158,f120]) ).
fof(f165,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f15,f158,f83]) ).
fof(f167,definition,
( spl0_17
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f169,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f13,f167,f101]) ).
fof(f171,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f11,f167,f110]) ).
fof(f172,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f9,f167,f115]) ).
fof(f173,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f7,f167,f120]) ).
fof(f174,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f5,f167,f83]) ).
fof(f175,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f112]) ).
fof(f176,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_12 ),
inference(superposition,[],[f3,f122]) ).
fof(f179,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f180,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f84]) ).
fof(f181,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f175]) ).
fof(f184,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f181,f1]) ).
fof(f185,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f179,f1]) ).
fof(f194,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(superposition,[],[f184,f103]) ).
fof(f221,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_12 ),
inference(superposition,[],[f185,f176]) ).
fof(f225,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f185,f84]) ).
fof(f227,plain,
( sk_c5 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f185,f175]) ).
fof(f228,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_11 ),
inference(superposition,[],[f185,f117]) ).
fof(f237,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f228,f122]) ).
fof(f238,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f180,f237]) ).
fof(f241,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f238,f194]) ).
fof(f247,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f92,f241]) ).
fof(f249,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f185,f241]) ).
fof(f251,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f249,f3]) ).
fof(f262,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f221,f251]) ).
fof(f264,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f262,f3]) ).
fof(f265,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f264,f251]) ).
fof(f269,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f176,f265]) ).
fof(f274,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f269,f237]) ).
fof(f277,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f274,f251]) ).
fof(f279,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f227,f274]) ).
fof(f283,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f279,f3]) ).
fof(f284,plain,
( sk_c8 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f283,f251]) ).
fof(f291,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f176,f277]) ).
fof(f300,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f291,f265]) ).
fof(f303,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f300,f84]) ).
fof(f305,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f303,f251]) ).
fof(f307,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f277]) ).
fof(f308,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f307,f247]) ).
fof(f309,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f310,plain,
( ! [X2] :
( sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f88,f277]) ).
fof(f316,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c5,sk_c6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f310,f112]) ).
fof(f319,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f316,f103]) ).
fof(f322,plain,
( sk_c7 = sk_c5
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f284,f277]) ).
fof(f336,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f175,f322]) ).
fof(f339,plain,
( identity = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f336,f194]) ).
fof(f340,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f339,f251]) ).
fof(f341,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f340,f277]) ).
fof(f342,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f341,f319]) ).
fof(f343,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f342]) ).
fof(f349,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f160]) ).
fof(f352,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c8,X0))
| ~ spl0_5 ),
inference(superposition,[],[f4,f91]) ).
fof(f354,plain,
( sk_c6 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f185,f128]) ).
fof(f356,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f354,f107]) ).
fof(f357,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f356,f91]) ).
fof(f358,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_15 ),
inference(superposition,[],[f185,f151]) ).
fof(f360,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f358,f142]) ).
fof(f366,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(superposition,[],[f225,f357]) ).
fof(f367,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f366,f3]) ).
fof(f368,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_17 ),
inference(superposition,[],[f185,f169]) ).
fof(f370,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f368,f160]) ).
fof(f372,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f221,f367]) ).
fof(f374,plain,
( identity = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f372,f3]) ).
fof(f375,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f374,f367]) ).
fof(f376,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c7)
| sk_c6 != inverse(X2) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f88,f357]) ).
fof(f377,plain,
( ! [X2] :
( sk_c7 != inverse(X2)
| sk_c8 != multiply(X2,sk_c7) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f376,f357]) ).
fof(f379,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f122,f375]) ).
fof(f389,plain,
( sk_c7 != sk_c7
| sk_c8 != multiply(sk_c2,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f377,f142]) ).
fof(f391,plain,
( sk_c8 != multiply(sk_c2,sk_c7)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f389]) ).
fof(f394,plain,
( sk_c8 != sk_c6
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f391,f151]) ).
fof(f400,definition,
( spl0_19
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f401,plain,
( sk_c8 = sk_c7
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f404,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f394,f357]) ).
fof(f405,plain,
( ~ spl0_19
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f404,f149,f140,f126,f105,f90,f87,f400]) ).
fof(f416,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f349,f367]) ).
fof(f422,plain,
( sk_c1 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f185,f416]) ).
fof(f424,plain,
( identity = sk_c1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f422,f3]) ).
fof(f426,plain,
( sk_c1 = sk_c8
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f424,f367]) ).
fof(f435,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f360,f357]) ).
fof(f438,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f185,f370]) ).
fof(f440,plain,
( identity = sk_c7
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f438,f3]) ).
fof(f445,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f367,f440]) ).
fof(f457,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f78,f357]) ).
fof(f458,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f445,f167,f158,f126,f105,f90,f83,f400]) ).
fof(f459,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f457,f160]) ).
fof(f472,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f459,f426]) ).
fof(f478,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f472,f370]) ).
fof(f479,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(duplicate_literal_removal,[],[f478]) ).
fof(f480,plain,
( ~ spl0_19
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f479,f167,f158,f126,f105,f90,f83,f77,f400]) ).
fof(f506,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_19 ),
inference(forward_demodulation,[],[f81,f401]) ).
fof(f507,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c7 != multiply(X3,sk_c7) )
| ~ spl0_2
| ~ spl0_19 ),
inference(forward_demodulation,[],[f506,f401]) ).
fof(f509,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f507,f160]) ).
fof(f511,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_19 ),
inference(superposition,[],[f507,f122]) ).
fof(f519,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_2
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f511,f401]) ).
fof(f521,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f509,f401]) ).
fof(f526,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f521,f426]) ).
fof(f530,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f526,f370]) ).
fof(f533,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f530,f401]) ).
fof(f534,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f533]) ).
fof(f535,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f95,f357]) ).
fof(f545,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16 ),
inference(superposition,[],[f535,f160]) ).
fof(f558,plain,
( sk_c7 != multiply(sk_c1,sk_c7)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f545,f401]) ).
fof(f564,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f558,f426]) ).
fof(f570,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f564,f370]) ).
fof(f573,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f570,f401]) ).
fof(f574,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f573]) ).
fof(f575,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8 )
| ~ spl0_7
| ~ spl0_19 ),
inference(forward_demodulation,[],[f98,f401]) ).
fof(f576,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_7
| ~ spl0_19 ),
inference(forward_demodulation,[],[f575,f401]) ).
fof(f588,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_7
| ~ spl0_19 ),
inference(superposition,[],[f576,f1]) ).
fof(f593,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c2)
| ~ spl0_7
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f576,f151]) ).
fof(f594,plain,
( sk_c7 != inverse(identity)
| ~ spl0_7
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f588]) ).
fof(f595,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f593,f357]) ).
fof(f599,plain,
( sk_c7 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f594,f367]) ).
fof(f600,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f595,f142]) ).
fof(f601,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f606,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f599,f379]) ).
fof(f611,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f606,f401]) ).
fof(f612,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f618,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f277,f120,f115,f110,f101,f83,f400]) ).
fof(f623,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f241,f91]) ).
fof(f645,plain,
( sk_c7 = multiply(sk_c4,sk_c7)
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f117,f401]) ).
fof(f691,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f95,f623]) ).
fof(f692,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f691,f122]) ).
fof(f700,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f692,f401]) ).
fof(f705,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f700,f645]) ).
fof(f706,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f705]) ).
fof(f716,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f519,f645]) ).
fof(f717,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f716]) ).
fof(f727,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f78,f623]) ).
fof(f728,plain,
( sk_c8 != sk_c7
| sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f727,f122]) ).
fof(f736,plain,
( sk_c7 != multiply(sk_c4,sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f728,f401]) ).
fof(f741,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f736,f645]) ).
fof(f742,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f741]) ).
fof(f760,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c4)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_19 ),
inference(superposition,[],[f576,f645]) ).
fof(f762,plain,
( sk_c7 != inverse(sk_c4)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f760]) ).
fof(f765,plain,
( sk_c8 != sk_c7
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_demodulation,[],[f762,f122]) ).
fof(f769,plain,
( $false
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f765,f401]) ).
fof(f770,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f784,plain,
( sk_c7 != multiply(sk_c7,sk_c8)
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f85,f357]) ).
fof(f835,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f352,f357]) ).
fof(f887,plain,
( multiply(sk_c7,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f835,f370]) ).
fof(f914,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f887,f435]) ).
fof(f918,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f914,f784]) ).
fof(f919,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f918]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f99]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f108]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f113]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f118]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f123]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f124]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s8,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s9,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s10,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s11,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f133]) ).
cnf(s12,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f134]) ).
cnf(s13,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f135]) ).
cnf(s14,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s15,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s16,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f138]) ).
cnf(s17,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s18,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f144]) ).
cnf(s19,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s20,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s22,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f152]) ).
cnf(s23,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f153]) ).
cnf(s24,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s25,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s27,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f161]) ).
cnf(s28,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f162]) ).
cnf(s29,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f163]) ).
cnf(s30,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s31,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s32,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f170]) ).
cnf(s33,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f171]) ).
cnf(s34,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f172]) ).
cnf(s35,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f173]) ).
cnf(s36,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f174]) ).
cnf(s37,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f309]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f343]) ).
cnf(s40,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f405]) ).
cnf(s43,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f458]) ).
cnf(s48,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f480]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f534]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f574]) ).
cnf(s58,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f601]) ).
cnf(s62,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(sat_conversion,[],[f612]) ).
cnf(s63,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f618]) ).
cnf(s66,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(sat_conversion,[],[f706]) ).
cnf(s68,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(sat_conversion,[],[f717]) ).
cnf(s75,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(sat_conversion,[],[f742]) ).
cnf(s78,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_19 ),
inference(sat_conversion,[],[f770]) ).
cnf(s81,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f919]) ).
cnf(s83,plain,
spl0_3,
inference(rat,[],[s81,s6,s11,s16,s21,s26,s31,s36]) ).
cnf(s84,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s58,s43,s2,s7,s17,s22,s27,s32,s83]) ).
cnf(s85,plain,
( spl0_17
| spl0_19
| ~ spl0_8 ),
inference(rat,[],[s63,s33,s34,s35,s83]) ).
cnf(s86,plain,
( spl0_19
| ~ spl0_13
| ~ spl0_9
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s63,s28,s29,s30,s43,s85,s83]) ).
cnf(s87,plain,
( ~ spl0_19
| ~ spl0_13
| ~ spl0_9
| ~ spl0_5
| ~ spl0_7 ),
inference(rat,[],[s58,s20,s25,s62,s83]) ).
cnf(s88,plain,
( ~ spl0_13
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s87,s86,s84]) ).
cnf(s89,plain,
( spl0_13
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s78,s63,s8,s9,s10,s83]) ).
cnf(s90,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s78,s63,s3,s4,s5,s88,s89,s84,s83]) ).
cnf(s91,plain,
( spl0_19
| ~ spl0_13
| ~ spl0_9
| ~ spl0_5 ),
inference(rat,[],[s43,s27,s32,s86,s83]) ).
cnf(s92,plain,
( spl0_11
| ~ spl0_13
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s29,s34,s91,s83]) ).
cnf(s93,plain,
( spl0_10
| ~ spl0_13
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s28,s33,s91,s83]) ).
cnf(s94,plain,
( spl0_12
| ~ spl0_13
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s30,s35,s91,s83]) ).
cnf(s95,plain,
( ~ spl0_13
| ~ spl0_9
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s57,s27,s32,s66,s94,s93,s92,s91,s83]) ).
cnf(s96,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s66,s63,s7,s8,s9,s10,s83]) ).
cnf(s97,plain,
( ~ spl0_13
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s66,s63,s2,s3,s4,s5,s95,s83]) ).
cnf(s98,plain,
( ~ spl0_6
| ~ spl0_5 ),
inference(rat,[],[s97,s96]) ).
cnf(s99,plain,
( spl0_7
| ~ spl0_5
| spl0_1
| spl0_2
| spl0_4 ),
inference(rat,[],[s98,s1,s83]) ).
cnf(s100,plain,
( ~ spl0_5
| spl0_4
| spl0_2
| spl0_1 ),
inference(rat,[],[s99,s90]) ).
cnf(s101,plain,
spl0_5,
inference(rat,[],[s37,s12,s13,s14,s15,s83]) ).
cnf(s104,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s40,s19,s24,s91,s101]) ).
cnf(s105,plain,
( spl0_10
| ~ spl0_9
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s40,s18,s23,s91,s101]) ).
cnf(s106,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s40,s20,s25,s91,s101]) ).
cnf(s107,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s40,s17,s22,s38,s106,s105,s104,s91,s101,s83]) ).
cnf(s108,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s38,s2,s3,s4,s5,s83]) ).
cnf(s109,plain,
( ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s38,s7,s8,s9,s10,s107,s83]) ).
cnf(s110,plain,
~ spl0_4,
inference(rat,[],[s109,s108]) ).
cnf(s111,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s52,s29,s34,s91,s83,s101]) ).
cnf(s112,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s52,s30,s35,s68,s111,s91,s83,s101]) ).
cnf(s113,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s68,s63,s2,s3,s4,s5,s83]) ).
cnf(s114,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s68,s63,s7,s8,s9,s10,s112,s83]) ).
cnf(s115,plain,
~ spl0_2,
inference(rat,[],[s114,s113]) ).
cnf(s116,plain,
spl0_1,
inference(rat,[],[s100,s110,s101,s115]) ).
cnf(s117,plain,
( spl0_10
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s48,s28,s33,s91,s83,s101,s116]) ).
cnf(s118,plain,
( spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s48,s27,s32,s91,s83,s101,s116]) ).
cnf(s119,plain,
( spl0_11
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s48,s29,s34,s91,s83,s101,s116]) ).
cnf(s120,plain,
( ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s48,s30,s35,s75,s119,s118,s117,s91,s116,s101,s83]) ).
cnf(s121,plain,
( ~ spl0_11
| ~ spl0_12
| ~ spl0_8
| ~ spl0_10 ),
inference(rat,[],[s75,s63,s116,s101,s83]) ).
cnf(s122,plain,
spl0_9,
inference(rat,[],[s121,s2,s3,s4,s5]) ).
cnf(s123,plain,
~ spl0_13,
inference(rat,[],[s120,s122]) ).
cnf(s124,plain,
spl0_12,
inference(rat,[],[s10,s123]) ).
cnf(s125,plain,
spl0_11,
inference(rat,[],[s9,s123]) ).
cnf(s126,plain,
spl0_10,
inference(rat,[],[s8,s123]) ).
cnf(s127,plain,
spl0_8,
inference(rat,[],[s7,s123]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s121,s126,s127,s124,s125]) ).
fof(f922,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 09:46:12 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.62/1.29 % (2584007)Input is clausal, will run a generic CNF schedule.
% 2.62/1.29 % (2584013)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=306386915:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.29 % (2584012)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=642498685:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.29 % (2584015)lrs+10_1_sil=8000:sp=occurrence:random_seed=2511090827:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.29 % (2584016)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1535438012:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.29 % (2584014)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4282190497:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.29 % (2584017)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=408866742:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.29 % (2584015)Refutation not found, incomplete strategy
% 2.62/1.29 % (2584015)------------------------------
% 2.62/1.29 % (2584015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (2584015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (2584015)CaDiCaL version: 2.1.3
% 2.62/1.29 % (2584015)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.29 % (2584015)Time elapsed: 0.003 s
% 2.62/1.29 % (2584015)Peak memory usage: 88 MB
% 2.62/1.29 % (2584015)Instructions burned: 3 (million)
% 2.62/1.29 % (2584018)dis-21_1_sil=8000:lcm=predicate:random_seed=4029755358: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)
% 2.62/1.29 % (2584018)Refutation not found, incomplete strategy
% 2.62/1.29 % (2584018)------------------------------
% 2.62/1.29 % (2584018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (2584018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (2584018)CaDiCaL version: 2.1.3
% 2.62/1.29 % (2584018)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.29 % (2584018)Time elapsed: 0.002 s
% 2.62/1.29 % (2584018)Peak memory usage: 88 MB
% 2.62/1.29 % (2584018)Instructions burned: 1 (million)
% 2.62/1.29 % (2584017)First to succeed.
% 2.62/1.29 % (2584017)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2584007"
% 2.62/1.29 % (2584016)Instruction limit reached!
% 2.62/1.29 % (2584016)------------------------------
% 2.62/1.29 % (2584016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (2584016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (2584016)CaDiCaL version: 2.1.3
% 2.62/1.29 % (2584016)Termination reason: Instruction limit
% 2.62/1.29 % (2584016)Termination phase: Saturation
% 2.62/1.29 % (2584016)Time elapsed: 0.068 s
% 2.62/1.29 % (2584016)Peak memory usage: 89 MB
% 2.62/1.29 % (2584016)Instructions burned: 114 (million)
% 2.62/1.29 % (2584026)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=161079525:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.62/1.29 % (2584026)Refutation not found, incomplete strategy
% 2.62/1.29 % (2584026)------------------------------
% 2.62/1.29 % (2584026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.29 % (2584026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.29 % (2584026)CaDiCaL version: 2.1.3
% 2.62/1.29 % (2584026)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.29 % (2584026)Time elapsed: 0.003 s
% 2.62/1.29 % (2584026)Peak memory usage: 88 MB
% 2.62/1.29 % (2584026)Instructions burned: 3 (million)
% 2.62/1.29 % (2584015)------------------------------
% 2.62/1.29 % (2584015)------------------------------
% 2.62/1.29 % (2584018)------------------------------
% 2.62/1.29 % (2584018)------------------------------
% 2.62/1.29 % (2584017)Refutation found. Thanks to Tanya!
% 2.62/1.29 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.39 % (2584017)------------------------------
% 3.45/1.39 % (2584017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.39 % (2584017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.39 % (2584017)CaDiCaL version: 2.1.3
% 3.45/1.39 % (2584017)Termination reason: Refutation
% 3.45/1.39 % (2584017)Time elapsed: 0.022 s
% 3.45/1.39 % (2584017)Peak memory usage: 89 MB
% 3.45/1.39 % (2584017)Instructions burned: 32 (million)
% 3.45/1.39 % (2584017)------------------------------
% 3.45/1.39 % (2584017)------------------------------
% 3.45/1.39 % (2584007)Success in time 0.42 s
% 3.45/1.39 % Vampire exiting
%------------------------------------------------------------------------------