%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP331-1 : 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 10:17:30 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 54
% Syntax : Number of formulae : 434 ( 21 unt; 20 def)
% Number of atoms : 1592 ( 351 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 2262 (1104 ~;1138 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/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_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl0_4
<=> ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f66,f83,f80,f77,f74,f71,f68]) ).
fof(f88,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f90,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c2,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f94,plain,
( sk_c7 = multiply(sk_c2,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f92,f88]) ).
fof(f97,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f99,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f92,f97]) ).
fof(f102,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f104,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f92,f102]) ).
fof(f107,definition,
( spl0_11
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f109,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f92,f107]) ).
fof(f112,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f92,f112]) ).
fof(f117,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f92,f117]) ).
fof(f122,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f124,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f52,f122,f88]) ).
fof(f126,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f50,f122,f97]) ).
fof(f127,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f48,f122,f102]) ).
fof(f128,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f46,f122,f107]) ).
fof(f129,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f44,f122,f112]) ).
fof(f130,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f42,f122,f117]) ).
fof(f132,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f134,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f40,f132,f88]) ).
fof(f136,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f38,f132,f97]) ).
fof(f137,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f36,f132,f102]) ).
fof(f138,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f34,f132,f107]) ).
fof(f139,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f32,f132,f112]) ).
fof(f140,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f30,f132,f117]) ).
fof(f142,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f28,f142,f88]) ).
fof(f146,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f26,f142,f97]) ).
fof(f147,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f24,f142,f102]) ).
fof(f148,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f22,f142,f107]) ).
fof(f149,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f20,f142,f112]) ).
fof(f150,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f18,f142,f117]) ).
fof(f151,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f83,f88]) ).
fof(f152,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f83,f97]) ).
fof(f153,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f83,f102]) ).
fof(f154,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f83,f107]) ).
fof(f155,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f83,f112]) ).
fof(f156,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f83,f117]) ).
fof(f157,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f99]) ).
fof(f158,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f104]) ).
fof(f159,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f114]) ).
fof(f162,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f163,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(sk_c7,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f119]) ).
fof(f164,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_11 ),
inference(superposition,[],[f4,f109]) ).
fof(f166,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f162,f1]) ).
fof(f169,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f157]) ).
fof(f170,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f169,f1]) ).
fof(f171,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c4,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f158]) ).
fof(f172,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c4,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f171,f1]) ).
fof(f179,plain,
( sk_c8 = multiply(sk_c6,sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f170,f90]) ).
fof(f192,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f172,f109]) ).
fof(f204,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_10 ),
inference(superposition,[],[f166,f158]) ).
fof(f205,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_10 ),
inference(superposition,[],[f166,f172]) ).
fof(f210,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f166,f119]) ).
fof(f223,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f210,f114]) ).
fof(f225,plain,
( sk_c4 = multiply(sk_c4,identity)
| ~ spl0_10 ),
inference(forward_demodulation,[],[f204,f205]) ).
fof(f228,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f163,f223]) ).
fof(f229,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f166,f223]) ).
fof(f231,plain,
( identity = sk_c7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f229,f3]) ).
fof(f232,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f228,f119]) ).
fof(f238,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1,f231]) ).
fof(f239,plain,
( sk_c4 = multiply(sk_c4,sk_c7)
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f225,f231]) ).
fof(f243,plain,
( sk_c6 = sk_c4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f239,f109]) ).
fof(f244,plain,
( sk_c7 = inverse(sk_c6)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f104,f243]) ).
fof(f248,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c6,X0)) = X0
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f172,f243]) ).
fof(f250,plain,
( ! [X0] : multiply(sk_c6,X0) = X0
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f248,f238]) ).
fof(f269,plain,
( multiply(sk_c4,sk_c7) = multiply(sk_c6,sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f164,f192]) ).
fof(f270,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f166,f192]) ).
fof(f272,plain,
( identity = sk_c6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f270,f3]) ).
fof(f273,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f269,f179]) ).
fof(f274,plain,
( sk_c7 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f272,f231]) ).
fof(f275,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f273,f243]) ).
fof(f276,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f275,f250]) ).
fof(f287,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f244,f274]) ).
fof(f290,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f157,f274]) ).
fof(f291,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f290,f238]) ).
fof(f294,plain,
( sk_c7 = sk_c5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f291,f231]) ).
fof(f311,plain,
( sk_c6 != multiply(sk_c7,sk_c7)
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f85,f276]) ).
fof(f314,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f159,f276]) ).
fof(f324,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f314,f238]) ).
fof(f326,plain,
( sk_c7 != sk_c6
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f311,f232]) ).
fof(f329,plain,
( sk_c7 = sk_c3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f324,f231]) ).
fof(f331,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f326,f274]) ).
fof(f332,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f387,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f3,f124]) ).
fof(f416,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f166,f144]) ).
fof(f433,plain,
( sk_c7 != sk_c8
| sk_c8 != inverse(identity)
| ~ spl0_3 ),
inference(superposition,[],[f75,f1]) ).
fof(f436,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13 ),
inference(superposition,[],[f75,f119]) ).
fof(f437,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f436]) ).
fof(f438,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f437,f114]) ).
fof(f439,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f454,plain,
( sk_c6 = multiply(sk_c7,sk_c2)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f387,f272]) ).
fof(f456,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f416,f134]) ).
fof(f458,plain,
( sk_c8 != inverse(sk_c6)
| sk_c7 != sk_c8
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f433,f272]) ).
fof(f465,definition,
( spl0_18
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f466,plain,
( sk_c7 = sk_c6
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f467,plain,
( sk_c7 != sk_c6
| spl0_18 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f470,definition,
( spl0_19
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f471,plain,
( sk_c7 = sk_c8
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f472,plain,
( sk_c7 != sk_c8
| spl0_19 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f474,definition,
( spl0_20
<=> sk_c8 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f476,plain,
( sk_c8 != inverse(sk_c6)
| spl0_20 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f477,plain,
( ~ spl0_19
| ~ spl0_20
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f458,f107,f102,f74,f474,f470]) ).
fof(f484,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f166,f84]) ).
fof(f487,plain,
( sk_c8 = multiply(sk_c4,sk_c6)
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f484,f205]) ).
fof(f494,plain,
( sk_c6 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f166,f94]) ).
fof(f497,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f494,f124]) ).
fof(f499,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f166,f454]) ).
fof(f502,plain,
( sk_c2 = multiply(sk_c4,sk_c6)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f499,f205]) ).
fof(f504,plain,
( sk_c8 = sk_c2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f502,f487]) ).
fof(f516,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f124,f504]) ).
fof(f530,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f456,f84]) ).
fof(f534,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f166,f456]) ).
fof(f538,plain,
( identity = sk_c8
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f534,f3]) ).
fof(f542,plain,
( $false
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f530,f467]) ).
fof(f543,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f546,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_18
| spl0_20 ),
inference(superposition,[],[f476,f466]) ).
fof(f547,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f192,f466]) ).
fof(f553,plain,
( sk_c8 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f272,f538]) ).
fof(f554,plain,
( sk_c7 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f553,f466]) ).
fof(f558,plain,
( spl0_19
| ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f554,f465,f142,f132,f107,f102,f470]) ).
fof(f570,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_19 ),
inference(superposition,[],[f516,f471]) ).
fof(f578,plain,
( sk_c8 = multiply(sk_c7,sk_c2)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f387,f538]) ).
fof(f580,plain,
( sk_c8 != inverse(identity)
| ~ spl0_3
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f433,f471]) ).
fof(f584,plain,
( sk_c7 = multiply(sk_c7,sk_c2)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f578,f471]) ).
fof(f586,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f580,f538]) ).
fof(f587,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f586,f471]) ).
fof(f588,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f166,f584]) ).
fof(f591,plain,
( identity = sk_c2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f588,f3]) ).
fof(f592,plain,
( sk_c8 = sk_c2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f591,f538]) ).
fof(f593,plain,
( sk_c7 = sk_c2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_demodulation,[],[f592,f471]) ).
fof(f602,plain,
( sk_c7 = inverse(sk_c7)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f124,f593]) ).
fof(f603,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f602,f587]) ).
fof(f604,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f670,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_demodulation,[],[f484,f466]) ).
fof(f671,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_demodulation,[],[f670,f3]) ).
fof(f674,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_8
| ~ spl0_14 ),
inference(superposition,[],[f166,f497]) ).
fof(f677,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f674,f466]) ).
fof(f680,plain,
( identity = sk_c7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f677,f3]) ).
fof(f706,plain,
( sk_c7 = sk_c8
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f680,f538]) ).
fof(f711,plain,
( $false
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f706,f472]) ).
fof(f712,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f711]) ).
fof(f713,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_18 ),
inference(forward_demodulation,[],[f72,f466]) ).
fof(f719,plain,
( identity != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2
| ~ spl0_18 ),
inference(superposition,[],[f713,f3]) ).
fof(f720,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(superposition,[],[f713,f497]) ).
fof(f724,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f720,f466]) ).
fof(f728,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f724,f602]) ).
fof(f729,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f733,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f78,f466]) ).
fof(f742,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(identity)
| ~ spl0_4
| ~ spl0_18 ),
inference(superposition,[],[f733,f1]) ).
fof(f744,plain,
( identity != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_4
| ~ spl0_18 ),
inference(superposition,[],[f733,f3]) ).
fof(f746,plain,
( sk_c7 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(superposition,[],[f733,f144]) ).
fof(f747,plain,
( sk_c7 != inverse(identity)
| ~ spl0_4
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f742]) ).
fof(f748,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f746,f471]) ).
fof(f750,plain,
( sk_c7 != inverse(sk_c8)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f747,f538]) ).
fof(f751,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f748,f134]) ).
fof(f752,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f751]) ).
fof(f755,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f750,f471]) ).
fof(f756,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f755,f602]) ).
fof(f757,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f756]) ).
fof(f758,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_18 ),
inference(forward_demodulation,[],[f69,f466]) ).
fof(f759,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f758,f471]) ).
fof(f760,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f759,f466]) ).
fof(f769,plain,
( identity != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f760,f3]) ).
fof(f770,plain,
( sk_c7 != sk_c6
| sk_c7 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f760,f497]) ).
fof(f771,plain,
( sk_c7 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(superposition,[],[f760,f144]) ).
fof(f773,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_1
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f771,f471]) ).
fof(f774,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f770,f466]) ).
fof(f776,plain,
( $false
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f773,f134]) ).
fof(f777,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f776]) ).
fof(f778,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f774,f602]) ).
fof(f779,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f778]) ).
fof(f783,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f81,f471]) ).
fof(f794,plain,
( identity != sk_c7
| sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_5
| ~ spl0_19 ),
inference(superposition,[],[f783,f3]) ).
fof(f796,plain,
( sk_c7 != sk_c8
| sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_19 ),
inference(superposition,[],[f783,f144]) ).
fof(f798,plain,
( sk_c7 != inverse(sk_c1)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f796,f471]) ).
fof(f801,plain,
( $false
| ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f798,f134]) ).
fof(f802,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f801]) ).
fof(f817,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_demodulation,[],[f179,f466]) ).
fof(f829,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f272,f466]) ).
fof(f844,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f114,f329]) ).
fof(f855,plain,
( identity = sk_c7
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f671,f471]) ).
fof(f893,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_18
| ~ spl0_19
| spl0_20 ),
inference(forward_demodulation,[],[f546,f471]) ).
fof(f903,definition,
( spl0_23
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f904,plain,
( identity = sk_c7
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f911,plain,
( spl0_23
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f231,f117,f112,f903]) ).
fof(f915,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f817,f547]) ).
fof(f917,plain,
( spl0_23
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f829,f465,f107,f102,f903]) ).
fof(f921,plain,
( spl0_23
| ~ spl0_6
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f855,f470,f465,f83,f903]) ).
fof(f923,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f893,f570]) ).
fof(f924,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f923]) ).
fof(f936,plain,
( sk_c7 != inverse(sk_c7)
| identity != sk_c7
| ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f719,f570]) ).
fof(f954,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f936,f570]) ).
fof(f958,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f954,f904]) ).
fof(f959,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f958]) ).
fof(f980,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_4
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f744,f904]) ).
fof(f996,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f980,f287]) ).
fof(f999,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f996,f287]) ).
fof(f1000,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f999]) ).
fof(f1004,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_2
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f719,f904]) ).
fof(f1008,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1004,f287]) ).
fof(f1011,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1008,f287]) ).
fof(f1012,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1011]) ).
fof(f1017,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f769,f904]) ).
fof(f1025,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1017,f287]) ).
fof(f1032,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1025,f287]) ).
fof(f1033,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1032]) ).
fof(f1037,plain,
( sk_c7 != inverse(inverse(sk_c7))
| ~ spl0_5
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f794,f904]) ).
fof(f1048,plain,
( sk_c7 != inverse(sk_c7)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1037,f287]) ).
fof(f1055,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1048,f287]) ).
fof(f1056,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1055]) ).
fof(f1070,plain,
( sk_c7 = sk_c8
| ~ spl0_6
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_demodulation,[],[f671,f904]) ).
fof(f1074,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f844,f287]) ).
fof(f1075,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f915,f472]) ).
fof(f1076,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f1075]) ).
fof(f1084,plain,
( $false
| ~ spl0_6
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1070,f472]) ).
fof(f1085,plain,
( ~ spl0_6
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1084]) ).
fof(f1089,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f1074,f472]) ).
fof(f1090,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f1089]) ).
fof(f1109,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f484,f287]) ).
fof(f1111,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f99,f294]) ).
fof(f1118,plain,
( sk_c7 = sk_c6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f192,f238]) ).
fof(f1131,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1109,f238]) ).
fof(f1133,plain,
( sk_c7 = sk_c6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1111,f287]) ).
fof(f1138,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f1118,f467]) ).
fof(f1139,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f1138]) ).
fof(f1145,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1131,f471]) ).
fof(f1148,plain,
( $false
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f1133,f467]) ).
fof(f1149,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f1148]) ).
fof(f1151,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1145,f467]) ).
fof(f1152,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1151]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f86]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f95]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f100]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f110]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f115]) ).
cnf(s7,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s8,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f125]) ).
cnf(s9,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s10,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f127]) ).
cnf(s11,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f128]) ).
cnf(s12,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f129]) ).
cnf(s13,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f130]) ).
cnf(s14,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f135]) ).
cnf(s15,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f136]) ).
cnf(s16,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f137]) ).
cnf(s17,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f138]) ).
cnf(s18,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f139]) ).
cnf(s19,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f140]) ).
cnf(s20,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f145]) ).
cnf(s21,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f146]) ).
cnf(s22,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f147]) ).
cnf(s23,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f148]) ).
cnf(s24,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f149]) ).
cnf(s25,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f150]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f151]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f152]) ).
cnf(s28,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f153]) ).
cnf(s29,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s30,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f155]) ).
cnf(s31,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f156]) ).
cnf(s32,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f332]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f439]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f477]) ).
cnf(s46,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(sat_conversion,[],[f543]) ).
cnf(s47,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f558]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(sat_conversion,[],[f604]) ).
cnf(s53,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f712]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f729]) ).
cnf(s57,plain,
( ~ spl0_4
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f752]) ).
cnf(s59,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f757]) ).
cnf(s60,plain,
( ~ spl0_1
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f777]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f779]) ).
cnf(s63,plain,
( ~ spl0_5
| ~ spl0_15
| ~ spl0_16
| ~ spl0_19 ),
inference(sat_conversion,[],[f802]) ).
cnf(s76,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_23 ),
inference(sat_conversion,[],[f911]) ).
cnf(s77,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_23 ),
inference(sat_conversion,[],[f917]) ).
cnf(s78,plain,
( ~ spl0_6
| ~ spl0_18
| ~ spl0_19
| spl0_23 ),
inference(sat_conversion,[],[f921]) ).
cnf(s79,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f924]) ).
cnf(s84,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f959]) ).
cnf(s96,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(sat_conversion,[],[f1000]) ).
cnf(s99,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_23 ),
inference(sat_conversion,[],[f1012]) ).
cnf(s103,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s110,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f1056]) ).
cnf(s113,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_19 ),
inference(sat_conversion,[],[f1076]) ).
cnf(s115,plain,
( ~ spl0_6
| ~ spl0_18
| spl0_19
| ~ spl0_23 ),
inference(sat_conversion,[],[f1085]) ).
cnf(s117,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_19 ),
inference(sat_conversion,[],[f1090]) ).
cnf(s128,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f1139]) ).
cnf(s131,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f1149]) ).
cnf(s132,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1152]) ).
cnf(s134,plain,
spl0_6,
inference(rat,[],[s32,s26,s27,s28,s29,s30,s31]) ).
cnf(s135,plain,
( spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s110,s76,s117,s3,s4,s5,s6,s7]) ).
cnf(s136,plain,
( ~ spl0_13
| ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s110,s76,s117]) ).
cnf(s137,plain,
( spl0_13
| ~ spl0_11
| ~ spl0_10
| ~ spl0_5 ),
inference(rat,[],[s47,s46,s63,s19,s25,s134]) ).
cnf(s138,plain,
( ~ spl0_13
| ~ spl0_11
| ~ spl0_5
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7 ),
inference(rat,[],[s47,s46,s63,s18,s24,s136,s134]) ).
cnf(s139,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s138,s137]) ).
cnf(s140,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s53,s46,s63,s11,s17,s23,s134]) ).
cnf(s141,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s53,s46,s63,s10,s16,s22,s134]) ).
cnf(s142,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_5
| ~ spl0_7 ),
inference(rat,[],[s47,s46,s63,s15,s21,s139,s134]) ).
cnf(s143,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s142,s141,s140,s135]) ).
cnf(s144,plain,
~ spl0_5,
inference(rat,[],[s53,s46,s63,s2,s8,s14,s20,s143,s134]) ).
cnf(s145,plain,
( spl0_15
| ~ spl0_9
| ~ spl0_11
| ~ spl0_10
| ~ spl0_4 ),
inference(rat,[],[s96,s76,s131,s18,s19]) ).
cnf(s146,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_15
| ~ spl0_11
| ~ spl0_10
| ~ spl0_4 ),
inference(rat,[],[s96,s24,s25,s57,s78,s134]) ).
cnf(s147,plain,
( ~ spl0_19
| ~ spl0_15
| ~ spl0_4
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s132,s24,s25,s46,s146,s134]) ).
cnf(s148,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_10
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s128,s24,s25,s46,s113,s147,s145,s134]) ).
cnf(s149,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(rat,[],[s53,s147,s46,s3,s9,s15,s21,s148,s134]) ).
cnf(s150,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s53,s59,s46,s5,s11,s17,s23,s134]) ).
cnf(s151,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s53,s59,s46,s4,s10,s16,s22,s134]) ).
cnf(s152,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s53,s147,s46,s2,s8,s14,s20,s149,s134]) ).
cnf(s153,plain,
~ spl0_4,
inference(rat,[],[s152,s151,s150]) ).
cnf(s154,plain,
( spl0_15
| ~ spl0_3 ),
inference(rat,[],[s38,s18,s19]) ).
cnf(s155,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s38,s12,s13]) ).
cnf(s156,plain,
( ~ spl0_19
| ~ spl0_11
| ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s132,s24,s25,s79,s50,s42,s154,s155,s134]) ).
cnf(s157,plain,
( ~ spl0_18
| spl0_19
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s77,s115,s134]) ).
cnf(s158,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s117,s20,s21,s24,s25,s46,s157,s156,s154,s134]) ).
cnf(s159,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s53,s50,s46,s5,s23,s154,s155,s134]) ).
cnf(s160,plain,
~ spl0_3,
inference(rat,[],[s53,s50,s46,s4,s22,s158,s159,s155,s154,s134]) ).
cnf(s161,plain,
( ~ spl0_18
| ~ spl0_23
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(rat,[],[s99,s12,s13,s84,s134]) ).
cnf(s162,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s161,s78,s134]) ).
cnf(s163,plain,
( spl0_15
| spl0_18
| ~ spl0_19
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s132,s18,s19,s134]) ).
cnf(s164,plain,
( spl0_18
| ~ spl0_19
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s132,s24,s25,s46,s163,s134]) ).
cnf(s165,plain,
( ~ spl0_19
| ~ spl0_11
| ~ spl0_2
| ~ spl0_10 ),
inference(rat,[],[s164,s162]) ).
cnf(s166,plain,
( spl0_15
| spl0_19
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s117,s14,s15,s18,s19]) ).
cnf(s167,plain,
( spl0_19
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s117,s20,s21,s24,s25,s46,s166,s157,s134]) ).
cnf(s168,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s167,s165]) ).
cnf(s169,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s55,s53,s46,s5,s11,s17,s23,s134]) ).
cnf(s170,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s55,s53,s46,s4,s10,s16,s22,s168,s134]) ).
cnf(s171,plain,
~ spl0_2,
inference(rat,[],[s170,s169]) ).
cnf(s172,plain,
spl0_1,
inference(rat,[],[s1,s144,s134,s153,s160,s171]) ).
cnf(s173,plain,
( spl0_15
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s103,s18,s19,s78,s164,s167,s172,s134]) ).
cnf(s174,plain,
( ~ spl0_19
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s103,s24,s25,s60,s173,s78,s164,s134,s172]) ).
cnf(s175,plain,
( ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s174,s167]) ).
cnf(s176,plain,
( ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_18 ),
inference(rat,[],[s61,s53,s172]) ).
cnf(s177,plain,
spl0_11,
inference(rat,[],[s176,s46,s5,s11,s17,s23,s134]) ).
cnf(s178,plain,
~ spl0_10,
inference(rat,[],[s175,s177]) ).
cnf(s179,plain,
spl0_16,
inference(rat,[],[s22,s178]) ).
cnf(s180,plain,
spl0_15,
inference(rat,[],[s16,s178]) ).
cnf(s181,plain,
spl0_14,
inference(rat,[],[s10,s178]) ).
cnf(s182,plain,
spl0_8,
inference(rat,[],[s4,s178]) ).
cnf(s183,plain,
spl0_18,
inference(rat,[],[s46,s179,s134,s180]) ).
cnf(s184,plain,
$false,
inference(rat,[],[s176,s183,s179,s180,s181,s182]) ).
fof(f1155,plain,
$false,
inference(avatar_sat_refutation,[],[s184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP331-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:53:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.15/0.48 % (3260158)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (3260165)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=421159287:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (3260164)% WARNING: option uhcvi not known.
% 0.15/0.48 % (3260166)dis+10_1_sil=32000:sp=arity:random_seed=539962476:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (3260163)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1582402296_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % (3260164)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2046387349:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (3260168)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=321244205:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (3260167)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1935763873:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (3260169)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4158451317:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % (3260167) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3260158-3260167"...
% 0.15/0.48 % TRYING [5]
% 0.15/0.48 % (3260168) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3260158-3260168"...
% 0.15/0.48 % (3260166) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3260158-3260166"...
% 0.15/0.48 % (3260167)...printing done.
% 0.15/0.48 % (3260166)...printing done.
% 0.15/0.48 % (3260164) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3260158-3260164"...
% 0.15/0.48 % (3260167)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (3260167)------------------------------
% 0.15/0.48 % (3260167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (3260167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (3260167)CaDiCaL version: 2.1.3
% 0.15/0.48 % (3260167)Termination reason: Refutation
% 0.15/0.48 % (3260167)Time elapsed: 0.023 s
% 0.15/0.48 % (3260167)Peak memory usage: 12 MB
% 0.15/0.48 % (3260167)Instructions burned: 36 (million)
% 0.15/0.48 % (3260158)Success in time 0.065 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------