%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP308-1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:36 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.91s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 57
% Syntax : Number of formulae : 378 ( 23 unt; 17 def)
% Number of atoms : 1379 ( 370 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1908 ( 907 ~; 984 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c8,sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c8
| multiply(sk_c8,X0) != sk_c7
| multiply(X1,sk_c8) != X0
| inverse(X1) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,X0)
| multiply(X1,sk_c8) != X0
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(equality_resolution,[],[f78]) ).
fof(f81,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f85,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f88,plain,
( ! [X2] :
( sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X1] :
( sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c8 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f95,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f97,definition,
( spl0_6
<=> sk_c6 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = inverse(sk_c8)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( sk_c6 != inverse(sk_c8)
| spl0_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_7
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f102,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_7 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f79,f101,f97,f93,f90,f87,f84,f81]) ).
fof(f106,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f108,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f112,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f76,f110,f106]) ).
fof(f115,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f117,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f74,f110,f115]) ).
fof(f120,definition,
( spl0_11
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f122,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f110,f120]) ).
fof(f125,definition,
( spl0_12
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f127,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f70,f110,f125]) ).
fof(f130,definition,
( spl0_13
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f132,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_13
| spl0_9 ),
inference(avatar_split_clause,[],[f68,f110,f130]) ).
fof(f135,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f137,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_14
| spl0_9 ),
inference(avatar_split_clause,[],[f66,f110,f135]) ).
fof(f140,definition,
( spl0_15
<=> sk_c2 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f142,plain,
( sk_c2 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f64,f140,f106]) ).
fof(f144,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f62,f140,f115]) ).
fof(f145,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f140,f120]) ).
fof(f146,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f58,f140,f125]) ).
fof(f147,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f56,f140,f130]) ).
fof(f148,plain,
( spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f140,f135]) ).
fof(f150,definition,
( spl0_16
<=> sk_c7 = multiply(sk_c8,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f152,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f150,f106]) ).
fof(f154,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f50,f150,f115]) ).
fof(f155,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f48,f150,f120]) ).
fof(f156,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f150,f125]) ).
fof(f157,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f150,f130]) ).
fof(f158,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f42,f150,f135]) ).
fof(f159,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f40,f93,f106]) ).
fof(f160,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f38,f93,f115]) ).
fof(f161,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f36,f93,f120]) ).
fof(f162,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f34,f93,f125]) ).
fof(f163,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f32,f93,f130]) ).
fof(f164,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f30,f93,f135]) ).
fof(f165,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f28,f97,f106]) ).
fof(f166,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f26,f97,f115]) ).
fof(f167,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f24,f97,f120]) ).
fof(f168,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f22,f97,f125]) ).
fof(f169,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f20,f97,f130]) ).
fof(f170,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f18,f97,f135]) ).
fof(f171,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f101,f106]) ).
fof(f172,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f101,f115]) ).
fof(f173,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f101,f120]) ).
fof(f174,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f10,f101,f125]) ).
fof(f175,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f101,f130]) ).
fof(f176,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f101,f135]) ).
fof(f177,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f117]) ).
fof(f178,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f122]) ).
fof(f179,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f3,f132]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_14 ),
inference(superposition,[],[f4,f137]) ).
fof(f185,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f108]) ).
fof(f186,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f182,f1]) ).
fof(f193,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f179]) ).
fof(f194,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f193,f1]) ).
fof(f207,plain,
( multiply(sk_c6,sk_c3) = multiply(sk_c5,identity)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f185,f179]) ).
fof(f225,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_11 ),
inference(superposition,[],[f186,f178]) ).
fof(f227,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_10 ),
inference(superposition,[],[f186,f177]) ).
fof(f230,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_14 ),
inference(superposition,[],[f186,f137]) ).
fof(f232,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f186,f127]) ).
fof(f241,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f232,f122]) ).
fof(f243,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f230,f132]) ).
fof(f245,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f186,f241]) ).
fof(f247,plain,
( identity = sk_c6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f245,f3]) ).
fof(f250,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f183,f243]) ).
fof(f251,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f186,f243]) ).
fof(f253,plain,
( identity = sk_c7
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f251,f3]) ).
fof(f254,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f250,f137]) ).
fof(f258,plain,
( sk_c7 = sk_c6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f253,f247]) ).
fof(f261,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f225,f247]) ).
fof(f269,plain,
( sk_c5 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f227,f247]) ).
fof(f270,plain,
( identity = sk_c5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f269,f3]) ).
fof(f271,plain,
( sk_c6 = sk_c5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f270,f247]) ).
fof(f272,plain,
( sk_c7 = sk_c5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f271,f258]) ).
fof(f276,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f108,f272]) ).
fof(f279,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f276,f258]) ).
fof(f286,plain,
( sk_c4 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f261,f258]) ).
fof(f287,plain,
( identity = sk_c4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f286,f3]) ).
fof(f288,plain,
( sk_c6 = sk_c4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f287,f247]) ).
fof(f289,plain,
( sk_c7 = sk_c4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f288,f258]) ).
fof(f321,plain,
( multiply(sk_c6,sk_c3) = multiply(sk_c5,sk_c6)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f207,f247]) ).
fof(f322,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c5,sk_c7)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f321,f258]) ).
fof(f323,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f322,f272]) ).
fof(f338,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f186,f279]) ).
fof(f340,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f338,f3]) ).
fof(f344,plain,
( sk_c7 = multiply(sk_c7,sk_c3)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f323,f254]) ).
fof(f345,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f340,f253]) ).
fof(f351,plain,
( sk_c3 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f186,f344]) ).
fof(f353,plain,
( identity = sk_c3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f351,f3]) ).
fof(f355,plain,
( sk_c6 = sk_c3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f353,f247]) ).
fof(f357,plain,
( sk_c7 = sk_c3
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f355,f258]) ).
fof(f359,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f132,f357]) ).
fof(f367,plain,
( sk_c8 != multiply(sk_c6,sk_c8)
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f95,f345]) ).
fof(f388,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f367,f258]) ).
fof(f395,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f388,f279]) ).
fof(f397,plain,
( $false
| spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f395,f345]) ).
fof(f398,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f400,plain,
( sk_c8 = multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f94,f345]) ).
fof(f401,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f103,f258]) ).
fof(f402,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f400,f258]) ).
fof(f403,plain,
( sk_c8 != sk_c7
| spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f401,f243]) ).
fof(f404,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f402,f345]) ).
fof(f405,plain,
( $false
| spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f403,f345]) ).
fof(f406,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f407,plain,
( sk_c7 != inverse(sk_c8)
| spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f99,f258]) ).
fof(f409,plain,
( sk_c8 != inverse(sk_c8)
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f407,f345]) ).
fof(f424,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c8,X0))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f4,f404]) ).
fof(f437,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f186,f424]) ).
fof(f440,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f437,f186]) ).
fof(f471,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f359,f345]) ).
fof(f472,plain,
( $false
| spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f471,f409]) ).
fof(f473,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f474,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f85,f345]) ).
fof(f475,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f98,f258]) ).
fof(f476,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f474,f258]) ).
fof(f477,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f475,f345]) ).
fof(f478,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f476,f345]) ).
fof(f479,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f478,f345]) ).
fof(f486,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f479,f477]) ).
fof(f492,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f486]) ).
fof(f497,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f492,f404]) ).
fof(f498,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f497]) ).
fof(f511,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f82,f258]) ).
fof(f512,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f511,f345]) ).
fof(f513,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f512,f258]) ).
fof(f514,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f513,f345]) ).
fof(f515,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f514,f477]) ).
fof(f521,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f515]) ).
fof(f526,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f521,f404]) ).
fof(f527,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f540,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f91,f440]) ).
fof(f541,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(X1,sk_c8) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f540,f345]) ).
fof(f545,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f541,f122]) ).
fof(f550,plain,
( sk_c8 != multiply(sk_c4,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f545,f345]) ).
fof(f556,plain,
( sk_c8 != multiply(sk_c7,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f550,f289]) ).
fof(f562,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f556,f279]) ).
fof(f565,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f562,f345]) ).
fof(f566,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f629,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_9 ),
inference(superposition,[],[f3,f112]) ).
fof(f667,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_15 ),
inference(superposition,[],[f186,f142]) ).
fof(f669,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f667,f112]) ).
fof(f709,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_16 ),
inference(superposition,[],[f186,f152]) ).
fof(f715,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f88,f132]) ).
fof(f717,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f88,f112]) ).
fof(f718,plain,
( sk_c7 != multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f717]) ).
fof(f719,plain,
( sk_c7 != multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f715]) ).
fof(f723,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f719,f137]) ).
fof(f724,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f723]) ).
fof(f741,definition,
( spl0_18
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f742,plain,
( sk_c8 = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f792,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(sk_c8,multiply(X1,sk_c8)) )
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f91,f742]) ).
fof(f796,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c3,sk_c8))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[],[f792,f132]) ).
fof(f798,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_4
| ~ spl0_9
| ~ spl0_18 ),
inference(superposition,[],[f792,f112]) ).
fof(f799,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_4
| ~ spl0_9
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f798]) ).
fof(f800,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c3,sk_c8))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f796]) ).
fof(f802,plain,
( sk_c8 != multiply(sk_c8,sk_c2)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f799,f142]) ).
fof(f804,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f800,f194]) ).
fof(f805,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f804]) ).
fof(f807,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f802,f152]) ).
fof(f810,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f807,f742]) ).
fof(f811,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f810]) ).
fof(f812,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c8)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_18 ),
inference(forward_demodulation,[],[f85,f742]) ).
fof(f814,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f102,f742]) ).
fof(f815,plain,
( sk_c8 = multiply(sk_c6,sk_c8)
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f94,f742]) ).
fof(f816,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f709,f742]) ).
fof(f817,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c6 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_18 ),
inference(forward_demodulation,[],[f812,f742]) ).
fof(f818,plain,
( identity = sk_c2
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f816,f3]) ).
fof(f821,plain,
( identity = multiply(sk_c6,sk_c8)
| ~ spl0_6 ),
inference(superposition,[],[f3,f98]) ).
fof(f822,plain,
( sk_c2 = multiply(sk_c6,sk_c8)
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f821,f818]) ).
fof(f828,plain,
( sk_c2 = multiply(sk_c8,sk_c1)
| ~ spl0_9
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f629,f818]) ).
fof(f832,plain,
( sk_c8 != sk_c8
| sk_c6 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_18 ),
inference(superposition,[],[f817,f112]) ).
fof(f833,plain,
( sk_c6 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f832]) ).
fof(f835,plain,
( sk_c6 != sk_c2
| ~ spl0_2
| ~ spl0_9
| ~ spl0_15
| ~ spl0_18 ),
inference(forward_demodulation,[],[f833,f142]) ).
fof(f839,plain,
( sk_c8 = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f822,f815]) ).
fof(f843,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f828,f839]) ).
fof(f844,plain,
( sk_c1 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f186,f843]) ).
fof(f846,plain,
( identity = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f844,f3]) ).
fof(f847,plain,
( sk_c2 = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f846,f818]) ).
fof(f848,plain,
( sk_c8 = sk_c1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f847,f839]) ).
fof(f850,plain,
( sk_c2 = multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f142,f848]) ).
fof(f852,plain,
( sk_c6 = sk_c2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f850,f814]) ).
fof(f853,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f852,f835]) ).
fof(f854,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f853]) ).
fof(f894,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f152,f669]) ).
fof(f904,plain,
( spl0_18
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f894,f150,f140,f110,f741]) ).
fof(f921,plain,
( sk_c6 != sk_c6
| sk_c6 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f82,f98]) ).
fof(f926,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f921]) ).
fof(f937,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f926,f814]) ).
fof(f938,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f937]) ).
fof(f947,plain,
( sk_c7 != sk_c2
| ~ spl0_3
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f718,f142]) ).
fof(f955,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f947,f839]) ).
fof(f960,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f955,f742]) ).
fof(f961,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f960]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f118]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f123]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f128]) ).
cnf(s6,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f133]) ).
cnf(s7,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s9,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s10,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s11,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s12,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s13,plain,
( spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s14,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f153]) ).
cnf(s15,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f154]) ).
cnf(s16,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f155]) ).
cnf(s17,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f156]) ).
cnf(s18,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f157]) ).
cnf(s19,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f158]) ).
cnf(s20,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f159]) ).
cnf(s21,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f160]) ).
cnf(s22,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f161]) ).
cnf(s23,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f162]) ).
cnf(s24,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f163]) ).
cnf(s25,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f164]) ).
cnf(s26,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f165]) ).
cnf(s27,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f166]) ).
cnf(s28,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f167]) ).
cnf(s29,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f168]) ).
cnf(s30,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f169]) ).
cnf(s31,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f170]) ).
cnf(s32,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f171]) ).
cnf(s33,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f172]) ).
cnf(s34,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s35,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f174]) ).
cnf(s36,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f175]) ).
cnf(s37,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f176]) ).
cnf(s38,plain,
( spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f398]) ).
cnf(s39,plain,
( spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f406]) ).
cnf(s40,plain,
( spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f473]) ).
cnf(s41,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f498]) ).
cnf(s46,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f527]) ).
cnf(s55,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f566]) ).
cnf(s62,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f724]) ).
cnf(s72,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_18 ),
inference(sat_conversion,[],[f805]) ).
cnf(s74,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f811]) ).
cnf(s75,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f854]) ).
cnf(s80,plain,
( ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f904]) ).
cnf(s83,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_18 ),
inference(sat_conversion,[],[f938]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f961]) ).
cnf(s89,plain,
spl0_5,
inference(rat,[],[s38,s20,s21,s22,s23,s24,s25]) ).
cnf(s90,plain,
spl0_6,
inference(rat,[],[s40,s26,s27,s28,s29,s30,s31]) ).
cnf(s91,plain,
spl0_7,
inference(rat,[],[s39,s32,s33,s34,s35,s36,s37]) ).
cnf(s92,plain,
( spl0_9
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s55,s3,s4,s5,s6,s7,s89]) ).
cnf(s93,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s80,s13,s19,s72,s55,s92,s89]) ).
cnf(s94,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_4 ),
inference(rat,[],[s74,s80,s12,s18]) ).
cnf(s95,plain,
( spl0_12
| spl0_18
| ~ spl0_9 ),
inference(rat,[],[s80,s11,s17]) ).
cnf(s96,plain,
( spl0_11
| spl0_18
| ~ spl0_9 ),
inference(rat,[],[s80,s10,s16]) ).
cnf(s97,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s80,s9,s15,s93,s96,s95,s72,s94,s92]) ).
cnf(s98,plain,
~ spl0_4,
inference(rat,[],[s74,s80,s2,s8,s14,s97]) ).
cnf(s99,plain,
( spl0_14
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s88,s80,s13,s19,s89,s90]) ).
cnf(s100,plain,
( ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s88,s80,s12,s18,s62,s99,s90,s89]) ).
cnf(s101,plain,
~ spl0_3,
inference(rat,[],[s62,s6,s7,s100]) ).
cnf(s102,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_2
| ~ spl0_9 ),
inference(rat,[],[s80,s75,s91,s90,s89]) ).
cnf(s103,plain,
( spl0_16
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s41,s14,s15,s16,s17,s19,s89,s90]) ).
cnf(s104,plain,
( ~ spl0_13
| ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s41,s8,s9,s10,s11,s13,s102,s103,s89,s90]) ).
cnf(s105,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s102,s12,s18,s104]) ).
cnf(s106,plain,
~ spl0_2,
inference(rat,[],[s41,s2,s3,s4,s5,s6,s7,s105,s89,s90]) ).
cnf(s107,plain,
spl0_1,
inference(rat,[],[s1,s90,s89,s98,s91,s101,s106]) ).
cnf(s108,plain,
~ spl0_18,
inference(rat,[],[s83,s91,s90,s107]) ).
cnf(s109,plain,
( spl0_16
| ~ spl0_9 ),
inference(rat,[],[s46,s14,s15,s18,s19,s95,s96,s89,s90,s107,s108]) ).
cnf(s110,plain,
~ spl0_9,
inference(rat,[],[s46,s8,s9,s12,s13,s80,s109,s96,s95,s89,s90,s107,s108]) ).
cnf(s111,plain,
spl0_14,
inference(rat,[],[s7,s110]) ).
cnf(s112,plain,
spl0_13,
inference(rat,[],[s6,s110]) ).
cnf(s113,plain,
spl0_12,
inference(rat,[],[s5,s110]) ).
cnf(s114,plain,
spl0_11,
inference(rat,[],[s4,s110]) ).
cnf(s115,plain,
spl0_10,
inference(rat,[],[s3,s110]) ).
cnf(s116,plain,
spl0_8,
inference(rat,[],[s2,s110]) ).
cnf(s117,plain,
$false,
inference(rat,[],[s46,s113,s114,s115,s107,s90,s89,s111,s116,s112]) ).
fof(f962,plain,
$false,
inference(avatar_sat_refutation,[],[s117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP308-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:51:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.54/0.91 % (260335)Input is clausal, will run a generic CNF schedule.
% 0.54/0.91 % (260345)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3739287285:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.54/0.91 % (260346)dis-21_1_sil=8000:lcm=predicate:random_seed=1708250098: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)
% 0.54/0.91 % (260343)lrs+10_1_sil=8000:sp=occurrence:random_seed=1372953377:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.54/0.91 % (260341)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3405743530:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.54/0.91 % (260344)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4287106463:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.54/0.91 % (260340)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=2682011396:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.54/0.91 % (260342)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1848596590:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.54/0.91 % (260346)Refutation not found, incomplete strategy
% 0.54/0.91 % (260346)------------------------------
% 0.54/0.91 % (260346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.91 % (260346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.91 % (260346)CaDiCaL version: 2.1.3
% 0.54/0.91 % (260346)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.91 % (260346)Time elapsed: 0.002 s
% 0.54/0.91 % (260346)Peak memory usage: 88 MB
% 0.54/0.91 % (260346)Instructions burned: 2 (million)
% 0.54/0.91 % (260343)Refutation not found, incomplete strategy
% 0.54/0.91 % (260343)------------------------------
% 0.54/0.91 % (260343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.91 % (260343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.91 % (260343)CaDiCaL version: 2.1.3
% 0.54/0.91 % (260343)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.91 % (260343)Time elapsed: 0.002 s
% 0.54/0.91 % (260343)Peak memory usage: 88 MB
% 0.54/0.91 % (260343)Instructions burned: 3 (million)
% 0.54/0.91 % (260345)First to succeed.
% 0.54/0.91 % (260345)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-260335"
% 0.54/0.91 % (260344)Instruction limit reached!
% 0.54/0.91 % (260344)------------------------------
% 0.54/0.91 % (260344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.54/0.91 % (260344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.91 % (260344)CaDiCaL version: 2.1.3
% 0.54/0.91 % (260344)Termination reason: Instruction limit
% 0.54/0.91 % (260344)Termination phase: Saturation
% 0.54/0.91 % (260344)Time elapsed: 0.065 s
% 0.54/0.91 % (260344)Peak memory usage: 89 MB
% 0.54/0.91 % (260344)Instructions burned: 115 (million)
% 0.54/0.91 % (260345)Refutation found. Thanks to Tanya!
% 0.54/0.91 % SZS status Unsatisfiable for theBenchmark
% 0.54/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.11 % (260345)------------------------------
% 2.62/1.11 % (260345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.11 % (260345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.11 % (260345)CaDiCaL version: 2.1.3
% 2.62/1.11 % (260345)Termination reason: Refutation
% 2.62/1.11 % (260345)Time elapsed: 0.011 s
% 2.62/1.11 % (260345)Peak memory usage: 90 MB
% 2.62/1.11 % (260345)Instructions burned: 32 (million)
% 2.62/1.11 % (260345)------------------------------
% 2.62/1.11 % (260345)------------------------------
% 2.62/1.11 % (260335)Success in time 0.325 s
% 2.62/1.11 % Vampire exiting
%------------------------------------------------------------------------------