%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP320-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 10:17:29 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 53
% Syntax : Number of formulae : 327 ( 21 unt; 19 def)
% Number of atoms : 1092 ( 321 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1453 ( 688 ~; 746 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X3) != sk_c8
| multiply(X4,sk_c7) != sk_c6
| inverse(X4) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(sk_c6,sk_c8) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f71,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f73,definition,
( spl0_2
<=> ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X4] :
( sk_c6 != multiply(X4,sk_c7)
| sk_c7 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,definition,
( spl0_3
<=> ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f77,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,definition,
( spl0_4
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c7 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f76,f73,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f93,plain,
( spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f64,f90,f69]) ).
fof(f95,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f97,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f62,f90,f95]) ).
fof(f100,definition,
( spl0_9
<=> sk_c6 = multiply(sk_c5,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f102,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f60,f90,f100]) ).
fof(f105,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f107,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f90,f105]) ).
fof(f110,definition,
( spl0_11
<=> sk_c7 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f112,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f56,f90,f110]) ).
fof(f115,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f115,f69]) ).
fof(f119,plain,
( spl0_8
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f115,f95]) ).
fof(f120,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f115,f100]) ).
fof(f121,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f115,f105]) ).
fof(f122,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f115,f110]) ).
fof(f124,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_1
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f124,f69]) ).
fof(f128,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f124,f95]) ).
fof(f129,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f124,f100]) ).
fof(f130,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f124,f105]) ).
fof(f131,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f124,f110]) ).
fof(f133,definition,
( spl0_14
<=> sk_c7 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c7 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_1
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f133,f69]) ).
fof(f137,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f133,f95]) ).
fof(f138,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f133,f100]) ).
fof(f139,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f133,f105]) ).
fof(f140,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f26,f133,f110]) ).
fof(f142,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c8 = multiply(sk_c1,sk_c7)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_1
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f142,f69]) ).
fof(f146,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f142,f95]) ).
fof(f147,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f142,f100]) ).
fof(f148,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f142,f105]) ).
fof(f149,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f16,f142,f110]) ).
fof(f150,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f69]) ).
fof(f151,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f12,f85,f95]) ).
fof(f152,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f100]) ).
fof(f153,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f105]) ).
fof(f154,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f110]) ).
fof(f155,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f156,plain,
( identity = multiply(sk_c7,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f135]) ).
fof(f158,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(sk_c8,X0)
| ~ spl0_15 ),
inference(superposition,[],[f4,f144]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f158,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c2,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f155]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c2,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_7
| ~ spl0_12 ),
inference(superposition,[],[f168,f117]) ).
fof(f174,plain,
( sk_c7 = sk_c8
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f171,f126]) ).
fof(f181,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f86,f174]) ).
fof(f182,plain,
( sk_c3 = multiply(sk_c2,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f117,f174]) ).
fof(f183,plain,
( sk_c7 = multiply(sk_c7,sk_c3)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f126,f174]) ).
fof(f251,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f165,f144]) ).
fof(f257,plain,
( sk_c1 = multiply(inverse(sk_c7),identity)
| ~ spl0_14 ),
inference(superposition,[],[f165,f156]) ).
fof(f271,plain,
( sk_c7 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f251,f174]) ).
fof(f278,plain,
( sk_c7 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f271,f135]) ).
fof(f290,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c8,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f160,f278]) ).
fof(f291,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f165,f278]) ).
fof(f293,plain,
( identity = sk_c7
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f291,f3]) ).
fof(f294,plain,
( multiply(sk_c1,sk_c7) = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f290,f174]) ).
fof(f297,plain,
( sk_c6 = multiply(sk_c1,sk_c7)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f294,f181]) ).
fof(f299,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f297,f144]) ).
fof(f300,plain,
( sk_c7 = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f299,f174]) ).
fof(f334,plain,
( sk_c1 = multiply(inverse(identity),identity)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f257,f293]) ).
fof(f335,plain,
( identity = sk_c1
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f334,f3]) ).
fof(f340,plain,
( sk_c7 = inverse(identity)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f135,f335]) ).
fof(f341,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f340,f293]) ).
fof(f369,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f300,f293]) ).
fof(f379,plain,
( sk_c7 != multiply(identity,sk_c8)
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f71,f369]) ).
fof(f380,plain,
( sk_c7 != sk_c8
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f379,f1]) ).
fof(f384,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f380,f174]) ).
fof(f385,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f387,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| sk_c7 != inverse(X4) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f74,f293]) ).
fof(f389,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| sk_c7 != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f387,f369]) ).
fof(f391,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f389,f293]) ).
fof(f392,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f391,f1]) ).
fof(f396,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f392]) ).
fof(f446,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f341,f396]) ).
fof(f447,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f448,plain,
( ! [X3] :
( sk_c7 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f77,f174]) ).
fof(f449,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c8 != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f448,f293]) ).
fof(f450,plain,
( ! [X3] :
( sk_c7 != inverse(X3)
| identity != multiply(X3,identity) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f449,f174]) ).
fof(f451,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f450,f293]) ).
fof(f452,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f451,f1]) ).
fof(f456,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f452]) ).
fof(f457,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f341,f456]) ).
fof(f458,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f459,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c8 != inverse(X2) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f80,f174]) ).
fof(f471,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f83,f293]) ).
fof(f472,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f471,f174]) ).
fof(f473,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f472,f293]) ).
fof(f474,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f473,f293]) ).
fof(f475,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f474,f1]) ).
fof(f479,plain,
( identity != inverse(identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f475]) ).
fof(f480,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f341,f479]) ).
fof(f481,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f483,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c7,multiply(X2,sk_c7))
| sk_c7 != inverse(X2) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f459,f174]) ).
fof(f489,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f97]) ).
fof(f504,plain,
( sk_c7 != multiply(sk_c7,sk_c3)
| sk_c7 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f483,f182]) ).
fof(f522,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f504,f183]) ).
fof(f546,plain,
( sk_c7 != sk_c8
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f522,f92]) ).
fof(f555,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f546,f174]) ).
fof(f556,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f568,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[],[f74,f102]) ).
fof(f573,plain,
( sk_c7 != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f568]) ).
fof(f576,definition,
( spl0_23
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f577,plain,
( identity = sk_c6
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f582,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f573,f97]) ).
fof(f583,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f613,definition,
( spl0_24
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f614,plain,
( identity = sk_c7
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f654,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_10 ),
inference(superposition,[],[f3,f107]) ).
fof(f657,plain,
( sk_c8 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_11 ),
inference(superposition,[],[f165,f112]) ).
fof(f659,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f657,f107]) ).
fof(f662,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| sk_c8 != inverse(sk_c4)
| ~ spl0_4
| ~ spl0_11 ),
inference(superposition,[],[f80,f112]) ).
fof(f677,definition,
( spl0_27
<=> sk_c8 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f678,plain,
( sk_c8 = inverse(identity)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f679,plain,
( sk_c8 != inverse(identity)
| spl0_27 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f685,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f662,f107]) ).
fof(f691,definition,
( spl0_30
<=> sk_c7 = multiply(sk_c8,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f693,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| spl0_30 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f704,plain,
( ~ spl0_30
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f685,f110,f105,f79,f691]) ).
fof(f716,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f165,f659]) ).
fof(f718,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f716,f3]) ).
fof(f720,plain,
( spl0_24
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f718,f110,f105,f613]) ).
fof(f726,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_8
| ~ spl0_24 ),
inference(superposition,[],[f489,f614]) ).
fof(f729,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_24 ),
inference(forward_demodulation,[],[f726,f1]) ).
fof(f734,plain,
( sk_c6 = multiply(identity,sk_c7)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(superposition,[],[f102,f729]) ).
fof(f737,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[],[f734,f1]) ).
fof(f739,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(forward_demodulation,[],[f737,f614]) ).
fof(f740,plain,
( spl0_23
| ~ spl0_8
| ~ spl0_9
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f739,f613,f100,f95,f576]) ).
fof(f742,plain,
( sk_c7 = multiply(identity,sk_c8)
| ~ spl0_1
| ~ spl0_23 ),
inference(superposition,[],[f70,f577]) ).
fof(f743,plain,
( sk_c7 = sk_c8
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f742,f1]) ).
fof(f744,plain,
( identity = sk_c8
| ~ spl0_1
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f743,f614]) ).
fof(f773,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f654,f744]) ).
fof(f776,plain,
( sk_c7 != multiply(identity,sk_c7)
| ~ spl0_1
| ~ spl0_23
| ~ spl0_24
| spl0_30 ),
inference(superposition,[],[f693,f744]) ).
fof(f779,plain,
( $false
| ~ spl0_1
| ~ spl0_23
| ~ spl0_24
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f776,f1]) ).
fof(f780,plain,
( ~ spl0_1
| ~ spl0_23
| ~ spl0_24
| spl0_30 ),
inference(avatar_contradiction_clause,[],[f779]) ).
fof(f783,plain,
( identity = sk_c4
| ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f773,f1]) ).
fof(f801,plain,
( ! [X3] :
( sk_c7 != multiply(X3,identity)
| sk_c8 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f77,f744]) ).
fof(f805,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c8 != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f801,f614]) ).
fof(f809,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f805,f744]) ).
fof(f811,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f809,f1]) ).
fof(f815,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_23
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f811]) ).
fof(f821,plain,
( sk_c8 = inverse(identity)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f107,f783]) ).
fof(f822,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24
| spl0_27 ),
inference(forward_subsumption_resolution,[],[f821,f679]) ).
fof(f823,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24
| spl0_27 ),
inference(avatar_contradiction_clause,[],[f822]) ).
fof(f827,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_demodulation,[],[f678,f744]) ).
fof(f828,plain,
( identity = inverse(identity)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f821,f744]) ).
fof(f831,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f828,f815]) ).
fof(f832,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f831]) ).
fof(f833,plain,
( ! [X0] :
( sk_c8 != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_5
| ~ spl0_24 ),
inference(forward_demodulation,[],[f83,f614]) ).
fof(f834,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c7 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f833,f744]) ).
fof(f835,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f834,f614]) ).
fof(f836,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f835,f1]) ).
fof(f840,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f836]) ).
fof(f847,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f840,f827]) ).
fof(f848,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f847]) ).
fof(f849,plain,
( identity != multiply(sk_c7,sk_c8)
| spl0_6
| ~ spl0_23 ),
inference(forward_demodulation,[],[f87,f577]) ).
fof(f850,plain,
( identity != multiply(sk_c7,identity)
| ~ spl0_1
| spl0_6
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f849,f744]) ).
fof(f851,plain,
( identity != multiply(identity,identity)
| ~ spl0_1
| spl0_6
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f850,f614]) ).
fof(f852,plain,
( $false
| ~ spl0_1
| spl0_6
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f851,f1]) ).
fof(f853,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_23
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f852]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f93]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f98]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f103]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f108]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s9,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
( spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s15,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
( spl0_1
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s21,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f140]) ).
cnf(s22,plain,
( spl0_1
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f150]) ).
cnf(s28,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f154]) ).
cnf(s33,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f385]) ).
cnf(s34,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f447]) ).
cnf(s35,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f458]) ).
cnf(s37,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f481]) ).
cnf(s45,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f556]) ).
cnf(s49,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f583]) ).
cnf(s73,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_30 ),
inference(sat_conversion,[],[f704]) ).
cnf(s74,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_24 ),
inference(sat_conversion,[],[f720]) ).
cnf(s75,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f740]) ).
cnf(s76,plain,
( ~ spl0_1
| ~ spl0_23
| ~ spl0_24
| spl0_30 ),
inference(sat_conversion,[],[f780]) ).
cnf(s80,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24
| spl0_27 ),
inference(sat_conversion,[],[f823]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f832]) ).
cnf(s83,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_23
| ~ spl0_24
| ~ spl0_27 ),
inference(sat_conversion,[],[f848]) ).
cnf(s84,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f853]) ).
cnf(s85,plain,
spl0_1,
inference(rat,[],[s33,s2,s7,s12,s17,s22,s27]) ).
cnf(s86,plain,
spl0_6,
inference(rat,[],[s84,s75,s74,s28,s29,s30,s31,s85]) ).
cnf(s87,plain,
( ~ spl0_24
| ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s80,s83,s75,s85]) ).
cnf(s88,plain,
( spl0_11
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s37,s11,s16,s21,s26]) ).
cnf(s89,plain,
( ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_11
| ~ spl0_5 ),
inference(rat,[],[s74,s87]) ).
cnf(s90,plain,
( spl0_10
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s37,s10,s15,s20,s25]) ).
cnf(s91,plain,
( spl0_9
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s37,s9,s14,s19,s24]) ).
cnf(s92,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s37,s8,s13,s18,s23,s89,s91,s90,s88]) ).
cnf(s93,plain,
~ spl0_5,
inference(rat,[],[s89,s3,s4,s5,s6,s92]) ).
cnf(s95,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s45,s6,s11,s16]) ).
cnf(s96,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s45,s5,s10,s15]) ).
cnf(s97,plain,
( spl0_9
| ~ spl0_4 ),
inference(rat,[],[s45,s4,s9,s14]) ).
cnf(s98,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s45,s3,s8,s13,s75,s97,s76,s74,s73,s85]) ).
cnf(s99,plain,
~ spl0_4,
inference(rat,[],[s98,s96,s95]) ).
cnf(s101,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s35,s6,s11,s16,s21,s26]) ).
cnf(s103,plain,
( spl0_10
| ~ spl0_3 ),
inference(rat,[],[s35,s5,s10,s15,s20,s25]) ).
cnf(s104,plain,
( spl0_9
| ~ spl0_3 ),
inference(rat,[],[s35,s4,s9,s14,s19,s24]) ).
cnf(s105,plain,
( ~ spl0_24
| ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s35,s3,s8,s13,s18,s23,s75,s104,s82,s85]) ).
cnf(s106,plain,
~ spl0_3,
inference(rat,[],[s105,s74,s103,s101]) ).
cnf(s107,plain,
spl0_2,
inference(rat,[],[s1,s85,s86,s93,s99,s106]) ).
cnf(s108,plain,
spl0_9,
inference(rat,[],[s34,s4,s9,s14,s19,s24,s107,s86]) ).
cnf(s109,plain,
~ spl0_8,
inference(rat,[],[s49,s107,s108]) ).
cnf(s110,plain,
spl0_15,
inference(rat,[],[s23,s109]) ).
cnf(s111,plain,
spl0_14,
inference(rat,[],[s18,s109]) ).
cnf(s112,plain,
spl0_13,
inference(rat,[],[s13,s109]) ).
cnf(s113,plain,
spl0_12,
inference(rat,[],[s8,s109]) ).
cnf(s114,plain,
spl0_7,
inference(rat,[],[s3,s109]) ).
cnf(s116,plain,
$false,
inference(rat,[],[s34,s110,s111,s112,s86,s107,s114,s113]) ).
fof(f854,plain,
$false,
inference(avatar_sat_refutation,[],[s116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP320-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 09:50:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/0.33 Running first-order model finding
% 0.04/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37 % (2127826)Will run a generic schedule for satisfiability detection.
% 0.07/0.37 % (2127832)% WARNING: option uhcvi not known.
% 0.07/0.37 % (2127831)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1687337466_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.37 % (2127832)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1576797616:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.37 % (2127833)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2387260503:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.37 % (2127834)dis+10_1_sil=32000:sp=arity:random_seed=233198256:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.37 % (2127835)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=808357257:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.37 % (2127836)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3163845434:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.37 % (2127837)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4208334167:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.37 % TRYING [1]
% 0.07/0.37 % TRYING [2]
% 0.07/0.37 % TRYING [3]
% 0.07/0.37 % TRYING [4]
% 0.07/0.37 % (2127835) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2127826-2127835"...
% 0.07/0.37 % (2127834) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2127826-2127834"...
% 0.07/0.37 % TRYING [5]
% 0.07/0.37 % (2127834)...printing done.
% 0.07/0.37 % (2127835)...printing done.
% 0.07/0.37 % (2127836) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2127826-2127836"...
% 0.07/0.37 % (2127834)Refutation found. Thanks to Tanya!
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.37 % (2127834)------------------------------
% 0.07/0.37 % (2127834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.37 % (2127834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.37 % (2127834)CaDiCaL version: 2.1.3
% 0.07/0.37 % (2127834)Termination reason: Refutation
% 0.07/0.37 % (2127834)Time elapsed: 0.010 s
% 0.07/0.37 % (2127834)Peak memory usage: 12 MB
% 0.07/0.37 % (2127834)Instructions burned: 29 (million)
% 0.07/0.37 % (2127826)Success in time 0.035 s
% 0.07/0.37 % Vampire exiting
%------------------------------------------------------------------------------