TSTP Solution File: GRP025-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP025-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 : Tue Apr 30 11:50:30 EDT 2024
% Result : Unsatisfiable 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 340 ( 28 unt; 0 def)
% Number of atoms : 1163 ( 111 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 1620 ( 797 ~; 813 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 94 ( 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f606,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f62,f86,f117,f132,f180,f182,f184,f186,f188,f190,f192,f194,f196,f199,f201,f203,f205,f208,f220,f241,f247,f249,f252,f254,f259,f262,f265,f270,f272,f276,f279,f281,f283,f286,f288,f290,f292,f294,f296,f298,f300,f302,f304,f306,f308,f310,f312,f314,f355,f357,f361,f368,f381,f385,f387,f390,f452,f514,f532,f572,f605]) ).
fof(f605,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f604]) ).
fof(f604,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5
| spl0_6 ),
inference(subsumption_resolution,[],[f600,f106]) ).
fof(f106,plain,
( a != b
| ~ spl0_5
| spl0_6 ),
inference(forward_demodulation,[],[f84,f81]) ).
fof(f81,plain,
( a = d3
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f79,plain,
( spl0_5
<=> a = d3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f84,plain,
( b != d3
| spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f83,plain,
( spl0_6
<=> b = d3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f600,plain,
( a = b
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f588,f143]) ).
fof(f143,plain,
! [X0] :
( ~ product(g1,a,b,X0)
| b = X0 ),
inference(resolution,[],[f9,f19]) ).
fof(f19,axiom,
product(g1,a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2,X4)
| X3 = X4
| ~ product(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f588,plain,
( product(g1,a,b,a)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f587,f43]) ).
fof(f43,plain,
( a = d1
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f41,plain,
( spl0_1
<=> a = d1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f587,plain,
( product(g1,d1,b,a)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f585,f61]) ).
fof(f61,plain,
( b = d2
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f59,plain,
( spl0_4
<=> b = d2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f585,plain,
( product(g1,d1,d2,a)
| ~ spl0_5 ),
inference(superposition,[],[f31,f81]) ).
fof(f31,axiom,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
fof(f572,plain,
( ~ spl0_1
| ~ spl0_3
| spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f571]) ).
fof(f571,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| spl0_4
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f567,f73]) ).
fof(f73,plain,
( a != b
| ~ spl0_3
| spl0_4 ),
inference(forward_demodulation,[],[f60,f57]) ).
fof(f57,plain,
( a = d2
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f55,plain,
( spl0_3
<=> a = d2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f60,plain,
( b != d2
| spl0_4 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f567,plain,
( a = b
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(resolution,[],[f548,f142]) ).
fof(f142,plain,
! [X0] :
( ~ product(g1,a,a,X0)
| a = X0 ),
inference(resolution,[],[f9,f18]) ).
fof(f18,axiom,
product(g1,a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
fof(f548,plain,
( product(g1,a,a,b)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f547,f43]) ).
fof(f547,plain,
( product(g1,d1,a,b)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f545,f85]) ).
fof(f85,plain,
( b = d3
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f545,plain,
( product(g1,d1,a,d3)
| ~ spl0_3 ),
inference(superposition,[],[f31,f57]) ).
fof(f532,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f531]) ).
fof(f531,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f530,f23]) ).
fof(f23,axiom,
product(g2,c,d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_d_is_d) ).
fof(f530,plain,
( ~ product(g2,c,d,d)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f529,f26]) ).
fof(f26,axiom,
c = an_isomorphism(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_c) ).
fof(f529,plain,
( ~ product(g2,an_isomorphism(a),d,d)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f528,f27]) ).
fof(f27,axiom,
d = an_isomorphism(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_d) ).
fof(f528,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(b),d)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f527,f61]) ).
fof(f527,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),d)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f526,f27]) ).
fof(f526,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f523,f85]) ).
fof(f523,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_1 ),
inference(superposition,[],[f32,f43]) ).
fof(f32,axiom,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
fof(f514,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f513]) ).
fof(f513,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f510,f49]) ).
fof(f49,plain,
( a != b
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f42,f47]) ).
fof(f47,plain,
( b = d1
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f45,plain,
( spl0_2
<=> b = d1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f42,plain,
( a != d1
| spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f510,plain,
( a = b
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(resolution,[],[f148,f403]) ).
fof(f403,plain,
( product(g1,b,b,b)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f402,f47]) ).
fof(f402,plain,
( product(g1,d1,b,b)
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f397,f85]) ).
fof(f397,plain,
( product(g1,d1,b,d3)
| ~ spl0_4 ),
inference(superposition,[],[f31,f61]) ).
fof(f148,plain,
! [X0] :
( ~ product(g1,b,b,X0)
| a = X0 ),
inference(resolution,[],[f9,f21]) ).
fof(f21,axiom,
product(g1,b,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_a) ).
fof(f452,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f451,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_8 ),
inference(subsumption_resolution,[],[f448,f49]) ).
fof(f448,plain,
( a = b
| ~ spl0_8 ),
inference(resolution,[],[f438,f143]) ).
fof(f438,plain,
( ! [X0] : product(g1,X0,b,X0)
| ~ spl0_8 ),
inference(superposition,[],[f3,f116]) ).
fof(f116,plain,
( b = identity_for(g1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f114,plain,
( spl0_8
<=> b = identity_for(g1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f390,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f389,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(global_subsumption,[],[f388,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f7,f327,f332,f334,f336,f80,f85,f342]) ).
fof(f342,plain,
( a != b
| spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f80,f85]) ).
fof(f80,plain,
( a != d3
| spl0_5 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f336,plain,
b = multiply(g1,b,a),
inference(subsumption_resolution,[],[f335,f13]) ).
fof(f335,plain,
( ~ group_member(b,g1)
| b = multiply(g1,b,a) ),
inference(subsumption_resolution,[],[f330,f12]) ).
fof(f330,plain,
( ~ group_member(a,g1)
| ~ group_member(b,g1)
| b = multiply(g1,b,a) ),
inference(resolution,[],[f7,f145]) ).
fof(f334,plain,
b = multiply(g1,a,b),
inference(subsumption_resolution,[],[f333,f12]) ).
fof(f333,plain,
( ~ group_member(a,g1)
| b = multiply(g1,a,b) ),
inference(subsumption_resolution,[],[f329,f13]) ).
fof(f329,plain,
( ~ group_member(b,g1)
| ~ group_member(a,g1)
| b = multiply(g1,a,b) ),
inference(resolution,[],[f7,f143]) ).
fof(f332,plain,
a = multiply(g1,a,a),
inference(subsumption_resolution,[],[f331,f12]) ).
fof(f331,plain,
( ~ group_member(a,g1)
| a = multiply(g1,a,a) ),
inference(duplicate_literal_removal,[],[f328]) ).
fof(f328,plain,
( ~ group_member(a,g1)
| ~ group_member(a,g1)
| a = multiply(g1,a,a) ),
inference(resolution,[],[f7,f142]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ group_member(X0,X1)
| ~ group_member(X2,X1)
| multiply(X1,X2,X0) = X3
| ~ product(X1,X2,X0,X3) ),
inference(resolution,[],[f7,f9]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( product(X0,X1,X2,multiply(X0,X1,X2))
| ~ group_member(X2,X0)
| ~ group_member(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_1) ).
fof(f211,plain,
( a = b
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f47,f43]) ).
fof(f210,plain,
( a = b
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f43,f47]) ).
fof(f145,plain,
! [X0] :
( ~ product(g1,b,a,X0)
| b = X0 ),
inference(resolution,[],[f9,f20]) ).
fof(f158,plain,
! [X2,X0,X1] :
( identity_for(X1) = X0
| ~ product(X1,X2,inverse(X1,X2),X0) ),
inference(resolution,[],[f9,f6]) ).
fof(f157,plain,
! [X2,X0,X1] :
( identity_for(X1) = X0
| ~ product(X1,inverse(X1,X2),X2,X0) ),
inference(resolution,[],[f9,f5]) ).
fof(f156,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ product(X2,X1,identity_for(X2),X0) ),
inference(resolution,[],[f9,f3]) ).
fof(f155,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ product(X2,identity_for(X2),X1,X0) ),
inference(resolution,[],[f9,f2]) ).
fof(f154,plain,
! [X0] :
( c = X0
| ~ product(g2,d,d,X0) ),
inference(resolution,[],[f9,f25]) ).
fof(f153,plain,
! [X0] :
( d = X0
| ~ product(g2,d,c,X0) ),
inference(resolution,[],[f9,f24]) ).
fof(f152,plain,
! [X0] :
( d = X0
| ~ product(g2,c,d,X0) ),
inference(resolution,[],[f9,f23]) ).
fof(f151,plain,
! [X0] :
( ~ product(g2,c,c,X0)
| c = X0 ),
inference(resolution,[],[f9,f22]) ).
fof(f76,plain,
( d = identity_for(g2)
| c = identity_for(g2) ),
inference(resolution,[],[f17,f1]) ).
fof(f38,plain,
( b = identity_for(g1)
| a = identity_for(g1) ),
inference(resolution,[],[f16,f1]) ).
fof(f108,plain,
! [X0,X1] :
( ~ group_member(X0,g2)
| ~ group_member(X1,g2)
| d = multiply(g2,X1,X0)
| c = multiply(g2,X1,X0) ),
inference(resolution,[],[f8,f17]) ).
fof(f107,plain,
! [X0,X1] :
( ~ group_member(X0,g1)
| ~ group_member(X1,g1)
| b = multiply(g1,X1,X0)
| a = multiply(g1,X1,X0) ),
inference(resolution,[],[f8,f16]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( group_member(multiply(X0,X1,X2),X0)
| ~ group_member(X2,X0)
| ~ group_member(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_2) ).
fof(f37,plain,
( b = d3
| a = d3 ),
inference(resolution,[],[f16,f30]) ).
fof(f77,plain,
! [X0] :
( d = inverse(g2,X0)
| c = inverse(g2,X0)
| ~ group_member(X0,g2) ),
inference(resolution,[],[f17,f4]) ).
fof(f17,axiom,
! [X1] :
( ~ group_member(X1,g2)
| d = X1
| c = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_and_d_only_members_of_group2) ).
fof(f36,plain,
( b = d2
| a = d2 ),
inference(resolution,[],[f16,f29]) ).
fof(f53,plain,
( ~ product(g2,d,an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f50,f27]) ).
fof(f50,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_2 ),
inference(superposition,[],[f32,f47]) ).
fof(f51,plain,
( product(g1,b,d2,d3)
| ~ spl0_2 ),
inference(superposition,[],[f31,f47]) ).
fof(f35,plain,
( b = d1
| a = d1 ),
inference(resolution,[],[f16,f28]) ).
fof(f39,plain,
! [X0] :
( b = inverse(g1,X0)
| a = inverse(g1,X0)
| ~ group_member(X0,g1) ),
inference(resolution,[],[f16,f4]) ).
fof(f16,axiom,
! [X1] :
( ~ group_member(X1,g1)
| b = X1
| a = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
fof(f6,axiom,
! [X0,X1] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f5,axiom,
! [X0,X1] : product(X0,inverse(X0,X1),X1,identity_for(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f4,axiom,
! [X0,X1] :
( group_member(inverse(X0,X1),X0)
| ~ group_member(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_in_group) ).
fof(f2,axiom,
! [X0,X1] : product(X0,identity_for(X0),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f25,axiom,
product(g2,d,d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_d_is_c) ).
fof(f24,axiom,
product(g2,d,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_c_is_d) ).
fof(f22,axiom,
product(g2,c,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_c) ).
fof(f20,axiom,
product(g1,b,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).
fof(f1,axiom,
! [X0] : group_member(identity_for(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_in_group) ).
fof(f30,axiom,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_member_of_group1) ).
fof(f29,axiom,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_member_of_group1) ).
fof(f28,axiom,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_member_of_group1) ).
fof(f15,axiom,
group_member(d,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_member_of_group2) ).
fof(f14,axiom,
group_member(c,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_member_of_group2) ).
fof(f13,axiom,
group_member(b,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_member_of_group1) ).
fof(f12,axiom,
group_member(a,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_member_of_group1) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X7,X5] :
( ~ product(X0,X2,X3,X6)
| ~ product(X0,X1,X6,X7)
| ~ product(X0,X1,X2,X5)
| product(X0,X5,X3,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X6,X7,X5] :
( ~ product(X0,X5,X3,X7)
| ~ product(X0,X1,X2,X5)
| ~ product(X0,X2,X3,X6)
| product(X0,X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
fof(f388,plain,
( a != b
| ~ spl0_3
| spl0_4 ),
inference(forward_demodulation,[],[f60,f57]) ).
fof(f387,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f386,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(global_subsumption,[],[f73,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f7,f327,f332,f334,f336,f80,f85,f342]) ).
fof(f385,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f384,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(global_subsumption,[],[f383,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f7,f327,f332,f334,f336,f80,f85,f342]) ).
fof(f383,plain,
( product(g1,a,a,b)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f382,f57]) ).
fof(f382,plain,
( product(g1,a,d2,b)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f213,f85]) ).
fof(f213,plain,
( product(g1,a,d2,d3)
| ~ spl0_1 ),
inference(superposition,[],[f31,f43]) ).
fof(f381,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f380,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_6 ),
inference(global_subsumption,[],[f379,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f7,f327,f332,f334,f336,f80,f85,f342]) ).
fof(f379,plain,
( ~ product(g2,c,c,d)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f378,f26]) ).
fof(f378,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(a),d)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f377,f57]) ).
fof(f377,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),d)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f376,f27]) ).
fof(f376,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f212,f85]) ).
fof(f212,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_1 ),
inference(superposition,[],[f32,f43]) ).
fof(f368,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f367]) ).
fof(f367,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f366,f24]) ).
fof(f366,plain,
( ~ product(g2,d,c,d)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f365,f27]) ).
fof(f365,plain,
( ~ product(g2,an_isomorphism(b),c,d)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f364,f47]) ).
fof(f364,plain,
( ~ product(g2,an_isomorphism(d1),c,d)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f363,f26]) ).
fof(f363,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),d)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f345,f57]) ).
fof(f345,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),d)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f339,f27]) ).
fof(f339,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_6 ),
inference(superposition,[],[f32,f85]) ).
fof(f361,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f360,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f359,f24]) ).
fof(f359,plain,
( ~ product(g2,d,c,d)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f358,f26]) ).
fof(f358,plain,
( ~ product(g2,d,an_isomorphism(a),d)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f351,f57]) ).
fof(f351,plain,
( ~ product(g2,d,an_isomorphism(d2),d)
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f341,f27]) ).
fof(f341,plain,
( ~ product(g2,d,an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f53,f85]) ).
fof(f357,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f356,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_5
| ~ spl0_6 ),
inference(global_subsumption,[],[f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f7,f327,f332,f334,f336,f80,f85,f342]) ).
fof(f355,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f354,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(global_subsumption,[],[f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f61,f209,f57,f315,f321,f7,f327,f332,f334,f336,f80,f85,f342]) ).
fof(f321,plain,
( a = b
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f61,f57]) ).
fof(f315,plain,
( a = b
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f57,f61]) ).
fof(f209,plain,
( a = b
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f61,f57]) ).
fof(f314,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f313,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_7 ),
inference(global_subsumption,[],[f111,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f232,f277,f274,f268,f263,f260,f257,f230,f250]) ).
fof(f250,plain,
( ~ product(g2,d,d,an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f231,f27]) ).
fof(f231,plain,
( ~ product(g2,d,an_isomorphism(b),an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f53,f61]) ).
fof(f230,plain,
( product(g1,b,b,d3)
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f51,f61]) ).
fof(f257,plain,
( ~ product(g2,d,d,an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f256,f27]) ).
fof(f256,plain,
( ~ product(g2,an_isomorphism(b),d,an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f255,f47]) ).
fof(f255,plain,
( ~ product(g2,an_isomorphism(d1),d,an_isomorphism(d3))
| ~ spl0_4 ),
inference(forward_demodulation,[],[f229,f27]) ).
fof(f229,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(d3))
| ~ spl0_4 ),
inference(superposition,[],[f32,f61]) ).
fof(f260,plain,
( product(g1,b,b,d3)
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f228,f47]) ).
fof(f228,plain,
( product(g1,d1,b,d3)
| ~ spl0_4 ),
inference(superposition,[],[f31,f61]) ).
fof(f263,plain,
( product(g1,a,b,d3)
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f213,f61]) ).
fof(f268,plain,
( ~ product(g2,c,d,an_isomorphism(d3))
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f267,f26]) ).
fof(f267,plain,
( ~ product(g2,an_isomorphism(a),d,an_isomorphism(d3))
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f266,f27]) ).
fof(f266,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(b),an_isomorphism(d3))
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f212,f61]) ).
fof(f274,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| d3 = X0 )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f273,f47]) ).
fof(f273,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f150,f61]) ).
fof(f150,plain,
! [X0] :
( d3 = X0
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[],[f9,f31]) ).
fof(f277,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| d3 = X0 )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f149,f61]) ).
fof(f149,plain,
( ! [X0] :
( d3 = X0
| ~ product(g1,b,d2,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f9,f51]) ).
fof(f232,plain,
( a != b
| spl0_3
| ~ spl0_4 ),
inference(superposition,[],[f56,f61]) ).
fof(f56,plain,
( a != d2
| spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f111,plain,
( a != identity_for(g1)
| spl0_7 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f110,plain,
( spl0_7
<=> a = identity_for(g1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f312,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f311,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f116,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f232,f277,f274,f268,f263,f260,f257,f230,f250]) ).
fof(f310,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f309,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f232,f277,f274,f268,f263,f260,f257,f230,f250]) ).
fof(f308,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f307]) ).
fof(f307,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f232,f277,f274,f268,f263,f260,f257,f230]) ).
fof(f306,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f305]) ).
fof(f305,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f232,f277,f274,f268,f263,f260,f257]) ).
fof(f304,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f303,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f232,f277,f274,f268,f263,f260]) ).
fof(f302,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f301,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f232,f277,f274,f268,f263]) ).
fof(f300,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f299,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f263,f232,f277,f274,f268]) ).
fof(f298,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f297,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(global_subsumption,[],[f85,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f263,f268,f232,f277,f274]) ).
fof(f296,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f295]) ).
fof(f295,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f263,f268,f232,f277,f274]) ).
fof(f294,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f293]) ).
fof(f293,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f263,f268,f274,f232,f277]) ).
fof(f292,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f291]) ).
fof(f291,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f263,f268,f274,f277,f232]) ).
fof(f290,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f289]) ).
fof(f289,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| spl0_5 ),
inference(global_subsumption,[],[f80,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f76,f9,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f56,f61,f250,f230,f257,f260,f263,f268,f274,f277,f232]) ).
fof(f288,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f287,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_5
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f80,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f123,f284]) ).
fof(f284,plain,
( a != b
| ~ spl0_7
| spl0_8 ),
inference(forward_demodulation,[],[f115,f112]) ).
fof(f123,plain,
( a != b
| ~ spl0_7
| spl0_8 ),
inference(forward_demodulation,[],[f115,f112]) ).
fof(f144,plain,
( ! [X0,X1] :
( X0 = X1
| ~ product(g1,a,X1,X0) )
| ~ spl0_7 ),
inference(resolution,[],[f9,f121]) ).
fof(f141,plain,
( ! [X0,X1] :
( a = X0
| ~ product(g1,inverse(g1,X1),X1,X0) )
| ~ spl0_7 ),
inference(resolution,[],[f9,f119]) ).
fof(f140,plain,
( ! [X0,X1] :
( a = X0
| ~ product(g1,X1,inverse(g1,X1),X0) )
| ~ spl0_7 ),
inference(resolution,[],[f9,f118]) ).
fof(f139,plain,
( ! [X0,X1] :
( X0 = X1
| ~ product(g1,X1,a,X0) )
| ~ spl0_7 ),
inference(resolution,[],[f9,f120]) ).
fof(f119,plain,
( ! [X0] : product(g1,inverse(g1,X0),X0,a)
| ~ spl0_7 ),
inference(superposition,[],[f5,f112]) ).
fof(f118,plain,
( ! [X0] : product(g1,X0,inverse(g1,X0),a)
| ~ spl0_7 ),
inference(superposition,[],[f6,f112]) ).
fof(f121,plain,
( ! [X0] : product(g1,a,X0,X0)
| ~ spl0_7 ),
inference(superposition,[],[f2,f112]) ).
fof(f120,plain,
( ! [X0] : product(g1,X0,a,X0)
| ~ spl0_7 ),
inference(superposition,[],[f3,f112]) ).
fof(f112,plain,
( a = identity_for(g1)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f115,plain,
( b != identity_for(g1)
| spl0_8 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f286,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f285,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f123,f284]) ).
fof(f283,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f282,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f43,f210,f211,f123]) ).
fof(f281,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f280,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f232,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f279,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f278,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f277,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f276,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f275]) ).
fof(f275,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f274,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f272,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f271,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f85,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f270,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f269]) ).
fof(f269,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f268,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f265,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f264]) ).
fof(f264,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f263,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f262,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f261,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f260,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f259,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f257,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f254,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f253]) ).
fof(f253,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f230,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f252,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f251,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f250,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f17,f77,f37,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f123,f43,f210,f211]) ).
fof(f249,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f248,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f17,f77,f37,f8,f107,f108,f38,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f197,f56,f61,f232]) ).
fof(f197,plain,
( a = b
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f116,f112]) ).
fof(f247,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f246]) ).
fof(f246,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f245,f25]) ).
fof(f245,plain,
( ~ product(g2,d,d,c)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f244,f27]) ).
fof(f244,plain,
( ~ product(g2,d,an_isomorphism(b),c)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f243,f26]) ).
fof(f243,plain,
( ~ product(g2,d,an_isomorphism(b),an_isomorphism(a))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f231,f81]) ).
fof(f241,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f240,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f239,f25]) ).
fof(f239,plain,
( ~ product(g2,d,d,c)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f238,f27]) ).
fof(f238,plain,
( ~ product(g2,an_isomorphism(b),d,c)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f237,f47]) ).
fof(f237,plain,
( ~ product(g2,an_isomorphism(d1),d,c)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f236,f27]) ).
fof(f236,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),c)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f235,f26]) ).
fof(f235,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(a))
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f229,f81]) ).
fof(f220,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f219,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f218,f22]) ).
fof(f218,plain,
( ~ product(g2,c,c,c)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f217,f26]) ).
fof(f217,plain,
( ~ product(g2,c,an_isomorphism(a),c)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f216,f57]) ).
fof(f216,plain,
( ~ product(g2,c,an_isomorphism(d2),c)
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f215,f26]) ).
fof(f215,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f212,f81]) ).
fof(f208,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f207,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(global_subsumption,[],[f206,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f60,f57,f17,f77,f37,f8,f107,f108,f38,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f197,f73]) ).
fof(f206,plain,
( a = b
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f85,f81]) ).
fof(f205,plain,
( ~ spl0_1
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f204,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(global_subsumption,[],[f43,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f60,f57,f17,f77,f37,f8,f107,f108,f38,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f197,f73]) ).
fof(f203,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f202,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f60,f57,f17,f77,f37,f8,f107,f108,f38,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f197,f73]) ).
fof(f201,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f200,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_7
| ~ spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f60,f57,f17,f77,f37,f8,f107,f108,f38,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f73,f197]) ).
fof(f199,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f198]) ).
fof(f198,plain,
( $false
| ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f36,f17,f77,f37,f84,f81,f8,f107,f108,f38,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f148,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f106,f197]) ).
fof(f196,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f195]) ).
fof(f195,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f84,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f76,f9,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f106]) ).
fof(f178,plain,
( a = b
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f175,f81]) ).
fof(f175,plain,
( b = d3
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f145,f72]) ).
fof(f176,plain,
( a = b
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f145,f95]) ).
fof(f164,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| a = X0 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f163,f47]) ).
fof(f163,plain,
( ! [X0] :
( ~ product(g1,d1,a,X0)
| a = X0 )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f162,f57]) ).
fof(f162,plain,
( ! [X0] :
( a = X0
| ~ product(g1,d1,d2,X0) )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f150,f81]) ).
fof(f161,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| a = X0 )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f160,f57]) ).
fof(f160,plain,
( ! [X0] :
( a = X0
| ~ product(g1,b,d2,X0) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f149,f81]) ).
fof(f147,plain,
( ! [X0] :
( a = X0
| ~ product(g1,b,a,X0) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f9,f95]) ).
fof(f159,plain,
( ! [X0] :
( a = X0
| ~ product(g1,b,a,X0) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f146,f81]) ).
fof(f146,plain,
( ! [X0] :
( d3 = X0
| ~ product(g1,b,a,X0) )
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f9,f72]) ).
fof(f95,plain,
( product(g1,b,a,a)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f94,f47]) ).
fof(f94,plain,
( product(g1,d1,a,a)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f88,f57]) ).
fof(f88,plain,
( product(g1,d1,d2,a)
| ~ spl0_5 ),
inference(superposition,[],[f31,f81]) ).
fof(f100,plain,
( ~ product(g2,d,c,c)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f99,f27]) ).
fof(f99,plain,
( ~ product(g2,an_isomorphism(b),c,c)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f98,f47]) ).
fof(f98,plain,
( ~ product(g2,an_isomorphism(d1),c,c)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f97,f26]) ).
fof(f97,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),c)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f96,f57]) ).
fof(f96,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),c)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f89,f26]) ).
fof(f89,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_5 ),
inference(superposition,[],[f32,f81]) ).
fof(f93,plain,
( product(g1,b,a,a)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f72,f81]) ).
fof(f105,plain,
( ~ product(g2,d,c,c)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f92,f26]) ).
fof(f92,plain,
( ~ product(g2,d,c,an_isomorphism(a))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f71,f81]) ).
fof(f104,plain,
( ~ product(g2,d,c,c)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f103,f26]) ).
fof(f103,plain,
( ~ product(g2,d,an_isomorphism(a),c)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f102,f57]) ).
fof(f102,plain,
( ~ product(g2,d,an_isomorphism(d2),c)
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f91,f26]) ).
fof(f91,plain,
( ~ product(g2,d,an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f53,f81]) ).
fof(f101,plain,
( product(g1,b,a,a)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f90,f57]) ).
fof(f90,plain,
( product(g1,b,d2,a)
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f51,f81]) ).
fof(f72,plain,
( product(g1,b,a,d3)
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f66,f47]) ).
fof(f66,plain,
( product(g1,d1,a,d3)
| ~ spl0_3 ),
inference(superposition,[],[f31,f57]) ).
fof(f71,plain,
( ~ product(g2,d,c,an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f70,f27]) ).
fof(f70,plain,
( ~ product(g2,an_isomorphism(b),c,an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f69,f47]) ).
fof(f69,plain,
( ~ product(g2,an_isomorphism(d1),c,an_isomorphism(d3))
| ~ spl0_3 ),
inference(forward_demodulation,[],[f65,f26]) ).
fof(f65,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(d3))
| ~ spl0_3 ),
inference(superposition,[],[f32,f57]) ).
fof(f64,plain,
( product(g1,b,a,d3)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f51,f57]) ).
fof(f68,plain,
( ~ product(g2,d,c,an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f63,f26]) ).
fof(f63,plain,
( ~ product(g2,d,an_isomorphism(a),an_isomorphism(d3))
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f53,f57]) ).
fof(f194,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| spl0_6 ),
inference(global_subsumption,[],[f73,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f84,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f76,f9,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f106]) ).
fof(f192,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f191,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6 ),
inference(global_subsumption,[],[f43,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f84,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f76,f9,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f106]) ).
fof(f190,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f189,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f43,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f123]) ).
fof(f188,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f187,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f73,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f123]) ).
fof(f186,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f185,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f106,f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f123]) ).
fof(f184,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f183]) ).
fof(f183,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(global_subsumption,[],[f7,f10,f11,f12,f13,f14,f15,f28,f29,f30,f26,f27,f1,f18,f19,f20,f21,f22,f23,f24,f25,f31,f2,f3,f32,f4,f5,f6,f16,f39,f35,f47,f51,f53,f36,f57,f68,f64,f71,f17,f77,f72,f37,f81,f101,f104,f105,f93,f100,f95,f8,f107,f108,f38,f115,f112,f120,f121,f118,f119,f76,f9,f139,f140,f141,f144,f159,f147,f148,f161,f164,f151,f152,f153,f154,f155,f156,f157,f158,f142,f143,f145,f176,f178,f123]) ).
fof(f182,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f181,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f176,f49]) ).
fof(f180,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f179,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f178,f49]) ).
fof(f132,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f76,f129,f125]) ).
fof(f125,plain,
( spl0_9
<=> c = identity_for(g2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f129,plain,
( spl0_10
<=> d = identity_for(g2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f117,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f38,f114,f110]) ).
fof(f86,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f37,f83,f79]) ).
fof(f62,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f36,f59,f55]) ).
fof(f48,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f35,f45,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP025-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 04:19:06 EDT 2024
% 0.21/0.35 % CPUTime :
% 0.21/0.36 % (25408)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (25411)WARNING: value z3 for option sas not known
% 0.21/0.37 % (25412)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (25410)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (25409)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (25411)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)
% 0.21/0.37 % (25414)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)
% 0.21/0.37 % (25415)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)
% 0.21/0.37 % (25413)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)
% 0.21/0.37 TRYING [1]
% 0.21/0.37 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [4]
% 0.21/0.39 % (25411)First to succeed.
% 0.21/0.40 TRYING [3]
% 0.21/0.40 % (25411)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40 % (25411)------------------------------
% 0.21/0.40 % (25411)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.40 % (25411)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (25411)Memory used [KB]: 1082
% 0.21/0.40 % (25411)Time elapsed: 0.025 s
% 0.21/0.40 % (25411)Instructions burned: 41 (million)
% 0.21/0.40 % (25411)------------------------------
% 0.21/0.40 % (25411)------------------------------
% 0.21/0.40 % (25408)Success in time 0.042 s
%------------------------------------------------------------------------------