%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP339-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:32 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 64
% Syntax : Number of formulae : 403 ( 27 unt; 25 def)
% Number of atoms : 1148 ( 362 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1390 ( 645 ~; 720 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
multiply(sk_c8,sk_c9) = sk_c7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c9 = inverse(sk_c1)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f10]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c9 = inverse(sk_c1)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c9 = inverse(sk_c1)
| sk_c5 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f28]) ).
fof(f32,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| sk_c5 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| sk_c5 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c8 = inverse(sk_c2)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c8 = inverse(sk_c2)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
( sk_c8 = inverse(sk_c2)
| sk_c5 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != X5
| inverse(X5) != sk_c9
| multiply(X4,sk_c9) != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| inverse(X4) != X5
| sk_c9 != inverse(X5)
| multiply(X4,sk_c9) != X5 ),
inference(reorient_equations,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8)
| sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c7 != inverse(sk_c8)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) ),
inference(equality_resolution,[],[f79]) ).
fof(f82,definition,
( spl0_1
<=> ! [X4] :
( sk_c9 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f83,plain,
( ! [X4] :
( sk_c9 != inverse(inverse(X4))
| inverse(X4) != multiply(X4,sk_c9) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_3
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_4
<=> sk_c7 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f94,plain,
( sk_c7 != inverse(sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_5
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f97,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,definition,
( spl0_6
<=> ! [X1] :
( sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f100,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl0_7
<=> ! [X0] :
( inverse(X0) != sk_c9
| sk_c9 != multiply(X0,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f103,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c8)
| inverse(X0) != sk_c9 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,definition,
( spl0_8
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f106,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f80,f105,f102,f99,f96,f92,f88,f85,f82]) ).
fof(f110,definition,
( spl0_9
<=> sk_c5 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f112,plain,
( sk_c5 = multiply(sk_c6,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f114,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f77,f114,f110]) ).
fof(f119,definition,
( spl0_11
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f121,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_11
| spl0_10 ),
inference(avatar_split_clause,[],[f75,f114,f119]) ).
fof(f124,definition,
( spl0_12
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f126,plain,
( inverse(sk_c6) = sk_c5
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_12
| spl0_10 ),
inference(avatar_split_clause,[],[f73,f114,f124]) ).
fof(f129,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f131,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f132,plain,
( spl0_13
| spl0_10 ),
inference(avatar_split_clause,[],[f71,f114,f129]) ).
fof(f134,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f136,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_14
| spl0_10 ),
inference(avatar_split_clause,[],[f69,f114,f134]) ).
fof(f138,plain,
( spl0_3
| spl0_10 ),
inference(avatar_split_clause,[],[f67,f114,f88]) ).
fof(f139,plain,
( spl0_4
| spl0_10 ),
inference(avatar_split_clause,[],[f65,f114,f92]) ).
fof(f141,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f143,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_15
| spl0_10 ),
inference(avatar_split_clause,[],[f63,f114,f141]) ).
fof(f146,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f148,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_16
| spl0_10 ),
inference(avatar_split_clause,[],[f61,f114,f146]) ).
fof(f151,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f153,plain,
( sk_c9 = multiply(sk_c2,sk_c8)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f59,f151,f110]) ).
fof(f155,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f57,f151,f119]) ).
fof(f156,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f55,f151,f124]) ).
fof(f157,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f53,f151,f129]) ).
fof(f158,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f51,f151,f134]) ).
fof(f159,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f49,f151,f88]) ).
fof(f160,plain,
( spl0_4
| spl0_17 ),
inference(avatar_split_clause,[],[f47,f151,f92]) ).
fof(f161,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f45,f151,f141]) ).
fof(f162,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f43,f151,f146]) ).
fof(f164,definition,
( spl0_18
<=> sk_c9 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f166,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f41,f164,f110]) ).
fof(f168,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f39,f164,f119]) ).
fof(f169,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f37,f164,f124]) ).
fof(f170,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f35,f164,f129]) ).
fof(f171,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f33,f164,f134]) ).
fof(f173,plain,
( spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f29,f164,f92]) ).
fof(f174,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f27,f164,f141]) ).
fof(f175,plain,
( spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f25,f164,f146]) ).
fof(f177,definition,
( spl0_19
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f179,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f180,plain,
( spl0_9
| spl0_19 ),
inference(avatar_split_clause,[],[f23,f177,f110]) ).
fof(f181,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f21,f177,f119]) ).
fof(f182,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f19,f177,f124]) ).
fof(f183,plain,
( spl0_13
| spl0_19 ),
inference(avatar_split_clause,[],[f17,f177,f129]) ).
fof(f184,plain,
( spl0_14
| spl0_19 ),
inference(avatar_split_clause,[],[f15,f177,f134]) ).
fof(f186,plain,
( spl0_4
| spl0_19 ),
inference(avatar_split_clause,[],[f11,f177,f92]) ).
fof(f187,plain,
( spl0_15
| spl0_19 ),
inference(avatar_split_clause,[],[f9,f177,f141]) ).
fof(f188,plain,
( spl0_16
| spl0_19 ),
inference(avatar_split_clause,[],[f7,f177,f146]) ).
fof(f189,plain,
spl0_8,
inference(avatar_split_clause,[],[f5,f105]) ).
fof(f191,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f86,f131]) ).
fof(f192,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f191]) ).
fof(f194,plain,
( $false
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f192,f136]) ).
fof(f195,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f202,definition,
( spl0_21
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f203,plain,
( sk_c8 = sk_c7
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f206,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f93]) ).
fof(f209,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f3,f136]) ).
fof(f210,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_12 ),
inference(superposition,[],[f3,f126]) ).
fof(f211,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_11 ),
inference(superposition,[],[f3,f121]) ).
fof(f212,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f116]) ).
fof(f219,definition,
( spl0_23
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f220,plain,
( identity = sk_c8
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( identity != sk_c8
| spl0_23 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f225,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f226,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c9,X0)) = multiply(sk_c7,X0)
| ~ spl0_8 ),
inference(superposition,[],[f4,f106]) ).
fof(f227,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c7,X0)) = multiply(sk_c8,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f89]) ).
fof(f228,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f206]) ).
fof(f229,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f166]) ).
fof(f234,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f228,f1]) ).
fof(f235,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f225,f1]) ).
fof(f258,plain,
( sk_c9 = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f234,f106]) ).
fof(f283,plain,
( sk_c8 != sk_c9
| sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f86,f258]) ).
fof(f286,definition,
( spl0_24
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f287,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f288,plain,
( sk_c8 != inverse(sk_c7)
| spl0_24 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f290,definition,
( spl0_25
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f291,plain,
( sk_c8 = sk_c9
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f292,plain,
( sk_c8 != sk_c9
| spl0_25 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,plain,
( ~ spl0_24
| ~ spl0_25
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f283,f105,f92,f85,f290,f286]) ).
fof(f366,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f235,f3]) ).
fof(f367,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f235,f235]) ).
fof(f368,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c8),multiply(sk_c7,X0))
| ~ spl0_8 ),
inference(superposition,[],[f235,f226]) ).
fof(f370,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_14 ),
inference(superposition,[],[f235,f209]) ).
fof(f371,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_10 ),
inference(superposition,[],[f235,f212]) ).
fof(f381,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_18 ),
inference(superposition,[],[f235,f166]) ).
fof(f383,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f235,f148]) ).
fof(f387,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl0_12 ),
inference(superposition,[],[f235,f210]) ).
fof(f388,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f235,f153]) ).
fof(f395,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f388,f116]) ).
fof(f396,plain,
( sk_c6 = multiply(sk_c9,identity)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f387,f121]) ).
fof(f400,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f383,f143]) ).
fof(f402,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f381,f179]) ).
fof(f410,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f366,f367]) ).
fof(f419,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f106,f395]) ).
fof(f421,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c9,sk_c9)
| ~ spl0_10
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f229,f395]) ).
fof(f423,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f235,f395]) ).
fof(f425,plain,
( identity = sk_c9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_demodulation,[],[f423,f3]) ).
fof(f429,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f419,f151,f114,f105,f202]) ).
fof(f443,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_21
| spl0_24 ),
inference(superposition,[],[f288,f203]) ).
fof(f444,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(forward_demodulation,[],[f443,f93]) ).
fof(f450,plain,
( $false
| ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f444,f203]) ).
fof(f451,plain,
( ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f450]) ).
fof(f460,plain,
( inverse(sk_c8) = sk_c2
| ~ spl0_10 ),
inference(forward_demodulation,[],[f371,f410]) ).
fof(f461,plain,
( inverse(sk_c8) = sk_c4
| ~ spl0_14 ),
inference(forward_demodulation,[],[f370,f410]) ).
fof(f463,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(inverse(sk_c8),multiply(sk_c8,X0))
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f368,f203]) ).
fof(f464,plain,
( sk_c8 = multiply(sk_c1,sk_c8)
| ~ spl0_10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f421,f402]) ).
fof(f470,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f463,f235]) ).
fof(f481,plain,
( sk_c7 = sk_c4
| ~ spl0_4
| ~ spl0_14 ),
inference(forward_demodulation,[],[f461,f93]) ).
fof(f483,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_4 ),
inference(superposition,[],[f3,f93]) ).
fof(f485,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f136,f481]) ).
fof(f486,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f485,f288]) ).
fof(f487,plain,
( ~ spl0_4
| ~ spl0_14
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f486]) ).
fof(f493,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f235,f131]) ).
fof(f496,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f493,f136]) ).
fof(f497,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c9,identity)
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f227,f483]) ).
fof(f502,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f497,f396]) ).
fof(f503,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f502,f496]) ).
fof(f504,plain,
( sk_c8 != sk_c9
| sk_c9 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f97,f1]) ).
fof(f506,plain,
( identity != sk_c8
| sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_5 ),
inference(superposition,[],[f97,f3]) ).
fof(f508,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_16 ),
inference(superposition,[],[f97,f148]) ).
fof(f509,plain,
( sk_c8 != sk_c5
| sk_c9 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_9 ),
inference(superposition,[],[f97,f112]) ).
fof(f510,plain,
( sk_c9 != inverse(sk_c3)
| ~ spl0_5
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f508]) ).
fof(f512,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f510,f143]) ).
fof(f513,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f520,definition,
( spl0_28
<=> sk_c8 = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f521,plain,
( sk_c8 = sk_c5
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f531,plain,
( sk_c5 = inverse(sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f126,f503]) ).
fof(f532,plain,
( sk_c8 = sk_c5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(forward_demodulation,[],[f531,f287]) ).
fof(f533,plain,
( spl0_28
| ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f532,f286,f134,f129,f124,f119,f92,f88,f520]) ).
fof(f536,plain,
( identity != sk_c9
| sk_c9 != inverse(inverse(sk_c8))
| ~ spl0_7 ),
inference(superposition,[],[f103,f3]) ).
fof(f538,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c1)
| ~ spl0_7
| ~ spl0_18 ),
inference(superposition,[],[f103,f166]) ).
fof(f541,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_7
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f538]) ).
fof(f542,plain,
( $false
| ~ spl0_7
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f541,f179]) ).
fof(f543,plain,
( ~ spl0_7
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f545,plain,
( sk_c9 != inverse(sk_c7)
| identity != sk_c9
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f536,f93]) ).
fof(f548,definition,
( spl0_30
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f549,plain,
( identity = sk_c9
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f552,plain,
( sk_c8 != sk_c9
| identity != sk_c9
| ~ spl0_4
| ~ spl0_7
| ~ spl0_24 ),
inference(forward_demodulation,[],[f545,f287]) ).
fof(f553,plain,
( ~ spl0_30
| ~ spl0_25
| ~ spl0_4
| ~ spl0_7
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f552,f286,f102,f92,f290,f548]) ).
fof(f554,plain,
( identity = multiply(sk_c9,sk_c8)
| ~ spl0_11
| ~ spl0_28 ),
inference(superposition,[],[f211,f521]) ).
fof(f556,plain,
( sk_c9 = inverse(sk_c8)
| ~ spl0_11
| ~ spl0_28 ),
inference(superposition,[],[f121,f521]) ).
fof(f558,plain,
( identity = sk_c9
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_28 ),
inference(forward_demodulation,[],[f554,f400]) ).
fof(f559,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f558,f520,f146,f141,f119,f548]) ).
fof(f560,plain,
( sk_c9 != inverse(sk_c7)
| multiply(sk_c8,sk_c9) != sk_c7
| ~ spl0_1
| ~ spl0_4 ),
inference(superposition,[],[f83,f93]) ).
fof(f565,plain,
( sk_c9 != inverse(sk_c5)
| sk_c5 != multiply(sk_c6,sk_c9)
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[],[f83,f126]) ).
fof(f568,plain,
( sk_c5 != multiply(sk_c6,sk_c9)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f565,f121]) ).
fof(f581,plain,
( sk_c9 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f560,f106]) ).
fof(f583,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f568,f112]) ).
fof(f584,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f583]) ).
fof(f588,plain,
( sk_c8 != sk_c9
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_demodulation,[],[f581,f287]) ).
fof(f592,plain,
( ~ spl0_25
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f588,f286,f105,f92,f82,f290]) ).
fof(f595,plain,
( sk_c8 != sk_c9
| spl0_23
| ~ spl0_30 ),
inference(superposition,[],[f221,f549]) ).
fof(f597,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_30 ),
inference(superposition,[],[f1,f549]) ).
fof(f598,plain,
( ~ spl0_25
| spl0_23
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f595,f548,f219,f290]) ).
fof(f601,plain,
( identity != sk_c9
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_6 ),
inference(superposition,[],[f100,f3]) ).
fof(f603,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_18 ),
inference(superposition,[],[f100,f166]) ).
fof(f606,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f603]) ).
fof(f607,plain,
( sk_c8 != sk_c9
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f606,f179]) ).
fof(f609,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_6
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f601,f549]) ).
fof(f612,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_30 ),
inference(forward_demodulation,[],[f609,f93]) ).
fof(f613,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_24
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f612,f287]) ).
fof(f614,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_24
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f638,plain,
( sk_c9 = sk_c7
| ~ spl0_4
| ~ spl0_11
| ~ spl0_28 ),
inference(superposition,[],[f93,f556]) ).
fof(f660,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_28 ),
inference(superposition,[],[f131,f638]) ).
fof(f672,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_28 ),
inference(forward_demodulation,[],[f660,f481]) ).
fof(f676,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_28 ),
inference(forward_demodulation,[],[f672,f638]) ).
fof(f679,plain,
( sk_c8 = sk_c9
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_28
| ~ spl0_30 ),
inference(forward_demodulation,[],[f676,f597]) ).
fof(f680,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f679,f292]) ).
fof(f681,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f690,plain,
( ~ spl0_25
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f607,f177,f164,f99,f290]) ).
fof(f694,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f425,f151,f114,f548]) ).
fof(f696,plain,
( sk_c8 = sk_c9
| ~ spl0_10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f166,f464]) ).
fof(f717,plain,
( spl0_25
| ~ spl0_10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f696,f177,f164,f151,f114,f290]) ).
fof(f773,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_10 ),
inference(superposition,[],[f3,f116]) ).
fof(f774,plain,
( sk_c8 = multiply(sk_c8,sk_c2)
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f773,f220]) ).
fof(f782,plain,
( sk_c2 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f235,f774]) ).
fof(f785,plain,
( identity = sk_c2
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f782,f3]) ).
fof(f787,plain,
( sk_c8 = sk_c2
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f785,f220]) ).
fof(f806,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_demodulation,[],[f90,f470]) ).
fof(f823,plain,
( $false
| spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f806,f203]) ).
fof(f824,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f823]) ).
fof(f844,plain,
( sk_c9 != inverse(inverse(sk_c9))
| ~ spl0_5
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f506,f220]) ).
fof(f846,plain,
( sk_c9 != inverse(sk_c6)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f509,f521]) ).
fof(f863,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f844,f291]) ).
fof(f865,plain,
( sk_c9 != sk_c5
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_28 ),
inference(forward_demodulation,[],[f846,f126]) ).
fof(f876,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f863,f461]) ).
fof(f878,plain,
( sk_c8 != sk_c9
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_28 ),
inference(forward_demodulation,[],[f865,f521]) ).
fof(f887,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f876,f136]) ).
fof(f888,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f887]) ).
fof(f890,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_25
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f878,f291]) ).
fof(f891,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_25
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f890]) ).
fof(f944,plain,
( sk_c9 != inverse(identity)
| ~ spl0_5
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f504,f291]) ).
fof(f966,plain,
( sk_c9 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f944,f220]) ).
fof(f977,plain,
( sk_c9 != sk_c2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f966,f460]) ).
fof(f990,plain,
( sk_c8 != sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_demodulation,[],[f977,f787]) ).
fof(f999,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_23
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f990,f291]) ).
fof(f1000,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_23
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f999]) ).
fof(f1001,plain,
( sk_c7 != sk_c2
| spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f94,f460]) ).
fof(f1010,plain,
( sk_c8 != sk_c7
| spl0_4
| ~ spl0_10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1001,f787]) ).
fof(f1015,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1010,f203]) ).
fof(f1016,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1015]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f108]) ).
cnf(s2,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s3,plain,
( spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s4,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s5,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s6,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s7,plain,
( spl0_3
| spl0_10 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f139]) ).
cnf(s9,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s10,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f149]) ).
cnf(s11,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f154]) ).
cnf(s12,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f155]) ).
cnf(s13,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f156]) ).
cnf(s14,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f157]) ).
cnf(s15,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f158]) ).
cnf(s16,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f159]) ).
cnf(s17,plain,
( spl0_4
| spl0_17 ),
inference(sat_conversion,[],[f160]) ).
cnf(s18,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f161]) ).
cnf(s19,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f162]) ).
cnf(s20,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f167]) ).
cnf(s21,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f168]) ).
cnf(s22,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f169]) ).
cnf(s23,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f170]) ).
cnf(s24,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f171]) ).
cnf(s26,plain,
( spl0_4
| spl0_18 ),
inference(sat_conversion,[],[f173]) ).
cnf(s27,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f174]) ).
cnf(s28,plain,
( spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f175]) ).
cnf(s29,plain,
( spl0_9
| spl0_19 ),
inference(sat_conversion,[],[f180]) ).
cnf(s30,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f181]) ).
cnf(s31,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f182]) ).
cnf(s32,plain,
( spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f183]) ).
cnf(s33,plain,
( spl0_14
| spl0_19 ),
inference(sat_conversion,[],[f184]) ).
cnf(s35,plain,
( spl0_4
| spl0_19 ),
inference(sat_conversion,[],[f186]) ).
cnf(s36,plain,
( spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f187]) ).
cnf(s37,plain,
( spl0_16
| spl0_19 ),
inference(sat_conversion,[],[f188]) ).
cnf(s38,plain,
spl0_8,
inference(sat_conversion,[],[f189]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f195]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f293]) ).
cnf(s44,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f429]) ).
cnf(s46,plain,
( ~ spl0_4
| ~ spl0_21
| spl0_24 ),
inference(sat_conversion,[],[f451]) ).
cnf(s50,plain,
( ~ spl0_4
| ~ spl0_14
| spl0_24 ),
inference(sat_conversion,[],[f487]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f513]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_24
| spl0_28 ),
inference(sat_conversion,[],[f533]) ).
cnf(s55,plain,
( ~ spl0_7
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f543]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_24
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f553]) ).
cnf(s59,plain,
( ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_28
| spl0_30 ),
inference(sat_conversion,[],[f559]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f584]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_8
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f592]) ).
cnf(s67,plain,
( spl0_23
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f598]) ).
cnf(s69,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_24
| ~ spl0_30 ),
inference(sat_conversion,[],[f614]) ).
cnf(s72,plain,
( ~ spl0_4
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| spl0_25
| ~ spl0_28
| ~ spl0_30 ),
inference(sat_conversion,[],[f681]) ).
cnf(s76,plain,
( ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(sat_conversion,[],[f690]) ).
cnf(s79,plain,
( ~ spl0_10
| ~ spl0_17
| spl0_30 ),
inference(sat_conversion,[],[f694]) ).
cnf(s86,plain,
( ~ spl0_10
| ~ spl0_17
| ~ spl0_18
| ~ spl0_19
| spl0_25 ),
inference(sat_conversion,[],[f717]) ).
cnf(s96,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_21 ),
inference(sat_conversion,[],[f824]) ).
cnf(s100,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f888]) ).
cnf(s101,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_12
| ~ spl0_25
| ~ spl0_28 ),
inference(sat_conversion,[],[f891]) ).
cnf(s119,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f1000]) ).
cnf(s123,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f1016]) ).
cnf(s125,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(rat,[],[s1,s38]) ).
cnf(s126,plain,
spl0_3,
inference(rat,[],[s44,s7,s16,s96,s38]) ).
cnf(s127,plain,
spl0_4,
inference(rat,[],[s123,s67,s79,s44,s86,s8,s17,s26,s35,s38]) ).
cnf(s129,plain,
( spl0_19
| ~ spl0_7 ),
inference(rat,[],[s58,s72,s59,s54,s50,s30,s31,s32,s33,s36,s37,s127,s126]) ).
cnf(s130,plain,
( ~ spl0_19
| ~ spl0_7 ),
inference(rat,[],[s58,s72,s59,s54,s50,s21,s22,s23,s24,s27,s28,s55,s126,s127]) ).
cnf(s131,plain,
~ spl0_7,
inference(rat,[],[s130,s129]) ).
cnf(s132,plain,
( spl0_19
| ~ spl0_6 ),
inference(rat,[],[s59,s69,s54,s50,s30,s31,s32,s33,s36,s37,s127,s126]) ).
cnf(s133,plain,
( spl0_16
| spl0_25
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s86,s10,s19]) ).
cnf(s134,plain,
( spl0_15
| spl0_25
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s86,s9,s18]) ).
cnf(s135,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_18
| ~ spl0_6 ),
inference(rat,[],[s59,s69,s54,s50,s133,s134,s76,s132,s127,s126]) ).
cnf(s136,plain,
( spl0_14
| spl0_25
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s86,s6,s15]) ).
cnf(s137,plain,
( spl0_13
| spl0_25
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s86,s5,s14]) ).
cnf(s138,plain,
( spl0_12
| spl0_25
| ~ spl0_18
| ~ spl0_19 ),
inference(rat,[],[s86,s4,s13]) ).
cnf(s139,plain,
( ~ spl0_19
| ~ spl0_18
| ~ spl0_6 ),
inference(rat,[],[s86,s3,s12,s135,s138,s137,s136,s76]) ).
cnf(s140,plain,
( ~ spl0_19
| ~ spl0_6 ),
inference(rat,[],[s59,s69,s54,s50,s21,s22,s23,s24,s27,s28,s139,s126,s127]) ).
cnf(s141,plain,
~ spl0_6,
inference(rat,[],[s140,s132]) ).
cnf(s142,plain,
( spl0_25
| ~ spl0_19
| ~ spl0_18
| ~ spl0_5 ),
inference(rat,[],[s51,s134,s133]) ).
cnf(s143,plain,
( ~ spl0_25
| ~ spl0_28
| ~ spl0_14
| ~ spl0_12
| ~ spl0_5 ),
inference(rat,[],[s79,s67,s2,s11,s100,s101]) ).
cnf(s144,plain,
( spl0_19
| ~ spl0_5 ),
inference(rat,[],[s51,s36,s37]) ).
cnf(s145,plain,
( spl0_18
| ~ spl0_5 ),
inference(rat,[],[s51,s27,s28]) ).
cnf(s146,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s143,s54,s50,s142,s145,s144,s126,s127]) ).
cnf(s147,plain,
( spl0_14
| ~ spl0_5 ),
inference(rat,[],[s67,s119,s79,s6,s15,s142,s145,s144]) ).
cnf(s148,plain,
( spl0_13
| spl0_30 ),
inference(rat,[],[s79,s5,s14]) ).
cnf(s149,plain,
( spl0_12
| spl0_30 ),
inference(rat,[],[s79,s4,s13]) ).
cnf(s150,plain,
( ~ spl0_14
| ~ spl0_25
| ~ spl0_5 ),
inference(rat,[],[s79,s3,s12,s146,s149,s148,s67,s100]) ).
cnf(s151,plain,
( ~ spl0_18
| ~ spl0_5
| ~ spl0_19 ),
inference(rat,[],[s150,s147,s142]) ).
cnf(s152,plain,
~ spl0_5,
inference(rat,[],[s151,s145,s144]) ).
cnf(s153,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s137,s23,s32,s42,s39,s50,s38,s127]) ).
cnf(s154,plain,
~ spl0_2,
inference(rat,[],[s46,s42,s44,s136,s6,s15,s24,s33,s153,s127,s38]) ).
cnf(s155,plain,
spl0_1,
inference(rat,[],[s125,s141,s126,s131,s127,s152,s154]) ).
cnf(s156,plain,
( spl0_9
| spl0_25 ),
inference(rat,[],[s86,s2,s11,s20,s29]) ).
cnf(s157,plain,
( spl0_11
| spl0_25 ),
inference(rat,[],[s86,s3,s12,s21,s30]) ).
cnf(s158,plain,
spl0_25,
inference(rat,[],[s138,s22,s31,s62,s157,s156,s155]) ).
cnf(s159,plain,
~ spl0_24,
inference(rat,[],[s65,s155,s127,s38,s158]) ).
cnf(s160,plain,
~ spl0_21,
inference(rat,[],[s46,s127,s159]) ).
cnf(s161,plain,
~ spl0_14,
inference(rat,[],[s50,s127,s159]) ).
cnf(s164,plain,
spl0_17,
inference(rat,[],[s15,s161]) ).
cnf(s165,plain,
spl0_10,
inference(rat,[],[s6,s161]) ).
cnf(s166,plain,
$false,
inference(rat,[],[s44,s160,s38,s164,s165]) ).
fof(f1019,plain,
$false,
inference(avatar_sat_refutation,[],[s166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP339-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:54:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 Running first-order model finding
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45 % (3261375)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (3261384)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=493288967:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.45 % (3261381)% WARNING: option uhcvi not known.
% 0.14/0.45 % (3261380)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1900302857_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.45 % (3261381)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3891705531:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.45 % (3261382)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=717852296:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.45 % (3261386)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3746403847:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.45 % (3261383)dis+10_1_sil=32000:sp=arity:random_seed=3645342361:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (3261385)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3379280380:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.45 % (3261384) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3261375-3261384"...
% 0.14/0.45 % TRYING [1]
% 0.14/0.45 % TRYING [2]
% 0.14/0.45 % TRYING [3]
% 0.14/0.45 % (3261384)...printing done.
% 0.14/0.45 % (3261384)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (3261384)------------------------------
% 0.14/0.45 % (3261384)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (3261384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (3261384)CaDiCaL version: 2.1.3
% 0.14/0.45 % (3261384)Termination reason: Refutation
% 0.14/0.45 % (3261384)Time elapsed: 0.012 s
% 0.14/0.45 % (3261384)Peak memory usage: 12 MB
% 0.14/0.45 % (3261384)Instructions burned: 33 (million)
% 0.14/0.45 % (3261375)Success in time 0.041 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------