TSTP Solution File: GRP039-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP039-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:52:38 EDT 2024
% Result : Unsatisfiable 0.18s 0.39s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 38
% Syntax : Number of formulae : 355 ( 29 unt; 0 def)
% Number of atoms : 884 ( 134 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 988 ( 459 ~; 511 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 511 ( 511 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f766,plain,
$false,
inference(avatar_sat_refutation,[],[f74,f134,f255,f264,f294,f420,f486,f544,f684,f721,f724,f734,f749,f764]) ).
fof(f764,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f763]) ).
fof(f763,plain,
( $false
| ~ spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f760,f73]) ).
fof(f73,plain,
( subgroup_member(c)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl0_2
<=> subgroup_member(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f760,plain,
( ~ subgroup_member(c)
| ~ spl0_1 ),
inference(resolution,[],[f754,f14]) ).
fof(f14,axiom,
! [X6] :
( subgroup_member(inverse(X6))
| ~ subgroup_member(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subgroup_member_inverse_are_in_subgroup) ).
fof(f754,plain,
( ~ subgroup_member(inverse(c))
| ~ spl0_1 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f549,f526,f739,f475,f68,f127,f750,f745,f751,f743,f752,f466,f741]) ).
fof(f741,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(subsumption_resolution,[],[f470,f20]) ).
fof(f470,plain,
( ~ subgroup_member(a)
| subgroup_member(d)
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[],[f61,f19]) ).
fof(f466,plain,
( ~ subgroup_member(inverse(d))
| subgroup_member(inverse(c))
| ~ subgroup_member(inverse(a)) ),
inference(resolution,[],[f61,f337]) ).
fof(f752,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f549,f526,f739,f741,f475,f68,f127,f750,f745,f751,f743]) ).
fof(f743,plain,
( identity = multiply(element_in_O2(d,a),c)
| subgroup_member(a) ),
inference(subsumption_resolution,[],[f347,f20]) ).
fof(f347,plain,
( identity = multiply(element_in_O2(d,a),c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolution,[],[f298,f16]) ).
fof(f751,plain,
( ~ subgroup_member(inverse(c))
| ~ spl0_1 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f549,f526,f739,f741,f475,f743,f68,f127,f750,f745]) ).
fof(f745,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(subsumption_resolution,[],[f209,f20]) ).
fof(f209,plain,
( subgroup_member(d)
| ~ subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(superposition,[],[f108,f35]) ).
fof(f750,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f549,f526,f739,f741,f475,f743,f745,f68,f127]) ).
fof(f127,plain,
( c = element_in_O2(a,d)
| subgroup_member(a) ),
inference(subsumption_resolution,[],[f126,f20]) ).
fof(f126,plain,
( c = element_in_O2(a,d)
| subgroup_member(d)
| subgroup_member(a) ),
inference(resolution,[],[f124,f16]) ).
fof(f68,plain,
( subgroup_member(a)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl0_1
<=> subgroup_member(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f475,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ subgroup_member(inverse(c))
| ~ product(X0,identity,a) ),
inference(subsumption_resolution,[],[f461,f20]) ).
fof(f461,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(d)
| ~ subgroup_member(inverse(c))
| ~ product(X0,identity,a) ),
inference(resolution,[],[f61,f232]) ).
fof(f739,plain,
! [X0] :
( ~ product(a,b,X0)
| ~ subgroup_member(X0)
| ~ subgroup_member(a) ),
inference(subsumption_resolution,[],[f510,f20]) ).
fof(f510,plain,
! [X0] :
( ~ product(a,b,X0)
| ~ subgroup_member(X0)
| subgroup_member(d)
| ~ subgroup_member(a) ),
inference(resolution,[],[f428,f9]) ).
fof(f526,plain,
! [X0] :
( ~ subgroup_member(a)
| ~ product(a,b,X0)
| ~ subgroup_member(X0) ),
inference(forward_demodulation,[],[f525,f12]) ).
fof(f525,plain,
! [X0] :
( ~ product(a,b,X0)
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(inverse(a))) ),
inference(subsumption_resolution,[],[f518,f20]) ).
fof(f518,plain,
! [X0] :
( ~ product(a,b,X0)
| ~ subgroup_member(X0)
| subgroup_member(d)
| ~ subgroup_member(inverse(inverse(a))) ),
inference(resolution,[],[f428,f61]) ).
fof(f549,plain,
( c = multiply(element_in_O2(a,a),c)
| subgroup_member(a) ),
inference(duplicate_literal_removal,[],[f548]) ).
fof(f548,plain,
( c = multiply(element_in_O2(a,a),c)
| subgroup_member(a)
| subgroup_member(a) ),
inference(resolution,[],[f307,f16]) ).
fof(f642,plain,
! [X0] :
( ~ product(b,inverse(a),X0)
| product(c,identity,X0) ),
inference(resolution,[],[f277,f18]) ).
fof(f615,plain,
! [X0] :
( ~ product(inverse(a),d,X0)
| c = X0 ),
inference(resolution,[],[f613,f6]) ).
fof(f700,plain,
! [X2,X0,X1] :
( ~ product(d,X0,X1)
| product(X2,X0,X1)
| ~ product(a,c,X2) ),
inference(resolution,[],[f282,f643]) ).
fof(f282,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,X3)
| ~ product(X0,X1,X2)
| product(X3,X1,X2) ),
inference(resolution,[],[f8,f1]) ).
fof(f612,plain,
! [X0] :
( ~ product(inverse(a),X0,c)
| d = X0 ),
inference(superposition,[],[f117,f609]) ).
fof(f611,plain,
! [X0] :
( ~ product(X0,d,c)
| inverse(a) = X0 ),
inference(superposition,[],[f165,f609]) ).
fof(f667,plain,
( ~ product(a,c,identity)
| identity = inverse(d) ),
inference(resolution,[],[f643,f119]) ).
fof(f668,plain,
! [X0] :
( ~ product(a,c,multiply(d,X0))
| identity = X0 ),
inference(resolution,[],[f643,f117]) ).
fof(f665,plain,
! [X0,X1] :
( ~ product(a,c,X0)
| ~ product(d,identity,X1)
| product(X0,identity,X1) ),
inference(resolution,[],[f643,f277]) ).
fof(f664,plain,
! [X0,X1] :
( ~ product(a,c,X0)
| ~ product(X1,d,identity)
| product(X1,X0,identity) ),
inference(resolution,[],[f643,f223]) ).
fof(f661,plain,
! [X0,X1] :
( ~ product(a,c,X0)
| d = X1
| ~ product(X1,identity,X0) ),
inference(resolution,[],[f643,f11]) ).
fof(f660,plain,
! [X0,X1] :
( ~ product(a,c,X0)
| identity = X1
| ~ product(d,X1,X0) ),
inference(resolution,[],[f643,f10]) ).
fof(f659,plain,
! [X2,X3,X0,X1] :
( ~ product(a,c,X0)
| ~ product(X1,X0,X2)
| ~ product(X1,d,X3)
| product(X3,identity,X2) ),
inference(resolution,[],[f643,f8]) ).
fof(f658,plain,
! [X2,X3,X0,X1] :
( ~ product(a,c,X0)
| ~ product(X1,X2,d)
| ~ product(X2,identity,X3)
| product(X1,X3,X0) ),
inference(resolution,[],[f643,f7]) ).
fof(f657,plain,
! [X0,X1] :
( ~ product(a,c,X0)
| X0 = X1
| ~ product(d,identity,X1) ),
inference(resolution,[],[f643,f6]) ).
fof(f654,plain,
( ~ product(a,c,a)
| d = multiply(d,c) ),
inference(resolution,[],[f643,f241]) ).
fof(f650,plain,
! [X2,X0,X1] :
( ~ product(a,c,X0)
| ~ product(X1,d,X2)
| product(X1,X0,X2) ),
inference(resolution,[],[f643,f220]) ).
fof(f643,plain,
! [X0] :
( product(d,identity,X0)
| ~ product(a,c,X0) ),
inference(resolution,[],[f277,f19]) ).
fof(f645,plain,
! [X0] :
( ~ product(inverse(c),c,X0)
| product(identity,identity,X0) ),
inference(forward_demodulation,[],[f640,f325]) ).
fof(f640,plain,
! [X0] :
( ~ product(multiply(inverse(d),a),c,X0)
| product(identity,identity,X0) ),
inference(resolution,[],[f277,f323]) ).
fof(f639,plain,
! [X0] :
( ~ product(inverse(a),d,X0)
| product(c,identity,X0) ),
inference(resolution,[],[f277,f613]) ).
fof(f638,plain,
! [X0] :
( ~ product(inverse(d),a,X0)
| product(inverse(c),identity,X0) ),
inference(resolution,[],[f277,f337]) ).
fof(f637,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| product(identity,identity,X1) ),
inference(resolution,[],[f277,f3]) ).
fof(f636,plain,
! [X0,X1] :
( ~ product(identity,X0,X1)
| product(X0,identity,X1) ),
inference(resolution,[],[f277,f1]) ).
fof(f635,plain,
! [X0,X1] :
( ~ product(X0,d,X1)
| product(c,identity,X1)
| ~ product(X0,a,identity) ),
inference(resolution,[],[f277,f571]) ).
fof(f634,plain,
! [X0,X1] :
( ~ product(X0,d,X1)
| product(d,identity,X1)
| ~ product(X0,a,a) ),
inference(resolution,[],[f277,f234]) ).
fof(f633,plain,
! [X0,X1] :
( ~ product(X0,c,X1)
| product(inverse(a),identity,X1)
| ~ product(X0,b,identity) ),
inference(resolution,[],[f277,f570]) ).
fof(f632,plain,
! [X0,X1] :
( ~ product(X0,c,X1)
| product(c,identity,X1)
| ~ product(X0,b,b) ),
inference(resolution,[],[f277,f370]) ).
fof(f631,plain,
! [X0,X1] :
( ~ product(X0,c,X1)
| product(d,identity,X1)
| ~ product(X0,identity,a) ),
inference(resolution,[],[f277,f232]) ).
fof(f630,plain,
! [X2,X0,X1] :
( ~ product(X0,element_in_O2(X0,X1),X2)
| product(X1,identity,X2)
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(resolution,[],[f277,f16]) ).
fof(f629,plain,
! [X2,X0,X1] :
( ~ product(X0,multiply(X1,c),X2)
| product(d,identity,X2)
| ~ product(X0,X1,a) ),
inference(resolution,[],[f277,f231]) ).
fof(f628,plain,
! [X0,X1] :
( ~ product(X0,inverse(a),X1)
| product(d,identity,X1)
| ~ product(a,b,X0) ),
inference(resolution,[],[f277,f428]) ).
fof(f627,plain,
! [X0,X1] :
( ~ product(X0,inverse(a),X1)
| product(c,identity,X1)
| ~ product(X0,identity,b) ),
inference(resolution,[],[f277,f368]) ).
fof(f626,plain,
! [X0,X1] :
( ~ product(X0,inverse(a),X1)
| product(c,identity,X1)
| ~ product(identity,b,X0) ),
inference(resolution,[],[f277,f424]) ).
fof(f625,plain,
! [X0,X1] :
( ~ product(X0,inverse(X0),X1)
| product(identity,identity,X1) ),
inference(resolution,[],[f277,f4]) ).
fof(f623,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(multiply(X0,X1),identity,X2) ),
inference(resolution,[],[f277,f5]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| product(X3,identity,X2) ),
inference(resolution,[],[f8,f2]) ).
fof(f622,plain,
! [X0] :
( ~ product(X0,inverse(a),identity)
| product(X0,c,d) ),
inference(resolution,[],[f613,f223]) ).
fof(f619,plain,
! [X0] :
( inverse(a) = X0
| ~ product(X0,d,c) ),
inference(resolution,[],[f613,f11]) ).
fof(f618,plain,
! [X0] :
( d = X0
| ~ product(inverse(a),X0,c) ),
inference(resolution,[],[f613,f10]) ).
fof(f617,plain,
! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,inverse(a),X2)
| product(X2,d,X1) ),
inference(resolution,[],[f613,f8]) ).
fof(f616,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,inverse(a))
| ~ product(X1,d,X2)
| product(X0,X2,c) ),
inference(resolution,[],[f613,f7]) ).
fof(f614,plain,
! [X0] :
( ~ product(inverse(a),a,X0)
| product(X0,c,c) ),
inference(resolution,[],[f613,f285]) ).
fof(f613,plain,
product(inverse(a),d,c),
inference(superposition,[],[f5,f609]) ).
fof(f609,plain,
c = multiply(inverse(a),d),
inference(resolution,[],[f582,f3]) ).
fof(f582,plain,
! [X0] :
( ~ product(X0,a,identity)
| c = multiply(X0,d) ),
inference(resolution,[],[f571,f26]) ).
fof(f602,plain,
! [X0,X1] :
( ~ product(X0,b,identity)
| ~ product(X1,X0,identity)
| product(X1,inverse(a),c) ),
inference(resolution,[],[f570,f223]) ).
fof(f600,plain,
! [X0] :
( ~ product(X0,b,identity)
| inverse(a) = multiply(X0,c) ),
inference(resolution,[],[f570,f26]) ).
fof(f599,plain,
! [X0,X1] :
( ~ product(X0,b,identity)
| X0 = X1
| ~ product(X1,c,inverse(a)) ),
inference(resolution,[],[f570,f11]) ).
fof(f598,plain,
! [X0,X1] :
( ~ product(X0,b,identity)
| c = X1
| ~ product(X0,X1,inverse(a)) ),
inference(resolution,[],[f570,f10]) ).
fof(f597,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,b,identity)
| ~ product(X1,inverse(a),X2)
| ~ product(X1,X0,X3)
| product(X3,c,X2) ),
inference(resolution,[],[f570,f8]) ).
fof(f596,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,b,identity)
| ~ product(X1,X2,X0)
| ~ product(X2,c,X3)
| product(X1,X3,inverse(a)) ),
inference(resolution,[],[f570,f7]) ).
fof(f595,plain,
! [X0,X1] :
( ~ product(X0,b,identity)
| inverse(a) = X1
| ~ product(X0,c,X1) ),
inference(resolution,[],[f570,f6]) ).
fof(f593,plain,
! [X0,X1] :
( ~ product(X0,b,identity)
| ~ product(X1,X0,a)
| product(X1,inverse(a),d) ),
inference(resolution,[],[f570,f226]) ).
fof(f592,plain,
! [X0,X1] :
( ~ product(X0,b,identity)
| ~ product(X0,b,X1)
| product(X1,inverse(a),inverse(a)) ),
inference(resolution,[],[f570,f284]) ).
fof(f570,plain,
! [X0] :
( product(X0,c,inverse(a))
| ~ product(X0,b,identity) ),
inference(resolution,[],[f223,f18]) ).
fof(f584,plain,
! [X0,X1] :
( ~ product(X0,a,identity)
| ~ product(X1,X0,identity)
| product(X1,c,d) ),
inference(resolution,[],[f571,f223]) ).
fof(f581,plain,
! [X0,X1] :
( ~ product(X0,a,identity)
| X0 = X1
| ~ product(X1,d,c) ),
inference(resolution,[],[f571,f11]) ).
fof(f580,plain,
! [X0,X1] :
( ~ product(X0,a,identity)
| d = X1
| ~ product(X0,X1,c) ),
inference(resolution,[],[f571,f10]) ).
fof(f579,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,a,identity)
| ~ product(X1,c,X2)
| ~ product(X1,X0,X3)
| product(X3,d,X2) ),
inference(resolution,[],[f571,f8]) ).
fof(f578,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,a,identity)
| ~ product(X1,X2,X0)
| ~ product(X2,d,X3)
| product(X1,X3,c) ),
inference(resolution,[],[f571,f7]) ).
fof(f577,plain,
! [X0,X1] :
( ~ product(X0,a,identity)
| c = X1
| ~ product(X0,d,X1) ),
inference(resolution,[],[f571,f6]) ).
fof(f575,plain,
! [X0,X1] :
( ~ product(X0,a,identity)
| ~ product(X0,a,X1)
| product(X1,c,c) ),
inference(resolution,[],[f571,f285]) ).
fof(f571,plain,
! [X0] :
( product(X0,d,c)
| ~ product(X0,a,identity) ),
inference(resolution,[],[f223,f19]) ).
fof(f573,plain,
! [X0] :
( ~ product(X0,inverse(c),identity)
| product(X0,identity,c) ),
inference(forward_demodulation,[],[f568,f325]) ).
fof(f568,plain,
! [X0] :
( ~ product(X0,multiply(inverse(d),a),identity)
| product(X0,identity,c) ),
inference(resolution,[],[f223,f323]) ).
fof(f567,plain,
! [X0] :
( ~ product(X0,inverse(d),identity)
| product(X0,inverse(c),a) ),
inference(resolution,[],[f223,f337]) ).
fof(f566,plain,
! [X0,X1] :
( ~ product(X0,inverse(X1),identity)
| product(X0,identity,X1) ),
inference(resolution,[],[f223,f3]) ).
fof(f565,plain,
! [X0,X1] :
( ~ product(X0,identity,identity)
| product(X0,X1,X1) ),
inference(resolution,[],[f223,f1]) ).
fof(f564,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,d,d)
| ~ product(X1,a,a) ),
inference(resolution,[],[f223,f234]) ).
fof(f563,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,c,c)
| ~ product(X1,b,b) ),
inference(resolution,[],[f223,f370]) ).
fof(f562,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,d,c)
| ~ product(X1,identity,a) ),
inference(resolution,[],[f223,f232]) ).
fof(f561,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,X2,element_in_O2(X1,X2))
| subgroup_member(X2)
| subgroup_member(X1) ),
inference(resolution,[],[f223,f16]) ).
fof(f560,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,d,multiply(X2,c))
| ~ product(X1,X2,a) ),
inference(resolution,[],[f223,f231]) ).
fof(f559,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,d,inverse(a))
| ~ product(a,b,X1) ),
inference(resolution,[],[f223,f428]) ).
fof(f558,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,c,inverse(a))
| ~ product(X1,identity,b) ),
inference(resolution,[],[f223,f368]) ).
fof(f557,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,c,inverse(a))
| ~ product(identity,b,X1) ),
inference(resolution,[],[f223,f424]) ).
fof(f556,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,identity,inverse(X1)) ),
inference(resolution,[],[f223,f4]) ).
fof(f554,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,identity)
| product(X0,multiply(X1,X2),X2) ),
inference(resolution,[],[f223,f5]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( ~ product(X1,X2,X3)
| ~ product(X0,X1,identity)
| product(X0,X3,X2) ),
inference(resolution,[],[f7,f1]) ).
fof(f335,plain,
! [X0] :
( ~ product(X0,a,inverse(c))
| inverse(d) = X0 ),
inference(superposition,[],[f165,f325]) ).
fof(f404,plain,
! [X0] :
( ~ product(X0,b,b)
| c = multiply(X0,c) ),
inference(resolution,[],[f370,f26]) ).
fof(f307,plain,
! [X0] :
( ~ product(a,X0,a)
| c = multiply(X0,c) ),
inference(resolution,[],[f231,f124]) ).
fof(f305,plain,
! [X0] :
( ~ product(identity,X0,a)
| d = multiply(X0,c) ),
inference(resolution,[],[f231,f30]) ).
fof(f519,plain,
( ~ product(a,b,identity)
| inverse(a) = d ),
inference(resolution,[],[f428,f30]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( ~ product(X1,identity,X3)
| ~ product(X0,X1,X2)
| product(X0,X3,X2) ),
inference(resolution,[],[f7,f2]) ).
fof(f517,plain,
! [X0] :
( ~ product(a,b,X0)
| d = multiply(X0,inverse(a)) ),
inference(resolution,[],[f428,f26]) ).
fof(f516,plain,
! [X0,X1] :
( ~ product(a,b,X0)
| X0 = X1
| ~ product(X1,inverse(a),d) ),
inference(resolution,[],[f428,f11]) ).
fof(f515,plain,
! [X0,X1] :
( ~ product(a,b,X0)
| inverse(a) = X1
| ~ product(X0,X1,d) ),
inference(resolution,[],[f428,f10]) ).
fof(f514,plain,
! [X2,X3,X0,X1] :
( ~ product(a,b,X0)
| ~ product(X1,d,X2)
| ~ product(X1,X0,X3)
| product(X3,inverse(a),X2) ),
inference(resolution,[],[f428,f8]) ).
fof(f513,plain,
! [X2,X3,X0,X1] :
( ~ product(a,b,X0)
| ~ product(X1,X2,X0)
| ~ product(X2,inverse(a),X3)
| product(X1,X3,d) ),
inference(resolution,[],[f428,f7]) ).
fof(f512,plain,
! [X0,X1] :
( ~ product(a,b,X0)
| d = X1
| ~ product(X0,inverse(a),X1) ),
inference(resolution,[],[f428,f6]) ).
fof(f508,plain,
! [X0,X1] :
( ~ product(a,b,X0)
| ~ product(X1,X0,b)
| product(X1,d,c) ),
inference(resolution,[],[f428,f225]) ).
fof(f428,plain,
! [X0] :
( product(X0,inverse(a),d)
| ~ product(a,b,X0) ),
inference(resolution,[],[f284,f19]) ).
fof(f497,plain,
! [X0] :
( ~ product(identity,b,X0)
| c = multiply(X0,inverse(a)) ),
inference(resolution,[],[f424,f26]) ).
fof(f496,plain,
! [X0,X1] :
( ~ product(identity,b,X0)
| X0 = X1
| ~ product(X1,inverse(a),c) ),
inference(resolution,[],[f424,f11]) ).
fof(f495,plain,
! [X0,X1] :
( ~ product(identity,b,X0)
| inverse(a) = X1
| ~ product(X0,X1,c) ),
inference(resolution,[],[f424,f10]) ).
fof(f494,plain,
! [X2,X3,X0,X1] :
( ~ product(identity,b,X0)
| ~ product(X1,c,X2)
| ~ product(X1,X0,X3)
| product(X3,inverse(a),X2) ),
inference(resolution,[],[f424,f8]) ).
fof(f493,plain,
! [X2,X3,X0,X1] :
( ~ product(identity,b,X0)
| ~ product(X1,X2,X0)
| ~ product(X2,inverse(a),X3)
| product(X1,X3,c) ),
inference(resolution,[],[f424,f7]) ).
fof(f492,plain,
! [X0,X1] :
( ~ product(identity,b,X0)
| c = X1
| ~ product(X0,inverse(a),X1) ),
inference(resolution,[],[f424,f6]) ).
fof(f488,plain,
! [X0,X1] :
( ~ product(identity,b,X0)
| ~ product(X1,X0,b)
| product(X1,c,c) ),
inference(resolution,[],[f424,f225]) ).
fof(f424,plain,
! [X0] :
( product(X0,inverse(a),c)
| ~ product(identity,b,X0) ),
inference(resolution,[],[f284,f1]) ).
fof(f440,plain,
( ~ product(c,identity,b)
| identity = inverse(a) ),
inference(resolution,[],[f368,f118]) ).
fof(f474,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| ~ subgroup_member(inverse(multiply(X1,c)))
| ~ product(X0,X1,a) ),
inference(subsumption_resolution,[],[f459,f20]) ).
fof(f459,plain,
! [X0,X1] :
( ~ subgroup_member(X0)
| subgroup_member(d)
| ~ subgroup_member(inverse(multiply(X1,c)))
| ~ product(X0,X1,a) ),
inference(resolution,[],[f61,f231]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| ~ subgroup_member(X1)
| subgroup_member(X2)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[],[f9,f12]) ).
fof(f446,plain,
! [X0,X1] :
( ~ product(X0,identity,b)
| c = X1
| ~ product(X0,inverse(a),X1) ),
inference(resolution,[],[f368,f6]) ).
fof(f445,plain,
! [X0] :
( ~ product(X0,identity,b)
| c = multiply(X0,inverse(a)) ),
inference(resolution,[],[f368,f26]) ).
fof(f444,plain,
! [X0,X1] :
( ~ product(X0,identity,b)
| inverse(a) = X1
| ~ product(X0,X1,c) ),
inference(resolution,[],[f368,f10]) ).
fof(f443,plain,
! [X0,X1] :
( ~ product(X0,identity,b)
| X0 = X1
| ~ product(X1,inverse(a),c) ),
inference(resolution,[],[f368,f11]) ).
fof(f442,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,b)
| ~ product(X1,X2,X0)
| ~ product(X2,inverse(a),X3)
| product(X1,X3,c) ),
inference(resolution,[],[f368,f7]) ).
fof(f441,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,b)
| ~ product(X1,c,X2)
| ~ product(X1,X0,X3)
| product(X3,inverse(a),X2) ),
inference(resolution,[],[f368,f8]) ).
fof(f437,plain,
! [X0,X1] :
( ~ product(X0,identity,b)
| ~ product(X1,X0,b)
| product(X1,c,c) ),
inference(resolution,[],[f368,f225]) ).
fof(f368,plain,
! [X0] :
( product(X0,inverse(a),c)
| ~ product(X0,identity,b) ),
inference(resolution,[],[f225,f1]) ).
fof(f429,plain,
! [X0] :
( ~ product(inverse(c),b,X0)
| product(X0,inverse(a),identity) ),
inference(forward_demodulation,[],[f426,f325]) ).
fof(f426,plain,
! [X0] :
( ~ product(multiply(inverse(d),a),b,X0)
| product(X0,inverse(a),identity) ),
inference(resolution,[],[f284,f323]) ).
fof(f425,plain,
! [X0] :
( ~ product(inverse(c),b,X0)
| product(X0,inverse(a),identity) ),
inference(resolution,[],[f284,f3]) ).
fof(f423,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| product(X1,inverse(a),multiply(X0,c)) ),
inference(resolution,[],[f284,f5]) ).
fof(f422,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| product(X1,inverse(a),c)
| ~ product(X0,b,b) ),
inference(resolution,[],[f284,f370]) ).
fof(f421,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| product(X1,inverse(a),d)
| ~ product(X0,identity,a) ),
inference(resolution,[],[f284,f232]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ product(X0,c,X1)
| ~ product(X0,b,X2)
| product(X2,inverse(a),X1) ),
inference(resolution,[],[f8,f18]) ).
fof(f408,plain,
( ~ product(b,b,b)
| inverse(a) = c ),
inference(resolution,[],[f370,f123]) ).
fof(f405,plain,
! [X0,X1] :
( ~ product(X0,b,b)
| c = X1
| ~ product(X0,c,X1) ),
inference(resolution,[],[f370,f6]) ).
fof(f403,plain,
! [X0,X1] :
( ~ product(X0,b,b)
| c = X1
| ~ product(X0,X1,c) ),
inference(resolution,[],[f370,f10]) ).
fof(f402,plain,
! [X0,X1] :
( ~ product(X0,b,b)
| X0 = X1
| ~ product(X1,c,c) ),
inference(resolution,[],[f370,f11]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,b,b)
| ~ product(X1,X2,X0)
| ~ product(X2,c,X3)
| product(X1,X3,c) ),
inference(resolution,[],[f370,f7]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,b,b)
| ~ product(X1,c,X2)
| ~ product(X1,X0,X3)
| product(X3,c,X2) ),
inference(resolution,[],[f370,f8]) ).
fof(f397,plain,
! [X0,X1] :
( ~ product(X0,b,b)
| ~ product(X1,X0,a)
| product(X1,c,d) ),
inference(resolution,[],[f370,f226]) ).
fof(f370,plain,
! [X0] :
( product(X0,c,c)
| ~ product(X0,b,b) ),
inference(resolution,[],[f225,f18]) ).
fof(f366,plain,
! [X0] :
( ~ product(X0,a,b)
| product(X0,identity,c) ),
inference(resolution,[],[f225,f4]) ).
fof(f371,plain,
! [X0] :
( ~ product(X0,a,b)
| product(X0,identity,c) ),
inference(forward_demodulation,[],[f369,f12]) ).
fof(f369,plain,
! [X0] :
( ~ product(X0,inverse(inverse(a)),b)
| product(X0,identity,c) ),
inference(resolution,[],[f225,f3]) ).
fof(f367,plain,
! [X0,X1] :
( ~ product(X0,X1,b)
| product(X0,multiply(X1,inverse(a)),c) ),
inference(resolution,[],[f225,f5]) ).
fof(f225,plain,
! [X2,X0,X1] :
( ~ product(X1,inverse(a),X2)
| ~ product(X0,X1,b)
| product(X0,X2,c) ),
inference(resolution,[],[f7,f18]) ).
fof(f298,plain,
! [X0] :
( ~ product(d,X0,a)
| identity = multiply(X0,c) ),
inference(resolution,[],[f231,f118]) ).
fof(f344,plain,
! [X0] :
( inverse(c) = X0
| ~ product(inverse(d),a,X0) ),
inference(resolution,[],[f337,f6]) ).
fof(f342,plain,
! [X0] :
( a = X0
| ~ product(inverse(d),X0,inverse(c)) ),
inference(resolution,[],[f337,f10]) ).
fof(f341,plain,
! [X0] :
( inverse(d) = X0
| ~ product(X0,a,inverse(c)) ),
inference(resolution,[],[f337,f11]) ).
fof(f340,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,inverse(d))
| ~ product(X1,a,X2)
| product(X0,X2,inverse(c)) ),
inference(resolution,[],[f337,f7]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ product(X0,inverse(c),X1)
| ~ product(X0,inverse(d),X2)
| product(X2,a,X1) ),
inference(resolution,[],[f337,f8]) ).
fof(f337,plain,
product(inverse(d),a,inverse(c)),
inference(superposition,[],[f5,f325]) ).
fof(f336,plain,
! [X0] :
( ~ product(inverse(d),X0,inverse(c))
| a = X0 ),
inference(superposition,[],[f117,f325]) ).
fof(f334,plain,
( subgroup_member(inverse(c))
| ~ subgroup_member(inverse(d))
| ~ subgroup_member(inverse(a)) ),
inference(superposition,[],[f108,f325]) ).
fof(f325,plain,
inverse(c) = multiply(inverse(d),a),
inference(resolution,[],[f323,f170]) ).
fof(f332,plain,
! [X0] :
( identity = X0
| ~ product(multiply(inverse(d),a),c,X0) ),
inference(resolution,[],[f323,f6]) ).
fof(f331,plain,
identity = multiply(multiply(inverse(d),a),c),
inference(resolution,[],[f323,f26]) ).
fof(f330,plain,
! [X0] :
( c = X0
| ~ product(multiply(inverse(d),a),X0,identity) ),
inference(resolution,[],[f323,f10]) ).
fof(f329,plain,
! [X0] :
( multiply(inverse(d),a) = X0
| ~ product(X0,c,identity) ),
inference(resolution,[],[f323,f11]) ).
fof(f328,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,multiply(inverse(d),a))
| ~ product(X1,c,X2)
| product(X0,X2,identity) ),
inference(resolution,[],[f323,f7]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ~ product(X0,identity,X1)
| ~ product(X0,multiply(inverse(d),a),X2)
| product(X2,c,X1) ),
inference(resolution,[],[f323,f8]) ).
fof(f326,plain,
c = inverse(multiply(inverse(d),a)),
inference(resolution,[],[f323,f119]) ).
fof(f324,plain,
! [X0] :
( ~ product(X0,multiply(inverse(d),a),a)
| product(X0,identity,d) ),
inference(resolution,[],[f323,f226]) ).
fof(f323,plain,
product(multiply(inverse(d),a),c,identity),
inference(resolution,[],[f319,f5]) ).
fof(f319,plain,
! [X0] :
( ~ product(inverse(d),a,X0)
| product(X0,c,identity) ),
inference(resolution,[],[f285,f3]) ).
fof(f318,plain,
! [X0] :
( ~ product(identity,a,X0)
| product(X0,c,d) ),
inference(resolution,[],[f285,f1]) ).
fof(f317,plain,
! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,c,multiply(X0,d)) ),
inference(resolution,[],[f285,f5]) ).
fof(f316,plain,
! [X0,X1] :
( ~ product(X0,a,X1)
| product(X1,c,d)
| ~ product(X0,a,a) ),
inference(resolution,[],[f285,f234]) ).
fof(f285,plain,
! [X2,X0,X1] :
( ~ product(X0,d,X1)
| ~ product(X0,a,X2)
| product(X2,c,X1) ),
inference(resolution,[],[f8,f19]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,a)
| d = X2
| ~ product(X0,multiply(X1,c),X2) ),
inference(resolution,[],[f231,f6]) ).
fof(f303,plain,
! [X0,X1] :
( ~ product(X0,X1,a)
| d = multiply(X0,multiply(X1,c)) ),
inference(resolution,[],[f231,f26]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,a)
| multiply(X1,c) = X2
| ~ product(X0,X2,d) ),
inference(resolution,[],[f231,f10]) ).
fof(f301,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,a)
| X0 = X2
| ~ product(X2,multiply(X1,c),d) ),
inference(resolution,[],[f231,f11]) ).
fof(f300,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,a)
| ~ product(X2,X3,X0)
| ~ product(X3,multiply(X1,c),X4)
| product(X2,X4,d) ),
inference(resolution,[],[f231,f7]) ).
fof(f299,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,a)
| ~ product(X2,d,X3)
| ~ product(X2,X0,X4)
| product(X4,multiply(X1,c),X3) ),
inference(resolution,[],[f231,f8]) ).
fof(f231,plain,
! [X0,X1] :
( product(X0,multiply(X1,c),d)
| ~ product(X0,X1,a) ),
inference(resolution,[],[f226,f5]) ).
fof(f270,plain,
! [X0] :
( ~ product(X0,a,a)
| d = multiply(X0,d) ),
inference(resolution,[],[f234,f26]) ).
fof(f241,plain,
! [X0] :
( ~ product(X0,identity,a)
| d = multiply(X0,c) ),
inference(resolution,[],[f232,f26]) ).
fof(f233,plain,
! [X0] :
( ~ product(X0,inverse(c),a)
| product(X0,identity,d) ),
inference(resolution,[],[f226,f3]) ).
fof(f244,plain,
( ~ product(inverse(c),identity,a)
| identity = d ),
inference(resolution,[],[f232,f31]) ).
fof(f283,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,X1)
| ~ product(X0,inverse(X2),X3)
| product(X3,X2,X1) ),
inference(resolution,[],[f8,f3]) ).
fof(f281,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,d,X1)
| ~ product(X0,X2,X3)
| product(X3,d,X1)
| ~ product(X2,a,a) ),
inference(resolution,[],[f8,f234]) ).
fof(f280,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,d,X1)
| ~ product(X0,X2,X3)
| product(X3,c,X1)
| ~ product(X2,identity,a) ),
inference(resolution,[],[f8,f232]) ).
fof(f279,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| product(X4,element_in_O2(X3,X1),X2)
| subgroup_member(X1)
| subgroup_member(X3) ),
inference(resolution,[],[f8,f16]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,X1)
| ~ product(X0,X2,X3)
| product(X3,inverse(X2),X1) ),
inference(resolution,[],[f8,f4]) ).
fof(f276,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,multiply(X1,X2),X3)
| ~ product(X0,X1,X4)
| product(X4,X2,X3) ),
inference(resolution,[],[f8,f5]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X1,X2,X5)
| ~ product(X0,X5,X3)
| ~ product(X0,X1,X4)
| product(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f273,plain,
( ~ product(inverse(d),a,a)
| identity = d ),
inference(resolution,[],[f234,f31]) ).
fof(f271,plain,
! [X0,X1] :
( ~ product(X0,a,a)
| d = X1
| ~ product(X0,d,X1) ),
inference(resolution,[],[f234,f6]) ).
fof(f269,plain,
! [X0,X1] :
( ~ product(X0,a,a)
| d = X1
| ~ product(X0,X1,d) ),
inference(resolution,[],[f234,f10]) ).
fof(f268,plain,
! [X0,X1] :
( ~ product(X0,a,a)
| X0 = X1
| ~ product(X1,d,d) ),
inference(resolution,[],[f234,f11]) ).
fof(f267,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,a,a)
| ~ product(X1,X2,X0)
| ~ product(X2,d,X3)
| product(X1,X3,d) ),
inference(resolution,[],[f234,f7]) ).
fof(f234,plain,
! [X0] :
( product(X0,d,d)
| ~ product(X0,a,a) ),
inference(resolution,[],[f226,f19]) ).
fof(f243,plain,
( ~ product(identity,identity,a)
| c = d ),
inference(resolution,[],[f232,f30]) ).
fof(f237,plain,
( ~ product(d,identity,a)
| identity = c ),
inference(resolution,[],[f232,f118]) ).
fof(f242,plain,
! [X0,X1] :
( ~ product(X0,identity,a)
| d = X1
| ~ product(X0,c,X1) ),
inference(resolution,[],[f232,f6]) ).
fof(f240,plain,
! [X0,X1] :
( ~ product(X0,identity,a)
| c = X1
| ~ product(X0,X1,d) ),
inference(resolution,[],[f232,f10]) ).
fof(f239,plain,
! [X0,X1] :
( ~ product(X0,identity,a)
| X0 = X1
| ~ product(X1,c,d) ),
inference(resolution,[],[f232,f11]) ).
fof(f238,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,identity,a)
| ~ product(X1,X2,X0)
| ~ product(X2,c,X3)
| product(X1,X3,d) ),
inference(resolution,[],[f232,f7]) ).
fof(f236,plain,
! [X0,X1] :
( ~ product(X0,identity,a)
| ~ product(X1,X0,a)
| product(X1,d,d) ),
inference(resolution,[],[f232,f226]) ).
fof(f232,plain,
! [X0] :
( product(X0,c,d)
| ~ product(X0,identity,a) ),
inference(resolution,[],[f226,f1]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ product(X1,c,X2)
| ~ product(X0,X1,a)
| product(X0,X2,d) ),
inference(resolution,[],[f7,f19]) ).
fof(f213,plain,
identity = element_in_O2(inverse(d),inverse(d)),
inference(resolution,[],[f144,f20]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,inverse(X2))
| ~ product(X1,X2,X3)
| product(X0,X3,identity) ),
inference(resolution,[],[f7,f3]) ).
fof(f222,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ product(X1,element_in_O2(X2,X3),X4)
| product(X0,X4,X3)
| subgroup_member(X3)
| subgroup_member(X2) ),
inference(resolution,[],[f7,f16]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X1,inverse(X2),X3)
| product(X0,X3,identity) ),
inference(resolution,[],[f7,f4]) ).
fof(f219,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| product(X0,X4,multiply(X2,X3)) ),
inference(resolution,[],[f7,f5]) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| ~ product(X1,X2,X5)
| product(X0,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f144,plain,
! [X0] :
( subgroup_member(X0)
| identity = element_in_O2(inverse(X0),inverse(X0)) ),
inference(resolution,[],[f143,f23]) ).
fof(f108,plain,
! [X0,X1] :
( subgroup_member(multiply(X1,X0))
| ~ subgroup_member(X1)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[],[f57,f12]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ product(X0,X2,multiply(X1,X2))
| X0 = X1 ),
inference(resolution,[],[f11,f5]) ).
fof(f188,plain,
! [X0,X1] :
( element_in_O2(X0,multiply(X0,X1)) = X1
| subgroup_member(multiply(X0,X1))
| subgroup_member(X0) ),
inference(resolution,[],[f117,f16]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,multiply(X2,X1))
| X0 = X1 ),
inference(resolution,[],[f10,f5]) ).
fof(f170,plain,
! [X0,X1] :
( ~ product(X0,X1,identity)
| inverse(X1) = X0 ),
inference(resolution,[],[f11,f3]) ).
fof(f180,plain,
! [X0,X1] :
( ~ product(X1,X0,identity)
| inverse(X0) = X1 ),
inference(superposition,[],[f167,f12]) ).
fof(f167,plain,
! [X0,X1] :
( ~ product(X0,inverse(X1),identity)
| X0 = X1 ),
inference(resolution,[],[f11,f4]) ).
fof(f169,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| identity = X0 ),
inference(resolution,[],[f11,f1]) ).
fof(f171,plain,
! [X0] :
( ~ product(X0,inverse(a),c)
| b = X0 ),
inference(resolution,[],[f11,f18]) ).
fof(f172,plain,
! [X0] :
( ~ product(X0,c,d)
| a = X0 ),
inference(resolution,[],[f11,f19]) ).
fof(f168,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ product(X0,element_in_O2(X1,X2),X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
inference(resolution,[],[f11,f16]) ).
fof(f11,axiom,
! [X8,X6,X9,X7] :
( ~ product(X9,X7,X8)
| X6 = X9
| ~ product(X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f122,plain,
! [X0,X1] :
( ~ product(inverse(X1),X0,identity)
| X0 = X1 ),
inference(resolution,[],[f10,f3]) ).
fof(f119,plain,
! [X0,X1] :
( ~ product(X1,X0,identity)
| inverse(X1) = X0 ),
inference(resolution,[],[f10,f4]) ).
fof(f146,plain,
identity = element_in_O2(d,d),
inference(resolution,[],[f143,f20]) ).
fof(f143,plain,
! [X0] :
( subgroup_member(X0)
| identity = element_in_O2(X0,X0) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f141,plain,
! [X0] :
( identity = element_in_O2(X0,X0)
| subgroup_member(X0)
| subgroup_member(X0) ),
inference(resolution,[],[f118,f16]) ).
fof(f118,plain,
! [X0,X1] :
( ~ product(X1,X0,X1)
| identity = X0 ),
inference(resolution,[],[f10,f2]) ).
fof(f123,plain,
! [X0] :
( ~ product(b,X0,c)
| inverse(a) = X0 ),
inference(resolution,[],[f10,f18]) ).
fof(f124,plain,
! [X0] :
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[],[f10,f19]) ).
fof(f120,plain,
! [X2,X0,X1] :
( element_in_O2(X1,X2) = X0
| ~ product(X1,X0,X2)
| subgroup_member(X2)
| subgroup_member(X1) ),
inference(resolution,[],[f10,f16]) ).
fof(f10,axiom,
! [X8,X6,X9,X7] :
( ~ product(X6,X9,X8)
| X7 = X9
| ~ product(X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f57,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,inverse(X1)))
| ~ subgroup_member(X0)
| ~ subgroup_member(X1) ),
inference(resolution,[],[f9,f5]) ).
fof(f103,plain,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
inference(resolution,[],[f26,f16]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ product(X1,X2,X0)
| multiply(X1,X2) = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f65,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| ~ subgroup_member(X0)
| subgroup_member(X1) ),
inference(subsumption_resolution,[],[f62,f13]) ).
fof(f62,plain,
! [X0,X1] :
( ~ product(X0,identity,X1)
| ~ subgroup_member(X0)
| subgroup_member(X1)
| ~ subgroup_member(identity) ),
inference(superposition,[],[f9,f43]) ).
fof(f31,plain,
! [X0,X1] :
( ~ product(inverse(X1),X1,X0)
| identity = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f80,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(superposition,[],[f76,f12]) ).
fof(f76,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(resolution,[],[f28,f5]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(inverse(X0),X0,X1)
| identity = X1 ),
inference(superposition,[],[f28,f12]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| identity = X0 ),
inference(resolution,[],[f6,f4]) ).
fof(f64,plain,
( subgroup_member(c)
| ~ subgroup_member(a) ),
inference(subsumption_resolution,[],[f60,f17]) ).
fof(f60,plain,
( ~ subgroup_member(b)
| subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolution,[],[f9,f18]) ).
fof(f9,axiom,
! [X8,X6,X7] :
( ~ product(X6,inverse(X7),X8)
| ~ subgroup_member(X6)
| subgroup_member(X8)
| ~ subgroup_member(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_product_and_inverse) ).
fof(f51,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[],[f30,f5]) ).
fof(f30,plain,
! [X0,X1] :
( ~ product(identity,X1,X0)
| X0 = X1 ),
inference(resolution,[],[f6,f1]) ).
fof(f41,plain,
! [X0] : multiply(X0,identity) = X0,
inference(resolution,[],[f27,f5]) ).
fof(f43,plain,
identity = inverse(identity),
inference(resolution,[],[f27,f3]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(X1,identity,X0)
| X0 = X1 ),
inference(resolution,[],[f6,f2]) ).
fof(f38,plain,
c = multiply(b,inverse(a)),
inference(resolution,[],[f32,f5]) ).
fof(f32,plain,
! [X0] :
( ~ product(b,inverse(a),X0)
| c = X0 ),
inference(resolution,[],[f6,f18]) ).
fof(f35,plain,
d = multiply(a,c),
inference(resolution,[],[f33,f5]) ).
fof(f33,plain,
! [X0] :
( ~ product(a,c,X0)
| d = X0 ),
inference(resolution,[],[f6,f19]) ).
fof(f29,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ product(X2,element_in_O2(X2,X1),X0)
| subgroup_member(X1)
| subgroup_member(X2) ),
inference(resolution,[],[f6,f16]) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| X2 = X3
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f16,axiom,
! [X6,X7] :
( product(X6,element_in_O2(X6,X7),X7)
| subgroup_member(X7)
| subgroup_member(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f15,axiom,
! [X6,X7] :
( subgroup_member(element_in_O2(X6,X7))
| subgroup_member(X7)
| subgroup_member(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f5,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
fof(f23,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(superposition,[],[f14,f12]) ).
fof(f12,axiom,
! [X6] : inverse(inverse(X6)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f18,axiom,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f19,axiom,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f13,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_in_subgroup) ).
fof(f20,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
fof(f17,axiom,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f749,plain,
( ~ spl0_1
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f748]) ).
fof(f748,plain,
( $false
| ~ spl0_1
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526,f738,f739,f740,f741,f742,f475,f743,f744,f745,f746,f127,f747,f68]) ).
fof(f747,plain,
( c = element_in_O2(a,d)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526,f738,f739,f740,f741,f742,f475,f743,f744,f745,f746,f127]) ).
fof(f746,plain,
( ~ subgroup_member(a)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526,f738,f739,f740,f741,f742,f475,f743,f744,f745]) ).
fof(f744,plain,
( identity = multiply(element_in_O2(d,a),c)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526,f738,f739,f740,f741,f742,f475,f743]) ).
fof(f742,plain,
( ~ subgroup_member(a)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526,f738,f739,f740,f741]) ).
fof(f740,plain,
( ~ subgroup_member(a)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526,f738,f739]) ).
fof(f738,plain,
( ~ subgroup_member(a)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549,f737,f526]) ).
fof(f737,plain,
( c = multiply(element_in_O2(a,a),c)
| spl0_17 ),
inference(global_subsumption,[],[f17,f20,f13,f19,f18,f1,f2,f3,f4,f12,f14,f23,f5,f15,f16,f6,f29,f33,f35,f32,f38,f27,f43,f41,f30,f51,f9,f64,f28,f78,f76,f80,f31,f65,f26,f103,f57,f10,f120,f124,f123,f118,f143,f146,f119,f122,f11,f168,f172,f171,f169,f167,f180,f170,f117,f188,f165,f108,f144,f7,f219,f221,f222,f224,f213,f226,f232,f236,f238,f239,f240,f242,f237,f243,f234,f267,f268,f269,f271,f273,f8,f276,f278,f279,f280,f281,f283,f244,f233,f241,f270,f231,f299,f300,f301,f302,f303,f304,f285,f316,f317,f318,f319,f323,f324,f326,f327,f328,f329,f330,f331,f332,f325,f334,f336,f337,f339,f340,f341,f342,f344,f298,f225,f367,f371,f366,f370,f397,f400,f401,f402,f403,f405,f408,f284,f421,f422,f423,f425,f429,f368,f437,f441,f442,f443,f444,f445,f446,f61,f474,f440,f424,f488,f492,f493,f494,f495,f496,f497,f428,f508,f512,f513,f514,f515,f516,f517,f220,f519,f305,f307,f404,f335,f223,f554,f556,f557,f558,f559,f560,f561,f562,f563,f564,f565,f566,f567,f573,f571,f575,f577,f578,f579,f580,f581,f584,f570,f592,f593,f595,f596,f597,f598,f599,f600,f602,f582,f609,f613,f614,f616,f617,f618,f619,f622,f277,f623,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f645,f643,f650,f654,f657,f658,f659,f660,f661,f664,f665,f668,f667,f611,f612,f282,f700,f615,f642,f716,f727,f728,f725,f736,f549]) ).
fof(f736,plain,
( ! [X0] :
( ~ product(X0,b,identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(c)) )
| spl0_17 ),
inference(subsumption_resolution,[],[f601,f716]) ).
fof(f601,plain,
! [X0] :
( ~ product(X0,b,identity)
| ~ subgroup_member(X0)
| subgroup_member(inverse(a))
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[],[f570,f61]) ).
fof(f725,plain,
( ~ subgroup_member(a)
| spl0_17 ),
inference(resolution,[],[f716,f14]) ).
fof(f728,plain,
( identity = element_in_O2(a,a)
| spl0_17 ),
inference(forward_demodulation,[],[f726,f12]) ).
fof(f726,plain,
( identity = element_in_O2(inverse(inverse(a)),inverse(inverse(a)))
| spl0_17 ),
inference(resolution,[],[f716,f144]) ).
fof(f727,plain,
( identity = element_in_O2(inverse(a),inverse(a))
| spl0_17 ),
inference(resolution,[],[f716,f143]) ).
fof(f716,plain,
( ~ subgroup_member(inverse(a))
| spl0_17 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f715,plain,
( spl0_17
<=> subgroup_member(inverse(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f734,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f733]) ).
fof(f733,plain,
( $false
| ~ spl0_18 ),
inference(subsumption_resolution,[],[f730,f17]) ).
fof(f730,plain,
( ~ subgroup_member(b)
| ~ spl0_18 ),
inference(resolution,[],[f729,f14]) ).
fof(f729,plain,
( ~ subgroup_member(inverse(b))
| ~ spl0_18 ),
inference(resolution,[],[f720,f3]) ).
fof(f720,plain,
( ! [X0] :
( ~ product(X0,b,identity)
| ~ subgroup_member(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f719,plain,
( spl0_18
<=> ! [X0] :
( ~ product(X0,b,identity)
| ~ subgroup_member(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f724,plain,
( spl0_1
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f723]) ).
fof(f723,plain,
( $false
| spl0_1
| ~ spl0_17 ),
inference(subsumption_resolution,[],[f722,f69]) ).
fof(f69,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f722,plain,
( subgroup_member(a)
| ~ spl0_17 ),
inference(resolution,[],[f717,f23]) ).
fof(f717,plain,
( subgroup_member(inverse(a))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f721,plain,
( spl0_17
| spl0_18
| spl0_1 ),
inference(avatar_split_clause,[],[f607,f67,f719,f715]) ).
fof(f607,plain,
( ! [X0] :
( ~ product(X0,b,identity)
| ~ subgroup_member(X0)
| subgroup_member(inverse(a)) )
| spl0_1 ),
inference(subsumption_resolution,[],[f601,f380]) ).
fof(f380,plain,
( subgroup_member(inverse(c))
| spl0_1 ),
inference(subsumption_resolution,[],[f379,f20]) ).
fof(f379,plain,
( subgroup_member(inverse(c))
| subgroup_member(d)
| spl0_1 ),
inference(subsumption_resolution,[],[f376,f69]) ).
fof(f376,plain,
( subgroup_member(inverse(c))
| subgroup_member(a)
| subgroup_member(d)
| spl0_1 ),
inference(superposition,[],[f15,f358]) ).
fof(f358,plain,
( inverse(c) = element_in_O2(d,a)
| spl0_1 ),
inference(resolution,[],[f355,f170]) ).
fof(f355,plain,
( product(element_in_O2(d,a),c,identity)
| spl0_1 ),
inference(superposition,[],[f5,f349]) ).
fof(f349,plain,
( identity = multiply(element_in_O2(d,a),c)
| spl0_1 ),
inference(subsumption_resolution,[],[f348,f20]) ).
fof(f348,plain,
( identity = multiply(element_in_O2(d,a),c)
| subgroup_member(d)
| spl0_1 ),
inference(subsumption_resolution,[],[f347,f69]) ).
fof(f684,plain,
( spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f667,f681,f677]) ).
fof(f677,plain,
( spl0_15
<=> identity = inverse(d) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f681,plain,
( spl0_16
<=> product(a,c,identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f544,plain,
( spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f519,f541,f537]) ).
fof(f537,plain,
( spl0_13
<=> inverse(a) = d ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f541,plain,
( spl0_14
<=> product(a,b,identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f486,plain,
( spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f440,f483,f479]) ).
fof(f479,plain,
( spl0_11
<=> identity = inverse(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f483,plain,
( spl0_12
<=> product(c,identity,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f420,plain,
( spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f408,f417,f413]) ).
fof(f413,plain,
( spl0_9
<=> inverse(a) = c ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f417,plain,
( spl0_10
<=> product(b,b,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f294,plain,
( spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f244,f291,f287]) ).
fof(f287,plain,
( spl0_7
<=> identity = d ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f291,plain,
( spl0_8
<=> product(inverse(c),identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f264,plain,
( spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f243,f261,f257]) ).
fof(f257,plain,
( spl0_5
<=> c = d ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f261,plain,
( spl0_6
<=> product(identity,identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f255,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f237,f252,f248]) ).
fof(f248,plain,
( spl0_3
<=> identity = c ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f252,plain,
( spl0_4
<=> product(d,identity,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f134,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f133,plain,
( $false
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[],[f132,f69]) ).
fof(f132,plain,
( subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[],[f131,f20]) ).
fof(f131,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[],[f130,f72]) ).
fof(f72,plain,
( ~ subgroup_member(c)
| spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f130,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_1 ),
inference(superposition,[],[f15,f128]) ).
fof(f128,plain,
( c = element_in_O2(a,d)
| spl0_1 ),
inference(subsumption_resolution,[],[f127,f69]) ).
fof(f74,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f64,f71,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP039-3 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 20:44:22 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % (14322)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (14328)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.35 % (14324)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (14325)WARNING: value z3 for option sas not known
% 0.12/0.35 % (14327)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.35 % (14329)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.35 % (14326)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (14325)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.36 TRYING [3]
% 0.12/0.36 % (14323)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.36 TRYING [4]
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [2]
% 0.18/0.37 TRYING [3]
% 0.18/0.37 TRYING [5]
% 0.18/0.38 % (14325)First to succeed.
% 0.18/0.39 % (14325)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14322"
% 0.18/0.39 % (14325)Refutation found. Thanks to Tanya!
% 0.18/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.39 % (14325)------------------------------
% 0.18/0.39 % (14325)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.39 % (14325)Termination reason: Refutation
% 0.18/0.39
% 0.18/0.39 % (14325)Memory used [KB]: 1217
% 0.18/0.39 % (14325)Time elapsed: 0.034 s
% 0.18/0.39 % (14325)Instructions burned: 62 (million)
% 0.18/0.39 % (14322)Success in time 0.049 s
%------------------------------------------------------------------------------