%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP364-1 : 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 : n007.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 10:17:36 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 47
% Syntax : Number of formulae : 295 ( 16 unt; 19 def)
% Number of atoms : 1026 ( 313 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1403 ( 672 ~; 712 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( multiply(sk_c9,sk_c2) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c9,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c2
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c2
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f45]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c9
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c7 = inverse(sk_c3)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c9,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c7 = inverse(sk_c3)
| sk_c8 = multiply(sk_c9,sk_c6) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c9) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c7 = inverse(sk_c3)
| sk_c9 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| multiply(sk_c9,X0) != sk_c8
| multiply(X1,sk_c9) != X0
| inverse(X1) != sk_c9
| multiply(X2,sk_c7) != sk_c9
| inverse(X2) != sk_c7
| multiply(sk_c9,sk_c8) != sk_c7
| multiply(X3,sk_c9) != sk_c8
| inverse(X3) != sk_c9
| multiply(sk_c9,X4) != sk_c8
| multiply(X5,sk_c9) != X4
| inverse(X5) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != multiply(sk_c9,X0)
| multiply(X1,sk_c9) != X0
| sk_c9 != inverse(X1)
| sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(sk_c9,sk_c8)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X1,X4,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != multiply(sk_c9,multiply(X1,sk_c9))
| sk_c9 != inverse(X1)
| sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(sk_c9,sk_c8)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,X4)
| multiply(X5,sk_c9) != X4
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X1,X5] :
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != multiply(sk_c9,multiply(X1,sk_c9))
| sk_c9 != inverse(X1)
| sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2)
| sk_c7 != multiply(sk_c9,sk_c8)
| sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3)
| sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ),
inference(equality_resolution,[],[f79]) ).
fof(f82,definition,
( spl0_1
<=> ! [X5] :
( sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f83,plain,
( ! [X5] :
( sk_c8 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c9 != inverse(X5) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c9)
| sk_c9 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl0_3
<=> sk_c7 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f89,plain,
( sk_c7 = multiply(sk_c9,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( sk_c7 != multiply(sk_c9,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f93,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c7)
| sk_c7 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,definition,
( spl0_5
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f96,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( multiply(sk_c7,sk_c9) != sk_c8
| spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f80,f95,f82,f92,f88,f85,f82]) ).
fof(f100,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f102,plain,
( sk_c9 = inverse(sk_c5)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f104,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f106,plain,
( sk_c7 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f104,f100]) ).
fof(f109,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f111,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f74,f104,f109]) ).
fof(f114,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c9,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f116,plain,
( sk_c8 = multiply(sk_c9,sk_c6)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f72,f104,f114]) ).
fof(f119,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f121,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f70,f104,f119]) ).
fof(f124,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c4,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f126,plain,
( sk_c8 = multiply(sk_c4,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f68,f104,f124]) ).
fof(f128,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f66,f104,f88]) ).
fof(f130,definition,
( spl0_12
<=> sk_c9 = multiply(sk_c3,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 = multiply(sk_c3,sk_c7)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_6
| spl0_12 ),
inference(avatar_split_clause,[],[f64,f130,f100]) ).
fof(f134,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f62,f130,f109]) ).
fof(f135,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f60,f130,f114]) ).
fof(f136,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f58,f130,f119]) ).
fof(f137,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f56,f130,f124]) ).
fof(f138,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f130,f88]) ).
fof(f140,definition,
( spl0_13
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f142,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f146,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f140,f119]) ).
fof(f147,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f140,f124]) ).
fof(f150,definition,
( spl0_14
<=> sk_c2 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f152,plain,
( sk_c2 = multiply(sk_c1,sk_c9)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f156,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f150,f119]) ).
fof(f157,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f150,f124]) ).
fof(f160,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c9,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,plain,
( sk_c8 = multiply(sk_c9,sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f166,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f160,f119]) ).
fof(f167,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f160,f124]) ).
fof(f169,plain,
( spl0_6
| spl0_5 ),
inference(avatar_split_clause,[],[f16,f95,f100]) ).
fof(f170,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f14,f95,f109]) ).
fof(f171,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f12,f95,f114]) ).
fof(f172,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f10,f95,f119]) ).
fof(f173,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f95,f124]) ).
fof(f174,plain,
( spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f95,f88]) ).
fof(f175,plain,
( identity = multiply(sk_c9,sk_c5)
| ~ spl0_6 ),
inference(superposition,[],[f3,f102]) ).
fof(f176,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f121]) ).
fof(f179,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f182,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f126]) ).
fof(f183,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c9,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f111]) ).
fof(f184,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f179,f1]) ).
fof(f187,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c5,X0))
| ~ spl0_6 ),
inference(superposition,[],[f4,f175]) ).
fof(f188,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c5,X0)) = X0
| ~ spl0_6 ),
inference(forward_demodulation,[],[f187,f1]) ).
fof(f191,plain,
( sk_c9 = multiply(sk_c9,sk_c6)
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f188,f111]) ).
fof(f197,plain,
( sk_c9 = sk_c8
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f191,f116]) ).
fof(f205,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c9,X0))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f182,f197]) ).
fof(f209,plain,
( multiply(sk_c6,sk_c8) = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f183,f89]) ).
fof(f219,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c9)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f209,f197]) ).
fof(f231,plain,
( identity = multiply(sk_c4,identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f205,f176]) ).
fof(f252,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_9 ),
inference(superposition,[],[f184,f116]) ).
fof(f253,plain,
( sk_c5 = multiply(inverse(sk_c9),identity)
| ~ spl0_6 ),
inference(superposition,[],[f184,f175]) ).
fof(f254,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_11 ),
inference(superposition,[],[f184,f126]) ).
fof(f267,plain,
( sk_c9 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f254,f197]) ).
fof(f268,plain,
( sk_c6 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f252,f197]) ).
fof(f273,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f267,f121]) ).
fof(f274,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f268,f3]) ).
fof(f288,plain,
( sk_c9 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f273]) ).
fof(f290,plain,
( identity = sk_c9
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f288,f3]) ).
fof(f341,plain,
( sk_c5 = multiply(inverse(identity),identity)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f253,f290]) ).
fof(f342,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f341,f3]) ).
fof(f376,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c6,identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f219,f290]) ).
fof(f377,plain,
( multiply(sk_c5,sk_c7) = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f376,f274]) ).
fof(f378,plain,
( identity = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f377,f1]) ).
fof(f379,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f378,f342]) ).
fof(f380,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f379,f1]) ).
fof(f383,plain,
( sk_c8 != multiply(identity,sk_c9)
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f97,f380]) ).
fof(f384,plain,
( sk_c9 != sk_c8
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f383,f1]) ).
fof(f385,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f384,f197]) ).
fof(f386,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f387,plain,
( ! [X2] :
( sk_c9 != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f93,f380]) ).
fof(f389,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c7 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f387,f290]) ).
fof(f391,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f389,f380]) ).
fof(f396,plain,
( identity != identity
| identity != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f391,f231]) ).
fof(f397,plain,
( identity != inverse(sk_c4)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f396]) ).
fof(f400,plain,
( identity != sk_c9
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f397,f121]) ).
fof(f401,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f400,f290]) ).
fof(f402,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f401]) ).
fof(f403,plain,
( ! [X5] :
( sk_c8 != multiply(identity,multiply(X5,identity))
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f83,f290]) ).
fof(f404,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f403,f1]) ).
fof(f405,plain,
( ! [X5] :
( sk_c9 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f404,f197]) ).
fof(f406,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f405,f290]) ).
fof(f407,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f406,f290]) ).
fof(f411,plain,
( identity != identity
| identity != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f407,f231]) ).
fof(f412,plain,
( identity != inverse(sk_c4)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f411]) ).
fof(f415,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f412,f121]) ).
fof(f416,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f415,f290]) ).
fof(f417,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f416]) ).
fof(f418,plain,
( ! [X3] :
( sk_c8 != multiply(X3,identity)
| sk_c9 != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f86,f290]) ).
fof(f419,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c9 != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f418,f197]) ).
fof(f420,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c9 != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f419,f290]) ).
fof(f421,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f420,f290]) ).
fof(f425,plain,
( identity != identity
| identity != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f421,f231]) ).
fof(f426,plain,
( identity != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f425]) ).
fof(f429,plain,
( identity != sk_c9
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f426,f121]) ).
fof(f430,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f429,f290]) ).
fof(f431,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f430]) ).
fof(f432,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f254,f121]) ).
fof(f444,plain,
( identity = multiply(sk_c7,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f106]) ).
fof(f485,definition,
( spl0_17
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f486,plain,
( sk_c7 = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f494,definition,
( spl0_19
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f495,plain,
( identity = sk_c7
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f499,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_13 ),
inference(superposition,[],[f3,f142]) ).
fof(f502,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c9)
| ~ spl0_12 ),
inference(superposition,[],[f184,f132]) ).
fof(f504,plain,
( sk_c7 = multiply(sk_c7,sk_c9)
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f502,f106]) ).
fof(f506,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c1,multiply(sk_c9,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f152]) ).
fof(f514,plain,
( sk_c9 != sk_c9
| sk_c7 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_12 ),
inference(superposition,[],[f93,f132]) ).
fof(f515,plain,
( sk_c7 != inverse(sk_c3)
| ~ spl0_4
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f514]) ).
fof(f516,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f515,f106]) ).
fof(f517,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f516]) ).
fof(f519,definition,
( spl0_20
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f520,plain,
( identity = sk_c9
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f549,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f184,f432]) ).
fof(f551,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f549,f3]) ).
fof(f560,plain,
( sk_c7 = sk_c8
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f96,f504]) ).
fof(f561,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f184,f504]) ).
fof(f563,plain,
( identity = sk_c9
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f561,f3]) ).
fof(f564,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f560,f551]) ).
fof(f566,plain,
( spl0_20
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f563,f130,f104,f519]) ).
fof(f567,plain,
( spl0_19
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f564,f130,f124,f119,f104,f95,f494]) ).
fof(f570,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_7
| ~ spl0_19 ),
inference(superposition,[],[f444,f495]) ).
fof(f573,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_19 ),
inference(forward_demodulation,[],[f570,f1]) ).
fof(f578,plain,
( sk_c7 != multiply(identity,sk_c8)
| spl0_3
| ~ spl0_20 ),
inference(superposition,[],[f90,f520]) ).
fof(f584,plain,
( sk_c8 = multiply(identity,sk_c2)
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f162,f520]) ).
fof(f590,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[],[f499,f520]) ).
fof(f596,plain,
( identity = sk_c1
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f590,f1]) ).
fof(f602,plain,
( sk_c8 = sk_c2
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f584,f1]) ).
fof(f606,plain,
( sk_c7 != sk_c8
| spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f578,f1]) ).
fof(f622,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f560,f130,f104,f95,f485]) ).
fof(f623,plain,
( ~ spl0_17
| spl0_3
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f606,f519,f88,f485]) ).
fof(f626,plain,
( ! [X3] :
( sk_c8 != multiply(X3,identity)
| sk_c9 != inverse(X3) )
| ~ spl0_2
| ~ spl0_20 ),
inference(forward_demodulation,[],[f86,f520]) ).
fof(f628,plain,
( ! [X3] :
( identity != inverse(X3)
| sk_c8 != multiply(X3,identity) )
| ~ spl0_2
| ~ spl0_20 ),
inference(forward_demodulation,[],[f626,f520]) ).
fof(f631,plain,
( ! [X3] :
( sk_c7 != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f628,f486]) ).
fof(f632,plain,
( identity != sk_c7
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f631,f1]) ).
fof(f642,plain,
( sk_c7 = sk_c2
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f602,f486]) ).
fof(f656,plain,
( ! [X0] : multiply(sk_c2,X0) = multiply(sk_c1,multiply(identity,X0))
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f506,f520]) ).
fof(f657,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(sk_c2,X0)
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f656,f1]) ).
fof(f658,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,X0)
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f657,f642]) ).
fof(f659,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,X0)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f658,f596]) ).
fof(f660,plain,
( ! [X0] : multiply(sk_c7,X0) = X0
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f659,f1]) ).
fof(f672,plain,
( sk_c9 = sk_c8
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(superposition,[],[f96,f660]) ).
fof(f677,plain,
( sk_c7 = sk_c9
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f672,f486]) ).
fof(f690,plain,
( identity = sk_c7
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f677,f520]) ).
fof(f710,definition,
( spl0_24
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f713,plain,
( ~ spl0_24
| ~ spl0_19
| ~ spl0_2
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f632,f519,f485,f85,f494,f710]) ).
fof(f721,plain,
( spl0_19
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f690,f519,f485,f160,f150,f140,f95,f494]) ).
fof(f739,plain,
( sk_c7 = inverse(identity)
| ~ spl0_7
| ~ spl0_19 ),
inference(superposition,[],[f106,f573]) ).
fof(f740,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_19 ),
inference(forward_demodulation,[],[f739,f495]) ).
fof(f746,plain,
( ! [X5] :
( sk_c8 != multiply(identity,multiply(X5,identity))
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f83,f520]) ).
fof(f747,plain,
( spl0_24
| ~ spl0_7
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f740,f494,f104,f710]) ).
fof(f748,plain,
( ! [X5] :
( sk_c8 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_20 ),
inference(forward_demodulation,[],[f746,f1]) ).
fof(f749,plain,
( ! [X5] :
( sk_c7 != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_20 ),
inference(forward_demodulation,[],[f748,f486]) ).
fof(f750,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| sk_c9 != inverse(X5) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f749,f495]) ).
fof(f751,plain,
( ! [X5] :
( identity != multiply(X5,identity)
| identity != inverse(X5) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20 ),
inference(forward_demodulation,[],[f750,f520]) ).
fof(f752,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20 ),
inference(superposition,[],[f751,f1]) ).
fof(f758,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f752]) ).
fof(f761,plain,
( ~ spl0_24
| ~ spl0_1
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f758,f519,f494,f485,f82,f710]) ).
cnf(s1,plain,
( spl0_1
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f98]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f107]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f112]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f117]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f122]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f127]) ).
cnf(s8,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f128]) ).
cnf(s9,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f133]) ).
cnf(s10,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f134]) ).
cnf(s11,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s12,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f136]) ).
cnf(s13,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f137]) ).
cnf(s14,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f138]) ).
cnf(s18,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f146]) ).
cnf(s19,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f147]) ).
cnf(s24,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s25,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s30,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f166]) ).
cnf(s31,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s33,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f169]) ).
cnf(s34,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f171]) ).
cnf(s36,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f172]) ).
cnf(s37,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f173]) ).
cnf(s38,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f174]) ).
cnf(s39,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f386]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f402]) ).
cnf(s41,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f417]) ).
cnf(s42,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f431]) ).
cnf(s46,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f517]) ).
cnf(s50,plain,
( ~ spl0_7
| ~ spl0_12
| spl0_20 ),
inference(sat_conversion,[],[f566]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f567]) ).
cnf(s58,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f622]) ).
cnf(s60,plain,
( spl0_3
| ~ spl0_17
| ~ spl0_20 ),
inference(sat_conversion,[],[f623]) ).
cnf(s72,plain,
( ~ spl0_2
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f713]) ).
cnf(s77,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| spl0_19
| ~ spl0_20 ),
inference(sat_conversion,[],[f721]) ).
cnf(s80,plain,
( ~ spl0_7
| ~ spl0_19
| spl0_24 ),
inference(sat_conversion,[],[f747]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_24 ),
inference(sat_conversion,[],[f761]) ).
cnf(s84,plain,
spl0_3,
inference(rat,[],[s60,s58,s50,s8,s14,s38]) ).
cnf(s85,plain,
spl0_5,
inference(rat,[],[s39,s33,s34,s35,s36,s37,s84]) ).
cnf(s86,plain,
( spl0_12
| ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s40,s10,s11,s12,s13,s84]) ).
cnf(s87,plain,
( ~ spl0_6
| ~ spl0_4 ),
inference(rat,[],[s40,s4,s5,s6,s7,s46,s86,s84]) ).
cnf(s88,plain,
~ spl0_4,
inference(rat,[],[s46,s3,s9,s87]) ).
cnf(s89,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s72,s80,s77,s58,s50,s13,s19,s25,s31,s85]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s72,s80,s77,s58,s50,s12,s18,s24,s30,s85]) ).
cnf(s91,plain,
( ~ spl0_12
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s72,s80,s51,s58,s50,s89,s90,s85]) ).
cnf(s92,plain,
( ~ spl0_7
| ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s42,s10,s11,s91,s90,s89]) ).
cnf(s93,plain,
( ~ spl0_6
| ~ spl0_2 ),
inference(rat,[],[s42,s4,s5,s6,s7,s92]) ).
cnf(s94,plain,
~ spl0_2,
inference(rat,[],[s91,s3,s9,s93]) ).
cnf(s95,plain,
spl0_1,
inference(rat,[],[s2,s84,s85,s88,s94]) ).
cnf(s96,plain,
( spl0_11
| ~ spl0_7 ),
inference(rat,[],[s82,s80,s77,s58,s50,s13,s19,s25,s31,s95,s85]) ).
cnf(s97,plain,
( spl0_10
| ~ spl0_7 ),
inference(rat,[],[s82,s80,s77,s58,s50,s12,s18,s24,s30,s95,s85]) ).
cnf(s98,plain,
( ~ spl0_12
| ~ spl0_7 ),
inference(rat,[],[s82,s80,s51,s58,s50,s96,s97,s95,s85]) ).
cnf(s99,plain,
( ~ spl0_7
| ~ spl0_6 ),
inference(rat,[],[s41,s10,s11,s98,s97,s96,s95]) ).
cnf(s100,plain,
~ spl0_6,
inference(rat,[],[s41,s4,s5,s6,s7,s99,s95]) ).
cnf(s104,plain,
spl0_12,
inference(rat,[],[s9,s100]) ).
cnf(s105,plain,
spl0_7,
inference(rat,[],[s3,s100]) ).
cnf(s108,plain,
$false,
inference(rat,[],[s98,s105,s104]) ).
fof(f763,plain,
$false,
inference(avatar_sat_refutation,[],[s108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP364-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 % Computer : n007.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:54:10 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.49 % (1168123)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (1168128)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2010325709_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % TRYING [1]
% 0.16/0.49 % TRYING [2]
% 0.16/0.49 % (1168129)% WARNING: option uhcvi not known.
% 0.16/0.49 % TRYING [3]
% 0.16/0.49 % TRYING [4]
% 0.16/0.49 % (1168129)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1561008096:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (1168130)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2255188872:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (1168131)dis+10_1_sil=32000:sp=arity:random_seed=1692925283:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (1168132)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1822682866:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (1168133)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3224052389:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % (1168134)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2106897349:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % TRYING [5]
% 0.16/0.49 % (1168131) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1168123-1168131"...
% 0.16/0.49 % (1168132) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1168123-1168132"...
% 0.16/0.49 % (1168131)...printing done.
% 0.16/0.49 % (1168132)...printing done.
% 0.16/0.49 % (1168131)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (1168131)------------------------------
% 0.16/0.50 % (1168131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (1168131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (1168131)CaDiCaL version: 2.1.3
% 0.16/0.50 % (1168131)Termination reason: Refutation
% 0.16/0.50 % (1168131)Time elapsed: 0.016 s
% 0.16/0.50 % (1168131)Peak memory usage: 12 MB
% 0.16/0.50 % (1168131)Instructions burned: 26 (million)
% 0.16/0.50 % (1168123)Success in time 0.062 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------