%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP385-1 : 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 : 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 10:17:39 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 47
% Syntax : Number of formulae : 291 ( 20 unt; 18 def)
% Number of atoms : 1056 ( 313 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1471 ( 706 ~; 747 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 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,
inverse(sk_c10) = sk_c9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f18,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f38,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c10,sk_c2) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f54,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f62]) ).
fof(f70,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c10 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
( sk_c10 = inverse(sk_c1)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f79,plain,
( sk_c10 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f78]) ).
fof(f82,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f83,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c7) ),
inference(reorient_equations,[],[f82]) ).
fof(f84,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f85,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f84]) ).
fof(f86,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,X0) != sk_c9
| multiply(X1,sk_c10) != X0
| inverse(X1) != sk_c10
| multiply(sk_c10,X2) != sk_c9
| multiply(X3,sk_c10) != X2
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c8
| inverse(X4) != X5
| multiply(X5,sk_c9) != sk_c8
| inverse(X6) != sk_c10
| multiply(X6,sk_c8) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f87,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,X0)
| multiply(X1,sk_c10) != X0
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(reorient_equations,[],[f86]) ).
fof(f88,plain,
! [X2,X3,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f87]) ).
fof(f89,plain,
! [X3,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f88]) ).
fof(f90,plain,
! [X3,X1,X6,X4] :
( inverse(sk_c10) != sk_c9
| sk_c10 != multiply(sk_c9,sk_c8)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c9 != multiply(sk_c10,multiply(X1,sk_c10))
| sk_c10 != inverse(X1)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9)
| sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ),
inference(equality_resolution,[],[f89]) ).
fof(f92,definition,
( spl0_1
<=> ! [X6] :
( sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f93,plain,
( ! [X6] :
( sk_c10 != inverse(X6)
| sk_c10 != multiply(X6,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,definition,
( spl0_2
<=> ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f96,plain,
( ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f99,plain,
( ! [X3] :
( sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_4
<=> sk_c9 = multiply(sk_c10,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f102,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( sk_c9 != multiply(sk_c10,sk_c8)
| spl0_4 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl0_5
<=> sk_c10 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f106,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl0_6
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f110,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f90,f109,f105,f101,f98,f98,f95,f92]) ).
fof(f114,definition,
( spl0_7
<=> sk_c10 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f116,plain,
( sk_c10 = multiply(sk_c7,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl0_8
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f120,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f85,f118,f114]) ).
fof(f123,definition,
( spl0_9
<=> sk_c10 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f125,plain,
( sk_c10 = inverse(sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f83,f118,f123]) ).
fof(f133,definition,
( spl0_11
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f135,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f79,f118,f133]) ).
fof(f138,definition,
( spl0_12
<=> sk_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f140,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f77,f118,f138]) ).
fof(f143,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f145,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl0_13
| spl0_8 ),
inference(avatar_split_clause,[],[f75,f118,f143]) ).
fof(f148,definition,
( spl0_14
<=> sk_c4 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f150,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_14
| spl0_8 ),
inference(avatar_split_clause,[],[f73,f118,f148]) ).
fof(f153,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c10,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f154,plain,
( sk_c9 != multiply(sk_c10,sk_c4)
| spl0_15 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
( spl0_15
| spl0_8 ),
inference(avatar_split_clause,[],[f71,f118,f153]) ).
fof(f158,definition,
( spl0_16
<=> sk_c2 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f160,plain,
( sk_c2 = multiply(sk_c1,sk_c10)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f164,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f63,f158,f133]) ).
fof(f165,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f61,f158,f138]) ).
fof(f166,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f59,f158,f143]) ).
fof(f167,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f57,f158,f148]) ).
fof(f168,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f55,f158,f153]) ).
fof(f170,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c10,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f172,plain,
( sk_c9 = multiply(sk_c10,sk_c2)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f176,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f47,f170,f133]) ).
fof(f177,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f45,f170,f138]) ).
fof(f178,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f43,f170,f143]) ).
fof(f179,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f41,f170,f148]) ).
fof(f180,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f39,f170,f153]) ).
fof(f184,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f31,f101,f133]) ).
fof(f185,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f29,f101,f138]) ).
fof(f186,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f27,f101,f143]) ).
fof(f187,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f25,f101,f148]) ).
fof(f188,plain,
( spl0_15
| spl0_4 ),
inference(avatar_split_clause,[],[f23,f101,f153]) ).
fof(f189,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f21,f105,f114]) ).
fof(f190,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f19,f105,f123]) ).
fof(f197,plain,
spl0_6,
inference(avatar_split_clause,[],[f5,f109]) ).
fof(f198,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_6 ),
inference(superposition,[],[f3,f110]) ).
fof(f199,plain,
( identity = multiply(sk_c10,sk_c3)
| ~ spl0_13 ),
inference(superposition,[],[f3,f145]) ).
fof(f201,plain,
( identity = multiply(sk_c10,sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f3,f125]) ).
fof(f204,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f206,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c10,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f198]) ).
fof(f211,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c10,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f206,f1]) ).
fof(f212,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f204,f1]) ).
fof(f215,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c3,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f199]) ).
fof(f216,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c3,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f215,f1]) ).
fof(f225,plain,
( sk_c4 = multiply(sk_c9,sk_c9)
| ~ spl0_6
| ~ spl0_15 ),
inference(superposition,[],[f211,f155]) ).
fof(f226,plain,
( sk_c3 = multiply(sk_c9,identity)
| ~ spl0_6
| ~ spl0_13 ),
inference(superposition,[],[f211,f199]) ).
fof(f227,plain,
( sk_c7 = multiply(sk_c9,identity)
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f211,f201]) ).
fof(f253,plain,
( sk_c3 = sk_c7
| ~ spl0_6
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f227,f226]) ).
fof(f275,plain,
( sk_c10 = multiply(inverse(sk_c9),identity)
| ~ spl0_6 ),
inference(superposition,[],[f212,f198]) ).
fof(f277,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f212,f150]) ).
fof(f279,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c8)
| ~ spl0_12 ),
inference(superposition,[],[f212,f140]) ).
fof(f284,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_7 ),
inference(superposition,[],[f212,f116]) ).
fof(f289,plain,
( sk_c8 = multiply(sk_c10,sk_c10)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f284,f125]) ).
fof(f291,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f279,f135]) ).
fof(f293,plain,
( sk_c10 = multiply(sk_c10,sk_c4)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f277,f145]) ).
fof(f301,plain,
( sk_c10 = multiply(sk_c9,sk_c8)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f211,f289]) ).
fof(f305,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f301,f123,f114,f109,f105]) ).
fof(f307,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f212,f106]) ).
fof(f310,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f212,f291]) ).
fof(f312,plain,
( identity = sk_c8
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f310,f3]) ).
fof(f319,plain,
( sk_c9 != multiply(sk_c10,identity)
| spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f103,f312]) ).
fof(f329,plain,
( sk_c10 = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f293,f155]) ).
fof(f333,plain,
( sk_c4 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f212,f293]) ).
fof(f335,plain,
( identity = sk_c4
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f333,f3]) ).
fof(f353,plain,
( sk_c10 = multiply(inverse(sk_c10),identity)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f275,f329]) ).
fof(f354,plain,
( sk_c10 = multiply(sk_c9,identity)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f353,f110]) ).
fof(f355,plain,
( sk_c10 = multiply(sk_c10,identity)
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f354,f329]) ).
fof(f371,plain,
( sk_c8 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f307,f329]) ).
fof(f372,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f371,f3]) ).
fof(f453,plain,
( sk_c10 != sk_c9
| spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f319,f355]) ).
fof(f454,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f453,f329]) ).
fof(f455,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f456,plain,
( ! [X4] :
( identity != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c9) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f96,f312]) ).
fof(f458,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c10)
| identity != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f456,f329]) ).
fof(f460,plain,
( ! [X4] :
( identity != multiply(inverse(X4),sk_c10)
| identity != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f458,f312]) ).
fof(f464,plain,
( identity != multiply(sk_c10,sk_c10)
| identity != multiply(sk_c7,sk_c10)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f460,f125]) ).
fof(f465,plain,
( identity != identity
| identity != multiply(sk_c10,inverse(sk_c10))
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f460,f3]) ).
fof(f466,plain,
( identity != multiply(sk_c10,inverse(sk_c10))
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f465]) ).
fof(f467,plain,
( identity != multiply(sk_c10,sk_c9)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f466,f110]) ).
fof(f468,plain,
( identity != sk_c8
| identity != multiply(sk_c7,sk_c10)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f464,f289]) ).
fof(f472,plain,
( identity != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f467,f329]) ).
fof(f473,plain,
( identity != multiply(sk_c7,sk_c10)
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f468,f312]) ).
fof(f478,plain,
( identity != multiply(sk_c3,sk_c10)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f473,f253]) ).
fof(f484,plain,
( identity != sk_c4
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f478,f150]) ).
fof(f490,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f484,f335]) ).
fof(f491,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f498,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c2)
| ~ spl0_16 ),
inference(superposition,[],[f212,f160]) ).
fof(f500,plain,
( sk_c10 = multiply(sk_c10,sk_c2)
| ~ spl0_8
| ~ spl0_16 ),
inference(forward_demodulation,[],[f498,f120]) ).
fof(f537,definition,
( spl0_20
<=> identity = sk_c4 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f538,plain,
( identity = sk_c4
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f562,definition,
( spl0_21
<=> identity = multiply(sk_c9,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f563,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f571,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f500,f172]) ).
fof(f599,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c10)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f96,f571]) ).
fof(f600,plain,
( sk_c10 = multiply(sk_c10,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f102,f571]) ).
fof(f601,plain,
( sk_c8 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f307,f571]) ).
fof(f604,plain,
( identity = sk_c8
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f601,f3]) ).
fof(f614,plain,
( sk_c10 = multiply(sk_c10,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f600,f604]) ).
fof(f622,plain,
( ! [X4] :
( identity != multiply(inverse(X4),sk_c10)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f599,f604]) ).
fof(f623,plain,
( ! [X4] :
( identity != multiply(inverse(X4),sk_c10)
| identity != multiply(X4,inverse(X4)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f622,f604]) ).
fof(f629,plain,
( identity != identity
| identity != multiply(sk_c10,inverse(sk_c10))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f623,f3]) ).
fof(f630,plain,
( identity != multiply(sk_c10,inverse(sk_c10))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f629]) ).
fof(f631,plain,
( identity != multiply(sk_c10,sk_c9)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f630,f110]) ).
fof(f636,plain,
( identity != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f631,f571]) ).
fof(f653,plain,
( ! [X6] :
( sk_c10 != multiply(X6,identity)
| sk_c10 != inverse(X6) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f93,f604]) ).
fof(f654,plain,
( spl0_20
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f335,f148,f143,f537]) ).
fof(f665,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f653,f614]) ).
fof(f667,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f665]) ).
fof(f669,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f667,f110]) ).
fof(f685,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f669,f571]) ).
fof(f686,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f685]) ).
fof(f688,plain,
( ! [X3] :
( sk_c10 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f99,f571]) ).
fof(f696,plain,
( sk_c10 != multiply(sk_c10,sk_c2)
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f688,f160]) ).
fof(f701,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f696,f500]) ).
fof(f707,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f701,f120]) ).
fof(f708,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f707]) ).
fof(f731,plain,
( identity = multiply(sk_c9,sk_c9)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f225,f538]) ).
fof(f737,plain,
( spl0_21
| ~ spl0_6
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f731,f537,f153,f109,f562]) ).
fof(f756,plain,
( sk_c9 = multiply(sk_c10,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f102,f372]) ).
fof(f757,plain,
( sk_c10 = multiply(sk_c10,identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f756,f329]) ).
fof(f777,plain,
( ! [X6] :
( sk_c10 != multiply(X6,identity)
| sk_c10 != inverse(X6) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f93,f372]) ).
fof(f778,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f563,f329]) ).
fof(f782,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f777,f757]) ).
fof(f784,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f782]) ).
fof(f786,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f784,f110]) ).
fof(f790,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f786,f329]) ).
fof(f791,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f790]) ).
fof(f795,plain,
( ! [X3] :
( sk_c10 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) )
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f99,f329]) ).
fof(f805,plain,
( sk_c10 != sk_c10
| sk_c10 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f795,f216]) ).
fof(f806,plain,
( sk_c10 != inverse(sk_c3)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f805]) ).
fof(f807,plain,
( $false
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f806,f145]) ).
fof(f808,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f807]) ).
fof(f930,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f778,f472]) ).
fof(f931,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f930]) ).
fof(f932,plain,
( sk_c9 != multiply(sk_c10,identity)
| spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f154,f538]) ).
fof(f970,plain,
( sk_c10 != sk_c9
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f932,f614]) ).
fof(f971,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f970,f571]) ).
fof(f972,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f971]) ).
fof(f1017,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_8 ),
inference(superposition,[],[f3,f120]) ).
fof(f1019,plain,
( sk_c1 = multiply(inverse(sk_c10),identity)
| ~ spl0_8 ),
inference(superposition,[],[f212,f1017]) ).
fof(f1022,plain,
( sk_c1 = multiply(sk_c9,identity)
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1019,f110]) ).
fof(f1024,plain,
( sk_c1 = multiply(sk_c10,identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1022,f571]) ).
fof(f1026,plain,
( sk_c10 = sk_c1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1024,f614]) ).
fof(f1027,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1017,f1026]) ).
fof(f1031,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1027,f636]) ).
fof(f1032,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1031]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f112]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f121]) ).
cnf(s4,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f136]) ).
cnf(s7,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f141]) ).
cnf(s8,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s9,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s10,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f156]) ).
cnf(s14,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s15,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s16,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s17,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s18,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s22,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f176]) ).
cnf(s23,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f177]) ).
cnf(s24,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f178]) ).
cnf(s25,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f179]) ).
cnf(s26,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s30,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f184]) ).
cnf(s31,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f185]) ).
cnf(s32,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f186]) ).
cnf(s33,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f187]) ).
cnf(s34,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f188]) ).
cnf(s35,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f189]) ).
cnf(s36,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f190]) ).
cnf(s43,plain,
spl0_6,
inference(sat_conversion,[],[f197]) ).
cnf(s44,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f305]) ).
cnf(s46,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f455]) ).
cnf(s50,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f491]) ).
cnf(s69,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_20 ),
inference(sat_conversion,[],[f654]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f686]) ).
cnf(s75,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f708]) ).
cnf(s83,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f737]) ).
cnf(s86,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f791]) ).
cnf(s88,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f808]) ).
cnf(s104,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f931]) ).
cnf(s116,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_8
| spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f972]) ).
cnf(s124,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1032]) ).
cnf(s126,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s2,s43]) ).
cnf(s127,plain,
spl0_4,
inference(rat,[],[s46,s30,s31,s32,s33,s34,s43]) ).
cnf(s128,plain,
spl0_5,
inference(rat,[],[s44,s35,s36,s43]) ).
cnf(s129,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s88,s8,s9,s10]) ).
cnf(s130,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_3 ),
inference(rat,[],[s116,s18,s26,s69,s88,s129,s127,s128]) ).
cnf(s131,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s75,s17,s25,s129]) ).
cnf(s132,plain,
~ spl0_3,
inference(rat,[],[s75,s16,s24,s130,s131,s129]) ).
cnf(s133,plain,
( spl0_17
| ~ spl0_14
| ~ spl0_13
| ~ spl0_2 ),
inference(rat,[],[s104,s83,s22,s23,s26,s69,s43]) ).
cnf(s134,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s104,s83,s14,s15,s18,s124,s133,s69,s43,s127,s128]) ).
cnf(s135,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s124,s17,s25,s43,s127,s128]) ).
cnf(s136,plain,
( ~ spl0_14
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s124,s16,s24,s134,s128,s127,s43]) ).
cnf(s137,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s136,s135]) ).
cnf(s138,plain,
~ spl0_2,
inference(rat,[],[s50,s3,s4,s6,s7,s8,s9,s10,s137,s43]) ).
cnf(s139,plain,
spl0_1,
inference(rat,[],[s126,s128,s127,s132,s138]) ).
cnf(s140,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_8 ),
inference(rat,[],[s116,s18,s26,s86,s69,s127,s128,s43,s139]) ).
cnf(s141,plain,
( spl0_13
| ~ spl0_8 ),
inference(rat,[],[s73,s16,s24,s43,s127,s128,s139]) ).
cnf(s142,plain,
( ~ spl0_13
| ~ spl0_8 ),
inference(rat,[],[s73,s17,s25,s140,s139,s128,s127,s43]) ).
cnf(s143,plain,
~ spl0_8,
inference(rat,[],[s142,s141]) ).
cnf(s144,plain,
spl0_15,
inference(rat,[],[s10,s143]) ).
cnf(s145,plain,
spl0_14,
inference(rat,[],[s9,s143]) ).
cnf(s146,plain,
spl0_13,
inference(rat,[],[s8,s143]) ).
cnf(s152,plain,
$false,
inference(rat,[],[s86,s146,s139,s127,s43,s128,s145,s144]) ).
fof(f1035,plain,
$false,
inference(avatar_sat_refutation,[],[s152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP385-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:03:06 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.17/0.49 % (3307351)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (3307359)dis+10_1_sil=32000:sp=arity:random_seed=869761380:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (3307357)% WARNING: option uhcvi not known.
% 0.17/0.49 % (3307357)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2347541775:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (3307356)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2506932794_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (3307360)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=667130829:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (3307358)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3432489850:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (3307361)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=309467829:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (3307362)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2005950551:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % (3307359) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3307351-3307359"...
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % (3307359)...printing done.
% 0.17/0.49 % (3307359)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (3307359)------------------------------
% 0.17/0.49 % (3307359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3307359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3307359)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3307359)Termination reason: Refutation
% 0.17/0.49 % (3307359)Time elapsed: 0.013 s
% 0.17/0.49 % (3307359)Peak memory usage: 12 MB
% 0.17/0.49 % (3307359)Instructions burned: 36 (million)
% 0.17/0.49 % (3307351)Success in time 0.046 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------