%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 10:17:17 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 52
% Syntax : Number of formulae : 319 ( 23 unt; 18 def)
% Number of atoms : 934 ( 310 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1148 ( 533 ~; 597 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c9 = inverse(sk_c1)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = inverse(sk_c2)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f40]) ).
fof(f46,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(reorient_equations,[],[f50]) ).
fof(f54,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c9 = inverse(sk_c3)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f66,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f72]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| multiply(X1,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c7) != sk_c9
| inverse(sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,X5) != sk_c8
| inverse(X4) != X5
| multiply(X5,sk_c7) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7)
| inverse(sk_c8) != sk_c7
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c7) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7)
| inverse(sk_c8) != sk_c7
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c7) ),
inference(equality_resolution,[],[f77]) ).
fof(f80,definition,
( spl0_1
<=> ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f81,plain,
( ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c7) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f84,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,definition,
( spl0_3
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f87,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( inverse(sk_c8) != sk_c7
| spl0_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c7)
| sk_c9 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,definition,
( spl0_5
<=> ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f94,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl0_6
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f97,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f98,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f78,f96,f93,f90,f86,f83,f80]) ).
fof(f100,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f102,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f104,definition,
( spl0_8
<=> sk_c9 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f106,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f109,definition,
( spl0_9
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f111,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f73,f104,f109]) ).
fof(f114,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f71,f104,f114]) ).
fof(f119,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f121,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f69,f104,f119]) ).
fof(f124,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f126,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f67,f104,f124]) ).
fof(f130,definition,
( spl0_13
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f61,f130,f109]) ).
fof(f135,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f59,f130,f114]) ).
fof(f136,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f57,f130,f119]) ).
fof(f137,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f55,f130,f124]) ).
fof(f140,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f142,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f51,f140,f100]) ).
fof(f144,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f49,f140,f109]) ).
fof(f145,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f47,f140,f114]) ).
fof(f148,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f41,f140,f86]) ).
fof(f150,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f152,plain,
( sk_c7 = multiply(sk_c2,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f39,f150,f100]) ).
fof(f154,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f37,f150,f109]) ).
fof(f155,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f35,f150,f114]) ).
fof(f156,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f33,f150,f119]) ).
fof(f157,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f31,f150,f124]) ).
fof(f158,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f29,f150,f86]) ).
fof(f160,definition,
( spl0_16
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f162,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f163,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f27,f160,f100]) ).
fof(f164,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f25,f160,f109]) ).
fof(f165,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f23,f160,f114]) ).
fof(f166,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f21,f160,f119]) ).
fof(f167,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f19,f160,f124]) ).
fof(f168,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f17,f160,f86]) ).
fof(f170,definition,
( spl0_17
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f172,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f173,plain,
( spl0_7
| spl0_17 ),
inference(avatar_split_clause,[],[f15,f170,f100]) ).
fof(f174,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f13,f170,f109]) ).
fof(f175,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f11,f170,f114]) ).
fof(f176,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f9,f170,f119]) ).
fof(f177,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f7,f170,f124]) ).
fof(f178,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f5,f170,f86]) ).
fof(f179,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f84,f121]) ).
fof(f180,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f179]) ).
fof(f181,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f180,f126]) ).
fof(f182,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f200,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f162]) ).
fof(f201,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f3,f87]) ).
fof(f219,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f220,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c9,X0)) = multiply(sk_c8,X0)
| ~ spl0_17 ),
inference(superposition,[],[f4,f172]) ).
fof(f221,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f116]) ).
fof(f223,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c8,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f152]) ).
fof(f226,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f219,f1]) ).
fof(f229,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c1,X0))
| ~ spl0_16 ),
inference(superposition,[],[f4,f200]) ).
fof(f230,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c1,X0)) = X0
| ~ spl0_16 ),
inference(forward_demodulation,[],[f229,f1]) ).
fof(f242,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f230,f172]) ).
fof(f253,plain,
( multiply(sk_c1,sk_c9) = multiply(sk_c8,sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f220,f242]) ).
fof(f254,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c9)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f84,f242]) ).
fof(f256,plain,
( sk_c9 != inverse(sk_c9)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f254]) ).
fof(f257,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f253,f172]) ).
fof(f277,plain,
( multiply(sk_c2,sk_c8) = multiply(sk_c7,sk_c8)
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f223,f257]) ).
fof(f280,plain,
( identity = multiply(sk_c2,sk_c8)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f277,f201]) ).
fof(f281,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f280,f152]) ).
fof(f336,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f226,f3]) ).
fof(f337,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f226,f226]) ).
fof(f340,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(sk_c9),X0)
| ~ spl0_16 ),
inference(superposition,[],[f226,f230]) ).
fof(f346,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f226,f257]) ).
fof(f349,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f226,f116]) ).
fof(f355,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f226,f152]) ).
fof(f357,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_8 ),
inference(superposition,[],[f226,f106]) ).
fof(f363,plain,
( sk_c7 = multiply(sk_c9,sk_c9)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f357,f132]) ).
fof(f365,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f355,f142]) ).
fof(f370,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f349,f111]) ).
fof(f372,plain,
( identity = sk_c8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f346,f3]) ).
fof(f380,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f336,f337]) ).
fof(f389,plain,
( ! [X0] : multiply(X0,sk_c7) = X0
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f380,f281]) ).
fof(f421,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f226,f363]) ).
fof(f424,plain,
( sk_c9 = multiply(sk_c1,sk_c7)
| ~ spl0_8
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_demodulation,[],[f421,f340]) ).
fof(f426,plain,
( sk_c1 = sk_c9
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f424,f389]) ).
fof(f432,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f162,f426]) ).
fof(f433,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f432,f256]) ).
fof(f434,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f443,plain,
( ! [X0] : multiply(X0,sk_c8) = X0
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f380,f372]) ).
fof(f458,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f226,f365]) ).
fof(f460,plain,
( identity = sk_c7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f458,f3]) ).
fof(f462,plain,
( sk_c8 = sk_c7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f460,f372]) ).
fof(f472,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c8,sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f221,f370]) ).
fof(f475,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f226,f370]) ).
fof(f477,plain,
( identity = sk_c8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f475,f3]) ).
fof(f517,plain,
( identity = inverse(sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f443]) ).
fof(f524,plain,
( sk_c7 = sk_c2
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f152,f443]) ).
fof(f525,plain,
( sk_c8 = sk_c2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f524,f462]) ).
fof(f532,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f517,f372]) ).
fof(f566,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c8)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f81,f462]) ).
fof(f583,plain,
( ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f566,f443]) ).
fof(f595,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| sk_c8 != sk_c8
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f583,f142]) ).
fof(f600,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f595]) ).
fof(f602,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f600,f152]) ).
fof(f606,plain,
( $false
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f602,f462]) ).
fof(f607,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f606]) ).
fof(f622,plain,
( sk_c8 != sk_c8
| sk_c9 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f97,f172]) ).
fof(f624,plain,
( sk_c9 != inverse(sk_c1)
| ~ spl0_6
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f622]) ).
fof(f626,plain,
( $false
| ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f624,f162]) ).
fof(f627,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f656,plain,
( sk_c8 != inverse(sk_c8)
| spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f88,f462]) ).
fof(f658,plain,
( $false
| spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f656,f532]) ).
fof(f659,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f667,plain,
( ! [X1] :
( sk_c7 != X1
| sk_c8 != inverse(X1) )
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f94,f443]) ).
fof(f668,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != X1 )
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f667,f462]) ).
fof(f672,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f668,f142]) ).
fof(f674,plain,
( sk_c8 != sk_c2
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f672]) ).
fof(f678,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f674,f525]) ).
fof(f679,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f680,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f472,f116]) ).
fof(f687,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f3,f87]) ).
fof(f693,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f460,f477]) ).
fof(f696,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f1,f477]) ).
fof(f718,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c5,sk_c8)
| ~ spl0_7
| ~ spl0_10 ),
inference(superposition,[],[f221,f102]) ).
fof(f720,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f102]) ).
fof(f734,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_11 ),
inference(superposition,[],[f226,f121]) ).
fof(f735,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c8,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f121]) ).
fof(f737,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f734,f126]) ).
fof(f746,plain,
( sk_c8 != multiply(sk_c5,sk_c6)
| sk_c8 != multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f81,f111]) ).
fof(f768,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f746,f116]) ).
fof(f783,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f768,f102]) ).
fof(f784,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f783]) ).
fof(f848,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c8)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f91,f693]) ).
fof(f849,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f848,f150,f140,f114,f109,f90,f83]) ).
fof(f889,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f687,f477]) ).
fof(f891,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = X0
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f720,f696]) ).
fof(f892,plain,
( sk_c7 = multiply(sk_c5,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f718,f696]) ).
fof(f893,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,X0)
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f735,f696]) ).
fof(f898,plain,
( sk_c9 != sk_c9
| sk_c9 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f91,f106]) ).
fof(f906,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f94,f1]) ).
fof(f928,definition,
( spl0_26
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f929,plain,
( sk_c8 = sk_c7
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f930,plain,
( sk_c8 != sk_c7
| spl0_26 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f933,plain,
( sk_c8 != inverse(sk_c8)
| sk_c8 != sk_c7
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f906,f477]) ).
fof(f935,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f933,f87]) ).
fof(f936,plain,
( sk_c8 != sk_c7
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f935]) ).
fof(f938,plain,
( ~ spl0_26
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f936,f114,f109,f93,f86,f928]) ).
fof(f944,plain,
( sk_c8 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f891,f889]) ).
fof(f990,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| sk_c9 != inverse(sk_c4)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f97,f893]) ).
fof(f991,plain,
( sk_c9 != inverse(sk_c4)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f990,f737]) ).
fof(f994,plain,
( $false
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f991,f126]) ).
fof(f995,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f994]) ).
fof(f996,plain,
( sk_c9 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f898]) ).
fof(f997,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c8)
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_26 ),
inference(forward_demodulation,[],[f91,f929]) ).
fof(f998,plain,
( ~ spl0_13
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f996,f104,f90,f130]) ).
fof(f1001,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f997,f928,f90,f83]) ).
fof(f1046,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f221,f944]) ).
fof(f1051,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1046,f892]) ).
fof(f1053,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1051,f680]) ).
fof(f1054,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f1053,f930]) ).
fof(f1055,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f1054]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f98]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f112]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f117]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f122]) ).
cnf(s6,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f127]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f134]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f135]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f136]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f137]) ).
cnf(s14,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f143]) ).
cnf(s15,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f144]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f145]) ).
cnf(s19,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f148]) ).
cnf(s20,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f153]) ).
cnf(s21,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s22,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f155]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f157]) ).
cnf(s25,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f158]) ).
cnf(s26,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f163]) ).
cnf(s27,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s28,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s29,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s30,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s31,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s32,plain,
( spl0_7
| spl0_17 ),
inference(sat_conversion,[],[f173]) ).
cnf(s33,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f174]) ).
cnf(s34,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f175]) ).
cnf(s35,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f176]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f177]) ).
cnf(s37,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f178]) ).
cnf(s38,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f182]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f434]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f607]) ).
cnf(s51,plain,
( ~ spl0_6
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f627]) ).
cnf(s56,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f659]) ).
cnf(s58,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f679]) ).
cnf(s61,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f784]) ).
cnf(s69,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f849]) ).
cnf(s79,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| ~ spl0_26 ),
inference(sat_conversion,[],[f938]) ).
cnf(s84,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f995]) ).
cnf(s85,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f998]) ).
cnf(s87,plain,
( spl0_2
| ~ spl0_4
| ~ spl0_26 ),
inference(sat_conversion,[],[f1001]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| spl0_26 ),
inference(sat_conversion,[],[f1055]) ).
cnf(s89,plain,
spl0_3,
inference(rat,[],[s56,s19,s25,s31,s37]) ).
cnf(s91,plain,
( spl0_17
| ~ spl0_6 ),
inference(rat,[],[s84,s33,s34,s35,s36]) ).
cnf(s92,plain,
( ~ spl0_17
| ~ spl0_6 ),
inference(rat,[],[s84,s27,s28,s29,s30,s51]) ).
cnf(s93,plain,
~ spl0_6,
inference(rat,[],[s92,s91]) ).
cnf(s94,plain,
( spl0_17
| ~ spl0_5 ),
inference(rat,[],[s79,s88,s32,s33,s34,s89]) ).
cnf(s95,plain,
( spl0_7
| ~ spl0_16
| ~ spl0_5 ),
inference(rat,[],[s58,s14,s20,s94]) ).
cnf(s96,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s88,s79,s89]) ).
cnf(s97,plain,
( spl0_10
| ~ spl0_16
| ~ spl0_5 ),
inference(rat,[],[s58,s16,s22,s94]) ).
cnf(s98,plain,
( ~ spl0_16
| ~ spl0_5 ),
inference(rat,[],[s58,s15,s21,s96,s97,s95,s94]) ).
cnf(s99,plain,
~ spl0_5,
inference(rat,[],[s96,s26,s27,s28,s98]) ).
cnf(s100,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_4
| spl0_2 ),
inference(rat,[],[s69,s14,s20,s88,s87,s89]) ).
cnf(s101,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s85,s4,s10]) ).
cnf(s102,plain,
( ~ spl0_10
| spl0_2
| ~ spl0_4 ),
inference(rat,[],[s85,s3,s9,s100]) ).
cnf(s103,plain,
( spl0_1
| spl0_2 ),
inference(rat,[],[s102,s101,s1,s93,s89,s99]) ).
cnf(s104,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s38,s11,s12]) ).
cnf(s105,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s38,s5,s6]) ).
cnf(s106,plain,
( spl0_15
| ~ spl0_2 ),
inference(rat,[],[s38,s23,s24]) ).
cnf(s107,plain,
( spl0_17
| ~ spl0_2 ),
inference(rat,[],[s38,s35,s36]) ).
cnf(s108,plain,
( ~ spl0_17
| ~ spl0_15
| ~ spl0_2
| ~ spl0_13
| ~ spl0_8 ),
inference(rat,[],[s38,s29,s30,s42,s89]) ).
cnf(s109,plain,
~ spl0_2,
inference(rat,[],[s108,s107,s106,s105,s104]) ).
cnf(s110,plain,
spl0_1,
inference(rat,[],[s103,s109]) ).
cnf(s111,plain,
spl0_14,
inference(rat,[],[s61,s14,s15,s16,s110]) ).
cnf(s112,plain,
spl0_15,
inference(rat,[],[s61,s20,s21,s22,s110]) ).
cnf(s113,plain,
spl0_17,
inference(rat,[],[s61,s32,s33,s34,s110]) ).
cnf(s114,plain,
~ spl0_16,
inference(rat,[],[s49,s111,s112,s110,s113]) ).
cnf(s117,plain,
spl0_10,
inference(rat,[],[s28,s114]) ).
cnf(s118,plain,
spl0_9,
inference(rat,[],[s27,s114]) ).
cnf(s119,plain,
spl0_7,
inference(rat,[],[s26,s114]) ).
cnf(s120,plain,
$false,
inference(rat,[],[s61,s119,s110,s117,s118]) ).
fof(f1056,plain,
$false,
inference(avatar_sat_refutation,[],[s120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:45:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 % (3300326)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3300331)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3401754146_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (3300332)% WARNING: option uhcvi not known.
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (3300332)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3723027498:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3300334)dis+10_1_sil=32000:sp=arity:random_seed=3429540180:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3300333)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1849940360:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3300335)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2032250588:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3300336)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4280504437:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3300337)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1991891788:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % TRYING [6]
% 0.17/0.48 % (3300335) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3300326-3300335"...
% 0.17/0.48 % (3300334) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3300326-3300334"...
% 0.17/0.48 % (3300335)...printing done.
% 0.17/0.48 % (3300335)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3300335)------------------------------
% 0.17/0.48 % (3300335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3300335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3300335)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3300335)Termination reason: Refutation
% 0.17/0.48 % (3300335)Time elapsed: 0.022 s
% 0.17/0.48 % (3300335)Peak memory usage: 12 MB
% 0.17/0.48 % (3300335)Instructions burned: 34 (million)
% 0.17/0.48 % (3300326)Success in time 0.066 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------