%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP327-1 : 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 : n008.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 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 56
% Syntax : Number of formulae : 349 ( 23 unt; 21 def)
% Number of atoms : 1069 ( 319 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1338 ( 618 ~; 699 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 44 !; 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_c7,sk_c8) = sk_c6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = inverse(sk_c7) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = inverse(sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = inverse(sk_c7) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = inverse(sk_c7) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = inverse(sk_c7) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,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 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c6 != inverse(sk_c7)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c6 != inverse(sk_c7)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl0_4
<=> sk_c6 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f81,plain,
( sk_c6 = inverse(sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( sk_c6 != inverse(sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_5
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f85,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,definition,
( spl0_6
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f88,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl0_7
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f91,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f68,f90,f87,f84,f80,f76,f73,f70]) ).
fof(f95,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f97,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f99,definition,
( spl0_9
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f65,f99,f95]) ).
fof(f104,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_9 ),
inference(avatar_split_clause,[],[f63,f99,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_9 ),
inference(avatar_split_clause,[],[f61,f99,f109]) ).
fof(f114,definition,
( spl0_12
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_9 ),
inference(avatar_split_clause,[],[f59,f99,f114]) ).
fof(f118,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f57,f99,f76]) ).
fof(f119,plain,
( spl0_4
| spl0_9 ),
inference(avatar_split_clause,[],[f55,f99,f80]) ).
fof(f121,definition,
( spl0_13
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f122,plain,
( sk_c3 != multiply(sk_c2,sk_c8)
| spl0_13 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f53,f121,f95]) ).
fof(f125,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f51,f121,f104]) ).
fof(f126,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f49,f121,f109]) ).
fof(f127,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f47,f121,f114]) ).
fof(f128,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f45,f121,f76]) ).
fof(f129,plain,
( spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f43,f121,f80]) ).
fof(f131,definition,
( spl0_14
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f133,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f41,f131,f95]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f39,f131,f104]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f131,f109]) ).
fof(f137,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f131,f114]) ).
fof(f138,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f131,f76]) ).
fof(f139,plain,
( spl0_4
| spl0_14 ),
inference(avatar_split_clause,[],[f31,f131,f80]) ).
fof(f141,definition,
( spl0_15
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f143,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f29,f141,f95]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f27,f141,f104]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f141,f109]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f23,f141,f114]) ).
fof(f148,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f141,f76]) ).
fof(f149,plain,
( spl0_4
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f141,f80]) ).
fof(f151,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f153,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f17,f151,f95]) ).
fof(f155,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f15,f151,f104]) ).
fof(f156,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f13,f151,f109]) ).
fof(f157,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f11,f151,f114]) ).
fof(f158,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f9,f151,f76]) ).
fof(f159,plain,
( spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f7,f151,f80]) ).
fof(f160,plain,
spl0_7,
inference(avatar_split_clause,[],[f5,f90]) ).
fof(f161,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f74,f111]) ).
fof(f162,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f161]) ).
fof(f163,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f162,f116]) ).
fof(f164,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f163]) ).
fof(f165,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_16 ),
inference(superposition,[],[f74,f153]) ).
fof(f166,plain,
( sk_c8 != inverse(sk_c1)
| ~ spl0_2
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f165]) ).
fof(f167,plain,
( sk_c7 != sk_c8
| ~ spl0_2
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f166,f143]) ).
fof(f169,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_4 ),
inference(superposition,[],[f3,f81]) ).
fof(f170,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f143]) ).
fof(f172,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f106]) ).
fof(f173,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f177,definition,
( spl0_17
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f178,plain,
( identity = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f179,plain,
( identity != sk_c8
| spl0_17 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f186,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f190,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_7 ),
inference(superposition,[],[f4,f91]) ).
fof(f196,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f186,f1]) ).
fof(f199,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c7,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f169]) ).
fof(f200,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c7,X0)) = X0
| ~ spl0_4 ),
inference(forward_demodulation,[],[f199,f1]) ).
fof(f209,plain,
( sk_c8 = multiply(sk_c6,sk_c6)
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f200,f91]) ).
fof(f325,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f196,f153]) ).
fof(f329,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f196,f123]) ).
fof(f330,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f196,f97]) ).
fof(f345,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f330,f106]) ).
fof(f346,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f329,f101]) ).
fof(f350,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f325,f143]) ).
fof(f363,plain,
( sk_c7 = sk_c8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f346,f133]) ).
fof(f370,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f363,f167]) ).
fof(f371,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f380,plain,
( sk_c7 = multiply(identity,sk_c3)
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f133,f178]) ).
fof(f381,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f173,f178]) ).
fof(f390,plain,
( identity = sk_c2
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f381,f1]) ).
fof(f391,plain,
( sk_c7 = sk_c3
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f380,f1]) ).
fof(f416,definition,
( spl0_20
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f417,plain,
( identity = sk_c7
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f421,definition,
( spl0_21
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f422,plain,
( identity = inverse(identity)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f444,plain,
( sk_c8 = inverse(identity)
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f101,f390]) ).
fof(f445,plain,
( identity = inverse(identity)
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f444,f178]) ).
fof(f454,plain,
( spl0_21
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f445,f177,f99,f421]) ).
fof(f491,plain,
( sk_c7 != multiply(sk_c8,sk_c3)
| sk_c8 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_13 ),
inference(superposition,[],[f85,f123]) ).
fof(f492,plain,
( sk_c7 != multiply(sk_c8,sk_c8)
| sk_c8 != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f85,f1]) ).
fof(f506,plain,
( identity != sk_c8
| sk_c7 != multiply(sk_c8,sk_c8)
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f492,f422]) ).
fof(f507,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f491,f133]) ).
fof(f527,definition,
( spl0_29
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f528,plain,
( sk_c7 = sk_c6
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f529,plain,
( sk_c7 != sk_c6
| spl0_29 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f532,definition,
( spl0_30
<=> sk_c7 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f533,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f536,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f507,f101]) ).
fof(f537,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f536]) ).
fof(f543,plain,
( identity != sk_c7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_17 ),
inference(superposition,[],[f179,f363]) ).
fof(f556,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f350,f363]) ).
fof(f560,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f196,f556]) ).
fof(f562,plain,
( identity = sk_c7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f560,f3]) ).
fof(f570,plain,
( ~ spl0_20
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f543,f177,f131,f121,f99,f416]) ).
fof(f571,plain,
( spl0_20
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f562,f151,f141,f131,f121,f99,f416]) ).
fof(f590,plain,
( sk_c6 != inverse(identity)
| spl0_4
| ~ spl0_20 ),
inference(superposition,[],[f82,f417]) ).
fof(f591,plain,
( sk_c6 = multiply(identity,sk_c8)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f91,f417]) ).
fof(f593,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f170,f417]) ).
fof(f594,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f172,f417]) ).
fof(f603,plain,
( identity = sk_c5
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f594,f1]) ).
fof(f604,plain,
( identity = sk_c1
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f593,f1]) ).
fof(f606,plain,
( sk_c8 = sk_c6
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f591,f1]) ).
fof(f607,plain,
( identity != sk_c6
| spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f590,f422]) ).
fof(f611,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f606,f363]) ).
fof(f614,plain,
( identity = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f611,f417]) ).
fof(f631,plain,
( identity = sk_c3
| ~ spl0_14
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f391,f417]) ).
fof(f638,plain,
( sk_c7 = inverse(identity)
| ~ spl0_10
| ~ spl0_20 ),
inference(superposition,[],[f106,f603]) ).
fof(f651,plain,
( sk_c7 = inverse(identity)
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f143,f604]) ).
fof(f656,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f614,f607]) ).
fof(f657,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f658,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f71,f417]) ).
fof(f659,plain,
( sk_c6 = inverse(identity)
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f81,f417]) ).
fof(f677,plain,
( ! [X4] :
( identity != multiply(X4,sk_c6)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f658,f417]) ).
fof(f678,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f659,f422]) ).
fof(f703,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f677,f678]) ).
fof(f710,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f703,f3]) ).
fof(f712,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f710]) ).
fof(f714,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f712,f422]) ).
fof(f717,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f714,f422]) ).
fof(f718,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f719,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_6
| ~ spl0_20 ),
inference(forward_demodulation,[],[f88,f417]) ).
fof(f720,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f719,f363]) ).
fof(f721,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f720,f417]) ).
fof(f722,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f721,f417]) ).
fof(f724,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f722,f3]) ).
fof(f726,plain,
( identity != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f724]) ).
fof(f728,plain,
( identity != inverse(identity)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f726,f422]) ).
fof(f731,plain,
( $false
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f728,f422]) ).
fof(f732,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f731]) ).
fof(f733,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f78,f363]) ).
fof(f734,plain,
( identity != multiply(sk_c6,identity)
| spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f733,f417]) ).
fof(f735,plain,
( identity != multiply(identity,identity)
| spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f734,f678]) ).
fof(f736,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f735,f1]) ).
fof(f737,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f736]) ).
fof(f765,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_6
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f719,f178]) ).
fof(f768,plain,
( sk_c3 != multiply(sk_c2,identity)
| spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f122,f178]) ).
fof(f778,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f209,f678]) ).
fof(f798,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f765,f417]) ).
fof(f800,plain,
( sk_c3 != multiply(identity,identity)
| ~ spl0_9
| spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f768,f390]) ).
fof(f804,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_7
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f778,f1]) ).
fof(f810,plain,
( identity != sk_c3
| ~ spl0_9
| spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f800,f1]) ).
fof(f812,plain,
( $false
| ~ spl0_9
| spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f810,f631]) ).
fof(f813,plain,
( ~ spl0_9
| spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f812]) ).
fof(f824,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f798,f1]) ).
fof(f828,plain,
( identity != inverse(identity)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f824]) ).
fof(f834,plain,
( identity = inverse(identity)
| ~ spl0_10
| ~ spl0_20 ),
inference(forward_demodulation,[],[f638,f417]) ).
fof(f835,plain,
( identity = inverse(identity)
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f651,f417]) ).
fof(f851,plain,
( ~ spl0_21
| ~ spl0_6
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f828,f416,f177,f87,f421]) ).
fof(f852,plain,
( spl0_21
| ~ spl0_10
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f834,f416,f104,f421]) ).
fof(f853,plain,
( spl0_21
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f835,f416,f141,f421]) ).
fof(f918,plain,
( ~ spl0_30
| ~ spl0_17
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f506,f421,f84,f177,f532]) ).
fof(f920,plain,
( identity = multiply(sk_c6,sk_c7)
| ~ spl0_4 ),
inference(superposition,[],[f3,f81]) ).
fof(f929,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_11 ),
inference(superposition,[],[f196,f111]) ).
fof(f931,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f929,f116]) ).
fof(f932,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f931,f114,f109,f532]) ).
fof(f949,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_30 ),
inference(superposition,[],[f190,f533]) ).
fof(f952,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_30 ),
inference(forward_demodulation,[],[f949,f345]) ).
fof(f954,plain,
( identity = multiply(sk_c7,sk_c7)
| ~ spl0_4
| ~ spl0_29 ),
inference(forward_demodulation,[],[f920,f528]) ).
fof(f960,plain,
( identity = sk_c6
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_29 ),
inference(superposition,[],[f954,f345]) ).
fof(f971,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_29 ),
inference(superposition,[],[f528,f960]) ).
fof(f972,plain,
( spl0_20
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f971,f527,f104,f95,f80,f416]) ).
fof(f983,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f804,f179]) ).
fof(f984,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f983]) ).
fof(f1025,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_30 ),
inference(forward_demodulation,[],[f952,f77]) ).
fof(f1026,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| spl0_29
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1025,f529]) ).
fof(f1027,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| spl0_29
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f1026]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f93]) ).
cnf(s2,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s3,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s4,plain,
( spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s5,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s6,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f118]) ).
cnf(s7,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s9,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s10,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s11,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s12,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s13,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s14,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s15,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s16,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s17,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s20,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s21,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s22,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s23,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s24,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s25,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s26,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f154]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f155]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f156]) ).
cnf(s29,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f157]) ).
cnf(s30,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f158]) ).
cnf(s31,plain,
( spl0_4
| spl0_16 ),
inference(sat_conversion,[],[f159]) ).
cnf(s32,plain,
spl0_7,
inference(sat_conversion,[],[f160]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f164]) ).
cnf(s36,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f371]) ).
cnf(s44,plain,
( ~ spl0_9
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f454]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f537]) ).
cnf(s56,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f570]) ).
cnf(s57,plain,
( ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_20 ),
inference(sat_conversion,[],[f571]) ).
cnf(s61,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f657]) ).
cnf(s63,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f718]) ).
cnf(s65,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f732]) ).
cnf(s66,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f737]) ).
cnf(s67,plain,
( ~ spl0_9
| spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f813]) ).
cnf(s72,plain,
( ~ spl0_6
| ~ spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f851]) ).
cnf(s73,plain,
( ~ spl0_10
| ~ spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f852]) ).
cnf(s74,plain,
( ~ spl0_15
| ~ spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f853]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_17
| ~ spl0_21
| ~ spl0_30 ),
inference(sat_conversion,[],[f918]) ).
cnf(s92,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_30 ),
inference(sat_conversion,[],[f932]) ).
cnf(s95,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_10
| spl0_20
| ~ spl0_29 ),
inference(sat_conversion,[],[f972]) ).
cnf(s99,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_17
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f984]) ).
cnf(s102,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| spl0_29
| ~ spl0_30 ),
inference(sat_conversion,[],[f1027]) ).
cnf(s103,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(rat,[],[s1,s32]) ).
cnf(s104,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| spl0_3 ),
inference(rat,[],[s61,s66,s32]) ).
cnf(s105,plain,
spl0_3,
inference(rat,[],[s104,s74,s57,s6,s12,s18,s24,s30]) ).
cnf(s106,plain,
spl0_4,
inference(rat,[],[s74,s61,s57,s7,s13,s19,s25,s31,s32]) ).
cnf(s107,plain,
( ~ spl0_20
| ~ spl0_6
| ~ spl0_14
| ~ spl0_13
| ~ spl0_9 ),
inference(rat,[],[s44,s65,s56]) ).
cnf(s108,plain,
( spl0_8
| spl0_20
| ~ spl0_14
| ~ spl0_13
| ~ spl0_9 ),
inference(rat,[],[s57,s20,s26]) ).
cnf(s109,plain,
( spl0_16
| ~ spl0_8
| spl0_20 ),
inference(rat,[],[s95,s102,s92,s27,s28,s29,s106,s32,s105]) ).
cnf(s110,plain,
( spl0_20
| ~ spl0_14
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s95,s102,s92,s21,s22,s23,s57,s109,s108,s105,s32,s106]) ).
cnf(s111,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_9
| ~ spl0_13 ),
inference(rat,[],[s110,s107]) ).
cnf(s112,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_9
| spl0_2
| spl0_1 ),
inference(rat,[],[s111,s103,s51,s105,s106]) ).
cnf(s113,plain,
( spl0_14
| spl0_2
| spl0_1 ),
inference(rat,[],[s103,s72,s91,s99,s73,s95,s102,s92,s14,s15,s16,s17,s105,s106,s32]) ).
cnf(s114,plain,
( ~ spl0_14
| ~ spl0_9
| spl0_1
| spl0_2 ),
inference(rat,[],[s99,s67,s73,s95,s102,s92,s8,s9,s10,s11,s112,s105,s106,s32]) ).
cnf(s115,plain,
( ~ spl0_14
| spl0_2
| spl0_1 ),
inference(rat,[],[s103,s72,s91,s99,s73,s95,s102,s92,s2,s3,s4,s5,s114,s32,s106,s105]) ).
cnf(s116,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s115,s113]) ).
cnf(s117,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s33,s10,s11]) ).
cnf(s118,plain,
( spl0_12
| ~ spl0_9
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s36,s23,s29,s117]) ).
cnf(s119,plain,
( ~ spl0_9
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s36,s22,s28,s33,s118,s117]) ).
cnf(s120,plain,
( spl0_9
| ~ spl0_2 ),
inference(rat,[],[s33,s4,s5]) ).
cnf(s121,plain,
( ~ spl0_9
| ~ spl0_2 ),
inference(rat,[],[s33,s16,s17,s119]) ).
cnf(s122,plain,
~ spl0_2,
inference(rat,[],[s121,s120]) ).
cnf(s123,plain,
spl0_1,
inference(rat,[],[s116,s122]) ).
cnf(s124,plain,
( ~ spl0_20
| ~ spl0_13
| ~ spl0_9
| ~ spl0_14 ),
inference(rat,[],[s44,s63,s56,s123,s106]) ).
cnf(s125,plain,
( ~ spl0_13
| ~ spl0_9
| ~ spl0_14 ),
inference(rat,[],[s124,s110]) ).
cnf(s126,plain,
( ~ spl0_29
| ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s73,s63,s95,s123,s106]) ).
cnf(s127,plain,
( ~ spl0_8
| ~ spl0_30
| ~ spl0_10 ),
inference(rat,[],[s126,s102,s105,s32]) ).
cnf(s128,plain,
spl0_13,
inference(rat,[],[s127,s92,s8,s9,s10,s11]) ).
cnf(s129,plain,
spl0_9,
inference(rat,[],[s127,s92,s2,s3,s4,s5]) ).
cnf(s130,plain,
~ spl0_14,
inference(rat,[],[s125,s128,s129]) ).
cnf(s131,plain,
spl0_12,
inference(rat,[],[s17,s130]) ).
cnf(s132,plain,
spl0_11,
inference(rat,[],[s16,s130]) ).
cnf(s133,plain,
spl0_10,
inference(rat,[],[s15,s130]) ).
cnf(s134,plain,
spl0_8,
inference(rat,[],[s14,s130]) ).
cnf(s135,plain,
spl0_30,
inference(rat,[],[s92,s131,s132]) ).
cnf(s137,plain,
$false,
inference(rat,[],[s127,s133,s135,s134]) ).
fof(f1028,plain,
$false,
inference(avatar_sat_refutation,[],[s137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP327-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:51:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.41 Running first-order model finding
% 0.09/0.41 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
% 0.16/0.46 % (988342)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (988350)dis+10_1_sil=32000:sp=arity:random_seed=531275519:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (988348)% WARNING: option uhcvi not known.
% 0.16/0.46 % (988347)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3368904692_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (988348)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1983551528:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (988349)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3628208973:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (988351)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=43753673:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (988353)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1497892966:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (988352)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1250220472:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % (988350) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-988342-988350"...
% 0.16/0.46 % TRYING [3]
% 0.16/0.46 % (988350)...printing done.
% 0.16/0.46 % (988350)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (988350)------------------------------
% 0.16/0.47 % (988350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (988350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (988350)CaDiCaL version: 2.1.3
% 0.16/0.47 % (988350)Termination reason: Refutation
% 0.16/0.47 % (988350)Time elapsed: 0.012 s
% 0.16/0.47 % (988350)Peak memory usage: 12 MB
% 0.16/0.47 % (988350)Instructions burned: 35 (million)
% 0.16/0.47 % (988342)Success in time 0.041 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------