%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 10:13:24 AM UTC 2026
% Result : Unsatisfiable 2.79s 1.26s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 54
% Syntax : Number of formulae : 323 ( 22 unt; 20 def)
% Number of atoms : 981 ( 302 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1233 ( 575 ~; 638 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( inverse(sk_c8) = sk_c7
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c3) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| multiply(X2,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c8,X4) != sk_c7
| multiply(X5,sk_c8) != X4
| inverse(X5) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| multiply(X1,X2) != sk_c8
| inverse(X1) != X2
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X3,X0,X1,X4,X5] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,X4)
| multiply(X5,sk_c8) != X4
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X3,X0,X1,X5] :
( inverse(sk_c8) != sk_c7
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl0_1
<=> ! [X5] :
( sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f71,plain,
( ! [X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8)) )
| ~ 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 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> ! [X1] :
( sk_c8 != multiply(X1,inverse(X1))
| sk_c8 != multiply(inverse(X1),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( ! [X1] :
( sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != multiply(X1,inverse(X1)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,definition,
( spl0_4
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( inverse(sk_c8) != sk_c7
| spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f68,f82,f79,f76,f73,f70]) ).
fof(f87,definition,
( spl0_6
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f89,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl0_7
<=> sk_c8 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f93,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f91,f87]) ).
fof(f96,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f98,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f62,f91,f96]) ).
fof(f101,definition,
( spl0_9
<=> sk_c7 = multiply(sk_c8,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f102,plain,
( sk_c7 != multiply(sk_c8,sk_c6)
| spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f91,f101]) ).
fof(f106,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f108,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f91,f106]) ).
fof(f111,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f113,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f91,f111]) ).
fof(f116,definition,
( spl0_12
<=> sk_c3 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f118,plain,
( sk_c3 = inverse(sk_c2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f116,f87]) ).
fof(f120,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f116,f96]) ).
fof(f121,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f116,f101]) ).
fof(f122,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f116,f106]) ).
fof(f123,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f116,f111]) ).
fof(f125,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c2,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f127,plain,
( sk_c8 = multiply(sk_c2,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_6
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f125,f87]) ).
fof(f129,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f125,f96]) ).
fof(f130,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f125,f101]) ).
fof(f131,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f125,f106]) ).
fof(f132,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f125,f111]) ).
fof(f134,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f136,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f134,f87]) ).
fof(f138,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f134,f96]) ).
fof(f139,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f134,f101]) ).
fof(f140,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f134,f106]) ).
fof(f141,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f134,f111]) ).
fof(f143,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f145,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f143,f87]) ).
fof(f147,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f143,f96]) ).
fof(f148,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f143,f101]) ).
fof(f149,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f143,f106]) ).
fof(f150,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f143,f111]) ).
fof(f151,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f82,f87]) ).
fof(f152,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f82,f96]) ).
fof(f153,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f82,f101]) ).
fof(f154,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f82,f106]) ).
fof(f155,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f82,f111]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f89]) ).
fof(f157,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f113]) ).
fof(f160,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f162,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f156]) ).
fof(f165,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f162,f1]) ).
fof(f166,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f160,f1]) ).
fof(f174,plain,
( sk_c8 = multiply(sk_c8,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f165,f98]) ).
fof(f180,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f174,f103]) ).
fof(f204,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f166,f157]) ).
fof(f205,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f166,f174]) ).
fof(f206,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_9 ),
inference(superposition,[],[f166,f103]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f166,f108]) ).
fof(f217,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f208,f113]) ).
fof(f218,plain,
( sk_c6 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f206,f180]) ).
fof(f219,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f205,f3]) ).
fof(f222,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f217,f180]) ).
fof(f223,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f218,f3]) ).
fof(f227,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f166,f222]) ).
fof(f229,plain,
( identity = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f227,f3]) ).
fof(f231,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f229,f223]) ).
fof(f237,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f204,f223]) ).
fof(f245,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f237,f231]) ).
fof(f246,plain,
( identity = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f245,f3]) ).
fof(f247,plain,
( sk_c8 = sk_c4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f246,f229]) ).
fof(f251,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f113,f247]) ).
fof(f272,plain,
( sk_c8 != sk_c7
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f84,f251]) ).
fof(f276,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f272,f180]) ).
fof(f277,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f276]) ).
fof(f278,plain,
( ! [X1] :
( sk_c8 != multiply(inverse(X1),sk_c8)
| sk_c8 != multiply(X1,inverse(X1)) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f77,f180]) ).
fof(f280,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f278,f89]) ).
fof(f289,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f280,f222]) ).
fof(f292,plain,
( sk_c8 != sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f289,f98]) ).
fof(f297,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f292,f231]) ).
fof(f298,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f299,plain,
( sk_c8 != sk_c7
| ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(forward_demodulation,[],[f102,f174]) ).
fof(f301,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_5 ),
inference(superposition,[],[f3,f83]) ).
fof(f307,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f136]) ).
fof(f311,plain,
( sk_c3 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f166,f127]) ).
fof(f313,plain,
( sk_c3 = multiply(sk_c3,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f311,f118]) ).
fof(f315,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f145]) ).
fof(f317,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f301,f219]) ).
fof(f322,plain,
( sk_c8 != multiply(sk_c3,sk_c7)
| sk_c8 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_12 ),
inference(superposition,[],[f77,f118]) ).
fof(f325,plain,
( sk_c8 != multiply(sk_c2,sk_c3)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f322,f93]) ).
fof(f333,definition,
( spl0_17
<=> sk_c8 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f347,definition,
( spl0_20
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f348,plain,
( sk_c8 = sk_c6
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f351,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f325,f127]) ).
fof(f352,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f358,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f71,f89]) ).
fof(f362,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c5,sk_c8))
| ~ spl0_1
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f358]) ).
fof(f369,definition,
( spl0_22
<=> sk_c8 = sk_c3 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f370,plain,
( sk_c8 = sk_c3
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f374,plain,
( sk_c8 != sk_c7
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f362,f165]) ).
fof(f396,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c3)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f166,f313]) ).
fof(f398,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f396,f3]) ).
fof(f414,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f219,f398]) ).
fof(f416,plain,
( spl0_20
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f414,f125,f116,f96,f87,f347]) ).
fof(f420,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c7,sk_c6)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15 ),
inference(superposition,[],[f315,f174]) ).
fof(f429,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f420,f348]) ).
fof(f434,plain,
( sk_c6 = multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f429,f317]) ).
fof(f437,plain,
( sk_c7 = sk_c6
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f434,f145]) ).
fof(f439,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f437,f348]) ).
fof(f440,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f439,f299]) ).
fof(f441,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f442,plain,
( sk_c8 = sk_c7
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f103,f174]) ).
fof(f450,definition,
( spl0_24
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f451,plain,
( sk_c8 = sk_c7
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f454,plain,
( ~ spl0_24
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f374,f87,f70,f450]) ).
fof(f456,plain,
( spl0_24
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f442,f101,f96,f87,f450]) ).
fof(f457,plain,
( sk_c8 = multiply(sk_c3,sk_c8)
| ~ spl0_7
| ~ spl0_24 ),
inference(superposition,[],[f93,f451]) ).
fof(f470,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c8) )
| ~ spl0_2
| ~ spl0_24 ),
inference(forward_demodulation,[],[f74,f451]) ).
fof(f474,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_24 ),
inference(superposition,[],[f470,f89]) ).
fof(f475,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_24 ),
inference(superposition,[],[f470,f136]) ).
fof(f477,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f475]) ).
fof(f478,plain,
( sk_c8 != multiply(sk_c5,sk_c8)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f474]) ).
fof(f486,plain,
( sk_c8 != sk_c7
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_demodulation,[],[f477,f145]) ).
fof(f487,plain,
( sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_demodulation,[],[f478,f98]) ).
fof(f489,plain,
( $false
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f486,f451]) ).
fof(f490,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f491,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_20
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f487,f348]) ).
fof(f492,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f491]) ).
fof(f493,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c8) )
| ~ spl0_4
| ~ spl0_24 ),
inference(forward_demodulation,[],[f80,f451]) ).
fof(f495,plain,
( sk_c8 = sk_c3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(superposition,[],[f313,f457]) ).
fof(f499,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f495,f450,f125,f116,f91,f369]) ).
fof(f501,plain,
( sk_c8 != sk_c7
| sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_24 ),
inference(superposition,[],[f493,f83]) ).
fof(f504,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_24 ),
inference(superposition,[],[f493,f136]) ).
fof(f506,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_4
| ~ spl0_14
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f504]) ).
fof(f511,plain,
( sk_c8 != sk_c7
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_demodulation,[],[f506,f145]) ).
fof(f513,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f501,f451]) ).
fof(f514,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f511,f451]) ).
fof(f515,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f514]) ).
fof(f520,plain,
( ! [X5] :
( sk_c8 != inverse(X5)
| sk_c8 != multiply(sk_c8,multiply(X5,sk_c8)) )
| ~ spl0_1
| ~ spl0_24 ),
inference(forward_demodulation,[],[f71,f451]) ).
fof(f531,plain,
( sk_c8 = multiply(sk_c8,sk_c1)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f307,f398]) ).
fof(f544,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f93,f370]) ).
fof(f564,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_14
| ~ spl0_24 ),
inference(superposition,[],[f520,f136]) ).
fof(f566,plain,
( sk_c8 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_1
| ~ spl0_14
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f564]) ).
fof(f580,plain,
( spl0_17
| ~ spl0_7
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f544,f369,f91,f333]) ).
fof(f620,plain,
( sk_c1 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f166,f531]) ).
fof(f622,plain,
( identity = sk_c1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f620,f3]) ).
fof(f625,plain,
( sk_c8 = sk_c1
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f622,f398]) ).
fof(f630,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f136,f625]) ).
fof(f632,plain,
( sk_c8 = sk_c7
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f83,f630]) ).
fof(f654,plain,
( sk_c8 != multiply(sk_c8,sk_c7)
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(forward_demodulation,[],[f566,f145]) ).
fof(f657,plain,
( spl0_24
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f632,f134,f125,f116,f82,f450]) ).
fof(f664,definition,
( spl0_26
<=> sk_c8 = multiply(sk_c8,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f668,plain,
( ~ spl0_17
| ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f654,f450,f143,f134,f70,f333]) ).
fof(f686,plain,
( ~ spl0_26
| ~ spl0_4
| ~ spl0_5
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f513,f450,f82,f79,f664]) ).
fof(f689,plain,
( spl0_26
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f222,f111,f106,f101,f96,f87,f664]) ).
fof(f690,plain,
( spl0_20
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f231,f111,f106,f101,f96,f87,f347]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f85]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f94]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f99]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f104]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f109]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f114]) ).
cnf(s7,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f123]) ).
cnf(s12,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s13,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s14,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s15,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s16,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f132]) ).
cnf(s17,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s18,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s19,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s20,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s21,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f141]) ).
cnf(s22,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s23,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s24,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f150]) ).
cnf(s27,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f151]) ).
cnf(s28,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f152]) ).
cnf(s29,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f153]) ).
cnf(s30,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f154]) ).
cnf(s31,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f155]) ).
cnf(s32,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f277]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f298]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f352]) ).
cnf(s45,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| spl0_20 ),
inference(sat_conversion,[],[f416]) ).
cnf(s47,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f441]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_24 ),
inference(sat_conversion,[],[f454]) ).
cnf(s51,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| spl0_24 ),
inference(sat_conversion,[],[f456]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(sat_conversion,[],[f490]) ).
cnf(s55,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f492]) ).
cnf(s56,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(sat_conversion,[],[f499]) ).
cnf(s59,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15
| ~ spl0_24 ),
inference(sat_conversion,[],[f515]) ).
cnf(s65,plain,
( ~ spl0_7
| spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f580]) ).
cnf(s76,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_24 ),
inference(sat_conversion,[],[f657]) ).
cnf(s81,plain,
( ~ spl0_1
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_24 ),
inference(sat_conversion,[],[f668]) ).
cnf(s89,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f686]) ).
cnf(s92,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_26 ),
inference(sat_conversion,[],[f689]) ).
cnf(s93,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f690]) ).
cnf(s101,plain,
spl0_5,
inference(rat,[],[s32,s27,s28,s29,s30,s31]) ).
cnf(s103,plain,
( spl0_11
| ~ spl0_24
| ~ spl0_4 ),
inference(rat,[],[s59,s21,s26]) ).
cnf(s104,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s59,s20,s25,s92,s103,s89,s51,s101]) ).
cnf(s105,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s45,s47,s9,s14,s24,s104,s101]) ).
cnf(s106,plain,
( spl0_8
| ~ spl0_4 ),
inference(rat,[],[s76,s59,s8,s13,s18,s23,s101]) ).
cnf(s107,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s76,s59,s7,s12,s17,s22,s105,s101]) ).
cnf(s108,plain,
~ spl0_4,
inference(rat,[],[s107,s106]) ).
cnf(s109,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s36,s5,s6]) ).
cnf(s110,plain,
( spl0_13
| ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s36,s15,s16]) ).
cnf(s111,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_3
| ~ spl0_6 ),
inference(rat,[],[s36,s10,s11,s40,s110,s109]) ).
cnf(s112,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s40,s4,s9,s14]) ).
cnf(s113,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s40,s3,s8,s13]) ).
cnf(s114,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_3 ),
inference(rat,[],[s40,s2,s7,s12,s111]) ).
cnf(s115,plain,
~ spl0_3,
inference(rat,[],[s114,s113,s112]) ).
cnf(s116,plain,
( spl0_13
| spl0_20
| ~ spl0_9
| ~ spl0_8
| ~ spl0_6 ),
inference(rat,[],[s93,s15,s16]) ).
cnf(s117,plain,
( spl0_20
| ~ spl0_9
| ~ spl0_6
| ~ spl0_8 ),
inference(rat,[],[s93,s10,s11,s45,s116]) ).
cnf(s118,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s117,s55,s51]) ).
cnf(s119,plain,
( ~ spl0_8
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s45,s47,s9,s14,s24,s118,s101]) ).
cnf(s120,plain,
( spl0_8
| ~ spl0_2 ),
inference(rat,[],[s76,s54,s8,s13,s18,s23,s101]) ).
cnf(s121,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s76,s54,s7,s12,s17,s22,s119,s101]) ).
cnf(s122,plain,
~ spl0_2,
inference(rat,[],[s121,s120]) ).
cnf(s123,plain,
spl0_1,
inference(rat,[],[s1,s101,s108,s115,s122]) ).
cnf(s124,plain,
( spl0_9
| spl0_24 ),
inference(rat,[],[s76,s9,s14,s19,s101]) ).
cnf(s125,plain,
( ~ spl0_9
| spl0_24
| ~ spl0_6 ),
inference(rat,[],[s76,s8,s13,s18,s51,s101]) ).
cnf(s126,plain,
~ spl0_6,
inference(rat,[],[s125,s124,s49,s123]) ).
cnf(s127,plain,
spl0_15,
inference(rat,[],[s22,s126]) ).
cnf(s128,plain,
spl0_14,
inference(rat,[],[s17,s126]) ).
cnf(s129,plain,
spl0_13,
inference(rat,[],[s12,s126]) ).
cnf(s130,plain,
spl0_12,
inference(rat,[],[s7,s126]) ).
cnf(s131,plain,
spl0_7,
inference(rat,[],[s2,s126]) ).
cnf(s134,plain,
spl0_24,
inference(rat,[],[s76,s101,s128,s129,s130]) ).
cnf(s135,plain,
spl0_22,
inference(rat,[],[s56,s134,s130,s129,s131]) ).
cnf(s136,plain,
~ spl0_17,
inference(rat,[],[s81,s128,s127,s123,s134]) ).
cnf(s138,plain,
$false,
inference(rat,[],[s65,s131,s135,s136]) ).
fof(f694,plain,
$false,
inference(avatar_sat_refutation,[],[s138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:38:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.79/1.26 % (3743234)Input is clausal, will run a generic CNF schedule.
% 2.79/1.26 % (3743239)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1245944937:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.79/1.26 % (3743244)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1714734029:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.79/1.26 % (3743242)lrs+10_1_sil=8000:sp=occurrence:random_seed=3914679767:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.79/1.26 % (3743243)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=77087720:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.79/1.26 % (3743240)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2612301858:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.79/1.26 % (3743241)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3443618321:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.79/1.26 % (3743242)Refutation not found, incomplete strategy
% 2.79/1.26 % (3743242)------------------------------
% 2.79/1.26 % (3743242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.26 % (3743242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.26 % (3743242)CaDiCaL version: 2.1.3
% 2.79/1.26 % (3743242)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.26 % (3743242)Time elapsed: 0.003 s
% 2.79/1.26 % (3743242)Peak memory usage: 88 MB
% 2.79/1.26 % (3743242)Instructions burned: 3 (million)
% 2.79/1.26 % (3743244)First to succeed.
% 2.79/1.26 % (3743245)dis-21_1_sil=8000:lcm=predicate:random_seed=1609132716:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.79/1.26 % (3743244)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3743234"
% 2.79/1.26 % (3743245)Refutation not found, incomplete strategy
% 2.79/1.26 % (3743245)------------------------------
% 2.79/1.26 % (3743245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.26 % (3743245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.26 % (3743245)CaDiCaL version: 2.1.3
% 2.79/1.26 % (3743245)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.26 % (3743245)Time elapsed: 0.002 s
% 2.79/1.26 % (3743245)Peak memory usage: 88 MB
% 2.79/1.26 % (3743245)Instructions burned: 2 (million)
% 2.79/1.26 % (3743243)Instruction limit reached!
% 2.79/1.26 % (3743243)------------------------------
% 2.79/1.26 % (3743243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.26 % (3743243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.26 % (3743243)CaDiCaL version: 2.1.3
% 2.79/1.26 % (3743243)Termination reason: Instruction limit
% 2.79/1.26 % (3743243)Termination phase: Saturation
% 2.79/1.26 % (3743243)Time elapsed: 0.067 s
% 2.79/1.26 % (3743243)Peak memory usage: 89 MB
% 2.79/1.26 % (3743243)Instructions burned: 116 (million)
% 2.79/1.26 % (3743253)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2668813277:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.79/1.26 % (3743253)Refutation not found, incomplete strategy
% 2.79/1.26 % (3743253)------------------------------
% 2.79/1.26 % (3743253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.26 % (3743253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.26 % (3743253)CaDiCaL version: 2.1.3
% 2.79/1.26 % (3743253)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.26 % (3743253)Time elapsed: 0.003 s
% 2.79/1.26 % (3743253)Peak memory usage: 88 MB
% 2.79/1.26 % (3743253)Instructions burned: 3 (million)
% 2.79/1.26 % (3743242)------------------------------
% 2.79/1.26 % (3743242)------------------------------
% 2.79/1.26 % (3743245)------------------------------
% 2.79/1.26 % (3743245)------------------------------
% 2.79/1.26 % (3743244)Refutation found. Thanks to Tanya!
% 2.79/1.26 % SZS status Unsatisfiable for theBenchmark
% 2.79/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.35 % (3743244)------------------------------
% 3.44/1.35 % (3743244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.35 % (3743244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.35 % (3743244)CaDiCaL version: 2.1.3
% 3.44/1.35 % (3743244)Termination reason: Refutation
% 3.44/1.35 % (3743244)Time elapsed: 0.019 s
% 3.44/1.35 % (3743244)Peak memory usage: 89 MB
% 3.44/1.35 % (3743244)Instructions burned: 26 (million)
% 3.44/1.35 % (3743244)------------------------------
% 3.44/1.35 % (3743244)------------------------------
% 3.44/1.35 % (3743234)Success in time 0.417 s
% 3.44/1.35 % Vampire exiting
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