%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP280-1 : 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 : n001.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 10:17:22 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 55
% Syntax : Number of formulae : 405 ( 20 unt; 19 def)
% Number of atoms : 1522 ( 402 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2185 (1068 ~;1098 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 65 !; 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_c9,sk_c8) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c9 = inverse(sk_c1)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f49,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c9,sk_c3) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c4,sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c2)
| sk_c5 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(sk_c9,X1) != sk_c8
| multiply(X2,sk_c9) != X1
| inverse(X2) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(X3,X4) != sk_c9
| inverse(X3) != X4
| multiply(X4,sk_c8) != sk_c9
| multiply(X5,sk_c9) != sk_c7
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,X1)
| multiply(X2,sk_c9) != X1
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c9 != multiply(X4,sk_c8)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X4,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c9 != multiply(X4,sk_c8)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X5] :
( multiply(sk_c9,sk_c8) != sk_c7
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f79]) ).
fof(f82,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f83,plain,
( ! [X5] :
( sk_c7 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c9 != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8) )
| ~ 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
<=> ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( ! [X2] :
( sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| sk_c9 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f96,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_6
<=> multiply(sk_c9,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f99,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| spl0_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f80,f98,f95,f92,f88,f85,f82]) ).
fof(f103,definition,
( spl0_7
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f105,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,definition,
( spl0_8
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f109,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f76,f107,f103]) ).
fof(f112,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 != multiply(sk_c6,sk_c9)
| spl0_9 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f74,f107,f112]) ).
fof(f117,definition,
( spl0_10
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f119,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f72,f107,f117]) ).
fof(f122,definition,
( spl0_11
<=> sk_c5 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f124,plain,
( sk_c5 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f70,f107,f122]) ).
fof(f127,definition,
( spl0_12
<=> sk_c9 = multiply(sk_c4,sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f129,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f68,f107,f127]) ).
fof(f131,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f66,f107,f88]) ).
fof(f133,definition,
( spl0_13
<=> sk_c3 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f135,plain,
( sk_c3 = multiply(sk_c2,sk_c9)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f64,f133,f103]) ).
fof(f137,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f62,f133,f112]) ).
fof(f138,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f60,f133,f117]) ).
fof(f139,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f58,f133,f122]) ).
fof(f140,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f56,f133,f127]) ).
fof(f141,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f54,f133,f88]) ).
fof(f143,definition,
( spl0_14
<=> sk_c8 = multiply(sk_c9,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f145,plain,
( sk_c8 = multiply(sk_c9,sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f143,f103]) ).
fof(f147,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f143,f112]) ).
fof(f149,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f143,f122]) ).
fof(f150,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f143,f127]) ).
fof(f151,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f143,f88]) ).
fof(f153,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f155,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f153,f103]) ).
fof(f158,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f153,f117]) ).
fof(f159,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f153,f122]) ).
fof(f160,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f153,f127]) ).
fof(f161,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f153,f88]) ).
fof(f163,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f165,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f163,f103]) ).
fof(f168,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f163,f117]) ).
fof(f169,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f163,f122]) ).
fof(f170,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f163,f127]) ).
fof(f171,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f18,f163,f88]) ).
fof(f172,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f98,f103]) ).
fof(f173,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f98,f112]) ).
fof(f175,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f98,f122]) ).
fof(f176,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f98,f127]) ).
fof(f177,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f98,f88]) ).
fof(f178,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_7 ),
inference(superposition,[],[f3,f105]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f185,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c8,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f119]) ).
fof(f187,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f182,f1]) ).
fof(f190,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f178]) ).
fof(f191,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c6,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f190,f1]) ).
fof(f194,plain,
( sk_c9 = multiply(sk_c9,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f191,f114]) ).
fof(f200,plain,
( sk_c9 = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f194,f89]) ).
fof(f210,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c9,X0))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f185,f200]) ).
fof(f229,plain,
( identity = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f210,f178]) ).
fof(f246,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f187,f194]) ).
fof(f247,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f187,f89]) ).
fof(f252,plain,
( sk_c5 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_12 ),
inference(superposition,[],[f187,f129]) ).
fof(f266,plain,
( sk_c5 = multiply(sk_c5,sk_c9)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f252,f124]) ).
fof(f269,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f247,f200]) ).
fof(f270,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f246,f3]) ).
fof(f273,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f269,f3]) ).
fof(f281,plain,
( sk_c9 = multiply(inverse(sk_c5),sk_c5)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f187,f266]) ).
fof(f284,plain,
( identity = sk_c9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f281,f3]) ).
fof(f288,plain,
( sk_c7 != multiply(identity,sk_c8)
| spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f100,f284]) ).
fof(f290,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f178,f284]) ).
fof(f296,plain,
( sk_c5 = multiply(sk_c5,identity)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f266,f284]) ).
fof(f297,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f296,f229]) ).
fof(f303,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f290,f1]) ).
fof(f305,plain,
( sk_c8 != sk_c7
| spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f288,f1]) ).
fof(f309,plain,
( identity != sk_c8
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f305,f273]) ).
fof(f313,plain,
( identity != sk_c9
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f309,f200]) ).
fof(f314,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f313,f284]) ).
fof(f315,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f316,plain,
( ! [X2] :
( sk_c8 != multiply(identity,multiply(X2,identity))
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f93,f284]) ).
fof(f318,plain,
( ! [X2] :
( sk_c8 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f316,f1]) ).
fof(f320,plain,
( ! [X2] :
( sk_c9 != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f318,f200]) ).
fof(f322,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c9 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f320,f284]) ).
fof(f323,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f322,f284]) ).
fof(f324,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f323,f1]) ).
fof(f330,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f324]) ).
fof(f349,plain,
( sk_c9 = inverse(identity)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f105,f303]) ).
fof(f350,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f349,f284]) ).
fof(f355,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f350,f330]) ).
fof(f356,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f360,plain,
( identity = inverse(sk_c2)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f109,f284]) ).
fof(f361,plain,
( sk_c7 != multiply(sk_c6,identity)
| spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f113,f284]) ).
fof(f362,plain,
( sk_c3 = multiply(sk_c2,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f135,f284]) ).
fof(f363,plain,
( sk_c8 = multiply(identity,sk_c3)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f145,f284]) ).
fof(f364,plain,
( identity = inverse(sk_c1)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f155,f284]) ).
fof(f365,plain,
( sk_c8 = multiply(sk_c1,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_demodulation,[],[f165,f284]) ).
fof(f372,plain,
( sk_c7 = multiply(identity,sk_c8)
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f99,f284]) ).
fof(f374,plain,
( sk_c7 != multiply(identity,identity)
| ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f361,f303]) ).
fof(f375,plain,
( sk_c8 = sk_c3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[],[f363,f1]) ).
fof(f377,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f372,f1]) ).
fof(f378,plain,
( identity != sk_c7
| ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f374,f1]) ).
fof(f383,plain,
( identity != sk_c8
| ~ spl0_6
| ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f378,f377]) ).
fof(f385,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f3,f360]) ).
fof(f386,plain,
( identity = sk_c2
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f385,f1]) ).
fof(f390,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f3,f364]) ).
fof(f391,plain,
( identity = sk_c1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f390,f1]) ).
fof(f394,plain,
( sk_c3 = multiply(identity,identity)
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f362,f386]) ).
fof(f395,plain,
( identity = sk_c3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f394,f1]) ).
fof(f396,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f395,f375]) ).
fof(f400,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f396,f383]) ).
fof(f401,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f406,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f365,f391]) ).
fof(f407,plain,
( identity = sk_c8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f406,f1]) ).
fof(f429,plain,
( sk_c9 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f187,f135]) ).
fof(f430,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c9,X0)) = multiply(sk_c3,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f135]) ).
fof(f431,plain,
( sk_c9 = multiply(sk_c9,sk_c3)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f429,f109]) ).
fof(f434,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f187,f165]) ).
fof(f436,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f434,f155]) ).
fof(f441,plain,
( sk_c8 != multiply(sk_c9,sk_c3)
| sk_c9 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f93,f135]) ).
fof(f452,plain,
( sk_c9 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f441,f145]) ).
fof(f472,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f452,f109]) ).
fof(f473,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f478,plain,
( sk_c9 != sk_c7
| sk_c9 != inverse(identity)
| ~ spl0_1 ),
inference(superposition,[],[f83,f1]) ).
fof(f482,plain,
( sk_c7 != sk_c3
| sk_c9 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[],[f83,f135]) ).
fof(f483,plain,
( sk_c7 != sk_c3
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f482,f109]) ).
fof(f486,definition,
( spl0_23
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f487,plain,
( identity = sk_c7
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f502,plain,
( sk_c9 = sk_c8
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f431,f145]) ).
fof(f504,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f187,f431]) ).
fof(f506,plain,
( identity = sk_c3
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f504,f3]) ).
fof(f518,plain,
( multiply(sk_c3,sk_c7) = multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f430,f89]) ).
fof(f529,plain,
( multiply(sk_c2,sk_c9) = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f518,f502]) ).
fof(f535,plain,
( sk_c3 = multiply(sk_c3,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f529,f135]) ).
fof(f539,plain,
( identity != sk_c7
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f483,f506]) ).
fof(f542,plain,
( ~ spl0_23
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f539,f133,f107,f82,f486]) ).
fof(f543,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f436,f502]) ).
fof(f547,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f535,f506]) ).
fof(f548,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f547,f1]) ).
fof(f551,plain,
( ! [X0] :
( sk_c9 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f96,f502]) ).
fof(f552,plain,
( spl0_23
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f548,f143,f133,f107,f88,f486]) ).
fof(f556,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(superposition,[],[f551,f165]) ).
fof(f560,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f556,f502]) ).
fof(f563,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f560,f155]) ).
fof(f564,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f563]) ).
fof(f565,plain,
( ! [X3] :
( sk_c9 != multiply(inverse(X3),sk_c9)
| sk_c9 != multiply(X3,inverse(X3)) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f86,f502]) ).
fof(f572,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| sk_c9 != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f565,f155]) ).
fof(f580,definition,
( spl0_26
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f581,plain,
( identity = sk_c9
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f585,plain,
( sk_c9 != sk_c8
| sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f572,f165]) ).
fof(f587,plain,
( sk_c9 != multiply(sk_c9,sk_c9)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f585,f502]) ).
fof(f589,definition,
( spl0_27
<=> sk_c9 = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f590,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f593,plain,
( ~ spl0_27
| ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f587,f163,f153,f143,f133,f107,f85,f589]) ).
fof(f615,plain,
( spl0_27
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f543,f163,f153,f143,f133,f107,f589]) ).
fof(f619,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_27 ),
inference(superposition,[],[f187,f590]) ).
fof(f621,plain,
( identity = sk_c9
| ~ spl0_27 ),
inference(forward_demodulation,[],[f619,f3]) ).
fof(f627,plain,
( spl0_26
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f621,f589,f580]) ).
fof(f630,plain,
( sk_c7 = multiply(identity,sk_c8)
| ~ spl0_6
| ~ spl0_26 ),
inference(superposition,[],[f99,f581]) ).
fof(f656,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_26 ),
inference(forward_demodulation,[],[f630,f1]) ).
fof(f661,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f656,f487]) ).
fof(f664,plain,
( sk_c8 != multiply(identity,sk_c7)
| spl0_3
| ~ spl0_26 ),
inference(forward_demodulation,[],[f90,f581]) ).
fof(f666,plain,
( sk_c9 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f656,f502]) ).
fof(f668,plain,
( sk_c8 != sk_c7
| spl0_3
| ~ spl0_26 ),
inference(forward_demodulation,[],[f664,f1]) ).
fof(f670,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f666,f581]) ).
fof(f671,plain,
( sk_c9 != sk_c7
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f668,f502]) ).
fof(f672,plain,
( spl0_23
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f670,f580,f143,f133,f107,f98,f486]) ).
fof(f673,plain,
( identity != sk_c7
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f671,f581]) ).
fof(f674,plain,
( ~ spl0_23
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f673,f580,f143,f133,f107,f88,f486]) ).
fof(f675,plain,
( ! [X3] :
( identity != multiply(X3,inverse(X3))
| sk_c9 != multiply(inverse(X3),sk_c8) )
| ~ spl0_2
| ~ spl0_26 ),
inference(forward_demodulation,[],[f86,f581]) ).
fof(f684,plain,
( identity = inverse(sk_c6)
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f105,f581]) ).
fof(f686,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_26 ),
inference(forward_demodulation,[],[f194,f581]) ).
fof(f687,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f270,f112,f103,f486]) ).
fof(f691,plain,
( identity = multiply(sk_c4,sk_c5)
| ~ spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f129,f581]) ).
fof(f700,plain,
( ! [X3] :
( identity != multiply(inverse(X3),sk_c8)
| identity != multiply(X3,inverse(X3)) )
| ~ spl0_2
| ~ spl0_26 ),
inference(forward_demodulation,[],[f675,f581]) ).
fof(f703,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_9
| ~ spl0_26 ),
inference(forward_demodulation,[],[f686,f1]) ).
fof(f708,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_9
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f703,f580,f112,f103,f486]) ).
fof(f735,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f364,f391]) ).
fof(f737,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_7
| ~ spl0_26 ),
inference(superposition,[],[f3,f684]) ).
fof(f738,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f737,f1]) ).
fof(f757,plain,
( ! [X3] :
( identity != multiply(inverse(X3),identity)
| identity != multiply(X3,inverse(X3)) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f700,f407]) ).
fof(f770,plain,
( identity != multiply(sk_c9,identity)
| identity != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(superposition,[],[f757,f155]) ).
fof(f775,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f770,f581]) ).
fof(f782,plain,
( identity != multiply(sk_c1,sk_c9)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f775,f1]) ).
fof(f785,plain,
( identity != sk_c8
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f782,f165]) ).
fof(f790,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f785,f407]) ).
fof(f791,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f792,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c9 )
| ~ spl0_5
| ~ spl0_26 ),
inference(forward_demodulation,[],[f96,f581]) ).
fof(f793,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c9 )
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f792,f407]) ).
fof(f794,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f793,f581]) ).
fof(f797,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(superposition,[],[f794,f3]) ).
fof(f800,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f797]) ).
fof(f802,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f800,f735]) ).
fof(f805,plain,
( $false
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f802,f735]) ).
fof(f806,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f807,plain,
( ! [X5] :
( sk_c7 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_26 ),
inference(forward_demodulation,[],[f83,f581]) ).
fof(f808,plain,
( sk_c9 != sk_c8
| sk_c9 != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f478,f377]) ).
fof(f814,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f807,f377]) ).
fof(f815,plain,
( identity != sk_c9
| sk_c9 != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f808,f407]) ).
fof(f822,plain,
( sk_c9 != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f815,f581]) ).
fof(f825,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_demodulation,[],[f822,f735]) ).
fof(f826,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f825,f581]) ).
fof(f827,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f826]) ).
fof(f840,plain,
( spl0_26
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f284,f127,f122,f580]) ).
fof(f884,plain,
( identity = multiply(sk_c4,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_26 ),
inference(forward_demodulation,[],[f691,f297]) ).
fof(f948,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c9 )
| ~ spl0_5
| ~ spl0_26 ),
inference(forward_demodulation,[],[f96,f581]) ).
fof(f949,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c9 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f948,f661]) ).
fof(f950,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f949,f581]) ).
fof(f958,plain,
( identity != identity
| identity != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(superposition,[],[f950,f884]) ).
fof(f963,plain,
( identity != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f958]) ).
fof(f966,plain,
( identity != sk_c5
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f963,f124]) ).
fof(f967,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f966,f297]) ).
fof(f968,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f967]) ).
fof(f975,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f814,f661]) ).
fof(f984,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f975,f581]) ).
fof(f995,plain,
( identity != identity
| identity != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(superposition,[],[f984,f884]) ).
fof(f1000,plain,
( identity != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f995]) ).
fof(f1003,plain,
( identity != sk_c5
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1000,f124]) ).
fof(f1004,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1003,f297]) ).
fof(f1005,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
fof(f1007,plain,
( ! [X3] :
( identity != multiply(inverse(X3),identity)
| identity != multiply(X3,inverse(X3)) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f700,f661]) ).
fof(f1011,plain,
( identity != multiply(sk_c9,identity)
| identity != multiply(sk_c6,sk_c9)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(superposition,[],[f1007,f105]) ).
fof(f1015,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c6,sk_c9)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1011,f581]) ).
fof(f1017,plain,
( identity != multiply(sk_c6,sk_c9)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1015,f1]) ).
fof(f1019,plain,
( identity != multiply(sk_c6,identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1017,f581]) ).
fof(f1021,plain,
( identity != multiply(identity,identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1019,f738]) ).
fof(f1024,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1021,f1]) ).
fof(f1025,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1024]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f101]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f110]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f115]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f125]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f130]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f131]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f138]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f139]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f140]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f141]) ).
cnf(s14,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f146]) ).
cnf(s15,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f147]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s19,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s20,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s22,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f159]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f160]) ).
cnf(s25,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s26,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s28,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s29,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f169]) ).
cnf(s30,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f170]) ).
cnf(s31,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f171]) ).
cnf(s32,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f172]) ).
cnf(s33,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f173]) ).
cnf(s35,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f175]) ).
cnf(s36,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f176]) ).
cnf(s37,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f177]) ).
cnf(s38,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f315]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f356]) ).
cnf(s41,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f401]) ).
cnf(s47,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f473]) ).
cnf(s50,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_23 ),
inference(sat_conversion,[],[f542]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_23 ),
inference(sat_conversion,[],[f552]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f564]) ).
cnf(s57,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_27 ),
inference(sat_conversion,[],[f593]) ).
cnf(s59,plain,
( ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_27 ),
inference(sat_conversion,[],[f615]) ).
cnf(s62,plain,
( spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f627]) ).
cnf(s66,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f672]) ).
cnf(s67,plain,
( spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f674]) ).
cnf(s69,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_23 ),
inference(sat_conversion,[],[f687]) ).
cnf(s73,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f708]) ).
cnf(s82,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(sat_conversion,[],[f791]) ).
cnf(s84,plain,
( ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(sat_conversion,[],[f806]) ).
cnf(s88,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16
| ~ spl0_26 ),
inference(sat_conversion,[],[f827]) ).
cnf(s92,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_26 ),
inference(sat_conversion,[],[f840]) ).
cnf(s109,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f968]) ).
cnf(s110,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f1005]) ).
cnf(s112,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f1025]) ).
cnf(s113,plain,
spl0_3,
inference(rat,[],[s67,s66,s62,s59,s7,s13,s19,s25,s31,s37]) ).
cnf(s114,plain,
spl0_6,
inference(rat,[],[s38,s32,s33,s35,s36,s113]) ).
cnf(s115,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_23 ),
inference(rat,[],[s92,s109,s114,s113]) ).
cnf(s116,plain,
( spl0_12
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s54,s12,s18,s24,s30]) ).
cnf(s117,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s54,s11,s17,s23,s29]) ).
cnf(s118,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s84,s22,s28,s92,s117,s116]) ).
cnf(s119,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s115,s69,s116,s117,s118]) ).
cnf(s120,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s41,s9,s15,s119,s117,s116,s114]) ).
cnf(s121,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s115,s69,s3,s4,s5,s6,s120]) ).
cnf(s122,plain,
~ spl0_5,
inference(rat,[],[s54,s2,s8,s14,s20,s26,s121]) ).
cnf(s123,plain,
( spl0_12
| ~ spl0_4 ),
inference(rat,[],[s47,s6,s12,s18]) ).
cnf(s124,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s47,s5,s11,s17]) ).
cnf(s125,plain,
( ~ spl0_11
| ~ spl0_7
| ~ spl0_12
| ~ spl0_4 ),
inference(rat,[],[s41,s3,s9,s15,s39,s113,s114]) ).
cnf(s126,plain,
( ~ spl0_11
| ~ spl0_4
| ~ spl0_12 ),
inference(rat,[],[s47,s2,s8,s14,s125]) ).
cnf(s127,plain,
~ spl0_4,
inference(rat,[],[s126,s124,s123]) ).
cnf(s128,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s41,s3,s9,s15,s73,s112,s92,s114]) ).
cnf(s129,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s57,s59,s6,s12,s18,s24,s30]) ).
cnf(s130,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s57,s59,s5,s11,s17,s23,s29]) ).
cnf(s131,plain,
( ~ spl0_11
| ~ spl0_2
| ~ spl0_12 ),
inference(rat,[],[s82,s20,s26,s92,s128]) ).
cnf(s132,plain,
~ spl0_2,
inference(rat,[],[s131,s130,s129]) ).
cnf(s133,plain,
spl0_1,
inference(rat,[],[s1,s114,s122,s113,s127,s132]) ).
cnf(s134,plain,
( ~ spl0_13
| ~ spl0_8
| ~ spl0_26
| ~ spl0_7 ),
inference(rat,[],[s15,s52,s73,s50,s113,s133]) ).
cnf(s135,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_26 ),
inference(rat,[],[s69,s110,s114,s113,s133]) ).
cnf(s136,plain,
( spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s135,s9,s10,s92]) ).
cnf(s137,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s135,s3,s4,s134,s136,s92]) ).
cnf(s138,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_8 ),
inference(rat,[],[s50,s52,s113,s133]) ).
cnf(s139,plain,
spl0_12,
inference(rat,[],[s138,s6,s12,s18]) ).
cnf(s140,plain,
spl0_11,
inference(rat,[],[s138,s5,s11,s17]) ).
cnf(s141,plain,
~ spl0_7,
inference(rat,[],[s137,s139,s140]) ).
cnf(s142,plain,
spl0_26,
inference(rat,[],[s92,s139,s140]) ).
cnf(s144,plain,
spl0_16,
inference(rat,[],[s26,s141]) ).
cnf(s145,plain,
spl0_15,
inference(rat,[],[s20,s141]) ).
cnf(s151,plain,
$false,
inference(rat,[],[s88,s144,s139,s140,s114,s133,s142,s145]) ).
fof(f1026,plain,
$false,
inference(avatar_sat_refutation,[],[s151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP280-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:50:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.47 % (3309079)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3309087)dis+10_1_sil=32000:sp=arity:random_seed=115448589:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3309085)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3309086)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1622122231:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3309084)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3838040277_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3309085)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3606203740:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3309088)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=540178003:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3309090)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3527448001:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % (3309089)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2324360706:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3309087) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3309079-3309087"...
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (3309087)...printing done.
% 0.16/0.47 % (3309087)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3309087)------------------------------
% 0.16/0.47 % (3309087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3309087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3309087)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3309087)Termination reason: Refutation
% 0.16/0.47 % (3309087)Time elapsed: 0.013 s
% 0.16/0.47 % (3309087)Peak memory usage: 12 MB
% 0.16/0.47 % (3309087)Instructions burned: 37 (million)
% 0.16/0.47 % (3309079)Success in time 0.042 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------