%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:12:09 AM UTC 2026
% Result : Unsatisfiable 1.29s 1.60s
% Output : Refutation 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 37
% Syntax : Number of formulae : 321 ( 36 unt; 9 def)
% Number of atoms : 1010 ( 119 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 1416 ( 727 ~; 680 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2,X3)
| ~ product(X0,X1,X2,X4)
| X4 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f10,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3)
| X3 = X4 ),
inference(reorient_equations,[],[f9]) ).
fof(f19,axiom,
! [X0] :
( ~ group_member(X0,g1)
| X0 = a
| X0 = b
| X0 = c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).
fof(f20,plain,
! [X0] :
( ~ group_member(X0,g1)
| a = X0
| b = X0
| c = X0 ),
inference(reorient_equations,[],[f19]) ).
fof(f23,axiom,
product(g1,a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
fof(f24,axiom,
product(g1,a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).
fof(f25,axiom,
product(g1,b,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).
fof(f26,axiom,
product(g1,a,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_c) ).
fof(f27,axiom,
product(g1,c,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_a_is_c) ).
fof(f28,axiom,
product(g1,b,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_c) ).
fof(f29,axiom,
product(g1,b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_is_a) ).
fof(f30,axiom,
product(g1,c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_b_is_a) ).
fof(f31,axiom,
product(g1,c,c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_b) ).
fof(f32,axiom,
product(g2,f,f,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_f_is_f) ).
fof(f33,axiom,
product(g2,f,g,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_g_is_g) ).
fof(f34,axiom,
product(g2,g,f,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_f_is_g) ).
fof(f35,axiom,
product(g2,f,h,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_h_is_h) ).
fof(f36,axiom,
product(g2,h,f,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_f_is_h) ).
fof(f37,axiom,
product(g2,g,g,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_g_is_h) ).
fof(f38,axiom,
product(g2,g,h,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_h_is_f) ).
fof(f39,axiom,
product(g2,h,g,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_g_is_f) ).
fof(f40,axiom,
product(g2,h,h,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_h_is_g) ).
fof(f41,axiom,
an_isomorphism(a) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_f) ).
fof(f42,plain,
f = an_isomorphism(a),
inference(reorient_equations,[],[f41]) ).
fof(f43,axiom,
an_isomorphism(b) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_g) ).
fof(f44,plain,
g = an_isomorphism(b),
inference(reorient_equations,[],[f43]) ).
fof(f45,axiom,
an_isomorphism(c) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_maps_to_h) ).
fof(f46,plain,
h = an_isomorphism(c),
inference(reorient_equations,[],[f45]) ).
fof(f47,axiom,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_in_group1) ).
fof(f48,axiom,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_in_group1) ).
fof(f49,axiom,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_in_group1) ).
fof(f50,axiom,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
fof(f51,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
fof(f55,plain,
( a = d1
| b = d1
| c = d1 ),
inference(resolution,[],[f20,f47]) ).
fof(f56,plain,
( a = d2
| b = d2
| c = d2 ),
inference(resolution,[],[f20,f48]) ).
fof(f57,plain,
( a = d3
| b = d3
| c = d3 ),
inference(resolution,[],[f20,f49]) ).
fof(f59,definition,
( spl0_1
<=> c = d3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f60,plain,
( c != d3
| spl0_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( c = d3
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f63,definition,
( spl0_2
<=> b = d3 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f64,plain,
( b != d3
| spl0_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f65,plain,
( b = d3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f67,definition,
( spl0_3
<=> a = d3 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f68,plain,
( a != d3
| spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( a = d3
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f57,f67,f63,f59]) ).
fof(f72,definition,
( spl0_4
<=> c = d2 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f73,plain,
( c != d2
| spl0_4 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( c = d2
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl0_5
<=> b = d2 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f77,plain,
( b != d2
| spl0_5 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( b = d2
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl0_6
<=> a = d2 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f81,plain,
( a != d2
| spl0_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( a = d2
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f56,f80,f76,f72]) ).
fof(f85,definition,
( spl0_7
<=> c = d1 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f86,plain,
( c != d1
| spl0_7 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( c = d1
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f89,definition,
( spl0_8
<=> b = d1 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f91,plain,
( b = d1
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f93,definition,
( spl0_9
<=> a = d1 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f95,plain,
( a = d1
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f55,f93,f89,f85]) ).
fof(f100,plain,
( product(g1,d1,d2,b)
| ~ spl0_2 ),
inference(superposition,[],[f50,f65]) ).
fof(f102,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_2 ),
inference(superposition,[],[f51,f65]) ).
fof(f103,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),g)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f102,f44]) ).
fof(f105,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),g)
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f103,f74]) ).
fof(f107,plain,
( ~ product(g2,an_isomorphism(d1),h,g)
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f105,f46]) ).
fof(f108,plain,
( ~ product(g2,an_isomorphism(c),h,g)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f107,f87]) ).
fof(f109,plain,
( ~ product(g2,h,h,g)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f108,f46]) ).
fof(f110,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f109,f40]) ).
fof(f111,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f112,plain,
( product(g1,d1,b,b)
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f100,f78]) ).
fof(f113,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),g)
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f103,f78]) ).
fof(f114,plain,
( product(g1,c,b,b)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f112,f87]) ).
fof(f115,plain,
( ~ product(g2,an_isomorphism(d1),g,g)
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f113,f44]) ).
fof(f116,plain,
( ~ product(g2,an_isomorphism(c),g,g)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f115,f87]) ).
fof(f117,plain,
( ~ product(g2,h,g,g)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f116,f46]) ).
fof(f118,plain,
! [X0] :
( ~ product(g1,a,a,X0)
| a = X0 ),
inference(resolution,[],[f10,f23]) ).
fof(f123,plain,
! [X0] :
( ~ product(g1,b,c,X0)
| a = X0 ),
inference(resolution,[],[f10,f29]) ).
fof(f124,plain,
! [X0] :
( ~ product(g1,c,a,X0)
| c = X0 ),
inference(resolution,[],[f10,f27]) ).
fof(f125,plain,
! [X0] :
( ~ product(g1,c,b,X0)
| a = X0 ),
inference(resolution,[],[f10,f30]) ).
fof(f127,plain,
! [X0] :
( ~ product(g1,d1,d2,X0)
| d3 = X0 ),
inference(resolution,[],[f10,f50]) ).
fof(f184,plain,
( b != c
| spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f73,f78]) ).
fof(f194,plain,
( product(g1,c,d2,d3)
| ~ spl0_7 ),
inference(superposition,[],[f50,f87]) ).
fof(f196,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_7 ),
inference(superposition,[],[f51,f87]) ).
fof(f197,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f196,f65]) ).
fof(f198,plain,
( product(g1,c,d2,b)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f194,f65]) ).
fof(f199,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),g)
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f197,f44]) ).
fof(f215,plain,
( a = b
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f125,f114]) ).
fof(f223,plain,
( g = an_isomorphism(a)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f44,f215]) ).
fof(f230,plain,
( f = g
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f223,f42]) ).
fof(f237,plain,
( product(g2,h,f,f)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f39,f230]) ).
fof(f239,plain,
( ~ product(g2,h,f,f)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f117,f230]) ).
fof(f240,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f237,f239]) ).
fof(f241,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f242,plain,
( product(g1,d1,a,b)
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f100,f82]) ).
fof(f244,plain,
( ! [X0] :
( ~ product(g1,d1,a,X0)
| d3 = X0 )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f127,f82]) ).
fof(f247,plain,
( product(g1,c,a,b)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f198,f82]) ).
fof(f248,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(a),g)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f199,f82]) ).
fof(f253,plain,
( ~ product(g2,an_isomorphism(c),f,g)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f248,f42]) ).
fof(f257,plain,
( ~ product(g2,h,f,g)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f253,f46]) ).
fof(f259,plain,
( a != b
| spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f77,f82]) ).
fof(f260,plain,
( a != c
| spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f73,f82]) ).
fof(f261,plain,
( product(g1,d1,a,d3)
| ~ spl0_6 ),
inference(superposition,[],[f50,f82]) ).
fof(f263,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(d3))
| ~ spl0_6 ),
inference(superposition,[],[f51,f82]) ).
fof(f264,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(b))
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f263,f65]) ).
fof(f266,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),g)
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f264,f44]) ).
fof(f268,plain,
( ~ product(g2,an_isomorphism(d1),f,g)
| ~ spl0_2
| ~ spl0_6 ),
inference(forward_demodulation,[],[f266,f42]) ).
fof(f273,plain,
( b = c
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f247,f124]) ).
fof(f285,plain,
( h = an_isomorphism(b)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f46,f273]) ).
fof(f293,plain,
( g = h
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f285,f44]) ).
fof(f303,plain,
( ~ product(g2,g,f,g)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(superposition,[],[f257,f293]) ).
fof(f304,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f303,f34]) ).
fof(f305,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f312,plain,
( ~ product(g2,an_isomorphism(b),f,g)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f268,f91]) ).
fof(f317,plain,
( ~ product(g2,g,f,g)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f312,f44]) ).
fof(f321,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f317,f34]) ).
fof(f322,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f324,plain,
( product(g1,a,a,b)
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f242,f95]) ).
fof(f348,plain,
( a = b
| ~ spl0_2
| ~ spl0_6
| ~ spl0_9 ),
inference(resolution,[],[f324,f118]) ).
fof(f352,plain,
( $false
| ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f348,f259]) ).
fof(f353,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f358,plain,
( product(g1,d1,a,a)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f261,f69]) ).
fof(f363,plain,
( product(g1,c,a,a)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f358,f87]) ).
fof(f367,plain,
( a != b
| spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f64,f69]) ).
fof(f391,plain,
( a = c
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f363,f124]) ).
fof(f395,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f391,f260]) ).
fof(f396,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f395]) ).
fof(f397,plain,
( a != c
| ~ spl0_1
| spl0_3 ),
inference(forward_demodulation,[],[f68,f61]) ).
fof(f398,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(c))
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f263,f61]) ).
fof(f405,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),h)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f398,f46]) ).
fof(f410,plain,
( ~ product(g2,an_isomorphism(d1),f,h)
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f405,f42]) ).
fof(f412,plain,
( ~ product(g2,an_isomorphism(c),f,h)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f410,f87]) ).
fof(f414,plain,
( ~ product(g2,h,f,h)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[],[f412,f46]) ).
fof(f417,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f414,f36]) ).
fof(f418,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f442,plain,
( a != c
| spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f60,f69]) ).
fof(f446,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_3 ),
inference(superposition,[],[f51,f69]) ).
fof(f447,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f446,f42]) ).
fof(f451,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(a),f)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f447,f82]) ).
fof(f453,plain,
( ~ product(g2,an_isomorphism(d1),f,f)
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[],[f451,f42]) ).
fof(f465,plain,
( ~ product(g2,an_isomorphism(a),f,f)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f453,f95]) ).
fof(f470,plain,
( ~ product(g2,f,f,f)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f465,f42]) ).
fof(f474,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f470,f32]) ).
fof(f475,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f474]) ).
fof(f478,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| d3 = X0 )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f244,f91]) ).
fof(f487,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| a = X0 )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f478,f69]) ).
fof(f493,plain,
( b != c
| spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f86,f91]) ).
fof(f506,plain,
( a = b
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f487,f25]) ).
fof(f507,plain,
( $false
| ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f506,f259]) ).
fof(f508,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f509,plain,
( a = b
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f78,f82]) ).
fof(f512,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f509,f367]) ).
fof(f513,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f518,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| c = X0 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_demodulation,[],[f478,f61]) ).
fof(f533,plain,
( b != c
| ~ spl0_1
| spl0_2 ),
inference(superposition,[],[f64,f61]) ).
fof(f544,plain,
( b = c
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8 ),
inference(resolution,[],[f518,f25]) ).
fof(f545,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f544,f493]) ).
fof(f546,plain,
( ~ spl0_1
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f545]) ).
fof(f548,plain,
( ! [X0] :
( ~ product(g1,a,a,X0)
| d3 = X0 )
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f244,f95]) ).
fof(f555,plain,
( ! [X0] :
( ~ product(g1,a,a,X0)
| c = X0 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f548,f61]) ).
fof(f571,plain,
( a = c
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(resolution,[],[f555,f23]) ).
fof(f572,plain,
( $false
| ~ spl0_1
| spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f571,f260]) ).
fof(f573,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f579,plain,
( a != b
| ~ spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f68,f65]) ).
fof(f599,plain,
( ! [X0] :
( ~ product(g1,a,d2,X0)
| d3 = X0 )
| ~ spl0_9 ),
inference(forward_demodulation,[],[f127,f95]) ).
fof(f604,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| d3 = X0 )
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f599,f78]) ).
fof(f609,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| a = X0 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f604,f69]) ).
fof(f616,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_3 ),
inference(superposition,[],[f51,f69]) ).
fof(f617,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f616,f42]) ).
fof(f635,plain,
( a != b
| ~ spl0_5
| spl0_6 ),
inference(superposition,[],[f81,f78]) ).
fof(f636,plain,
( a = b
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[],[f609,f24]) ).
fof(f637,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f636,f635]) ).
fof(f638,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f639,plain,
( b != c
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f77,f74]) ).
fof(f640,plain,
( ! [X0] :
( ~ product(g1,a,c,X0)
| d3 = X0 )
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f599,f74]) ).
fof(f647,plain,
( ! [X0] :
( ~ product(g1,a,c,X0)
| a = X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f640,f69]) ).
fof(f665,plain,
( a = c
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(resolution,[],[f647,f26]) ).
fof(f666,plain,
( $false
| spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f665,f442]) ).
fof(f667,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f666]) ).
fof(f670,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f127,f78]) ).
fof(f675,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| d3 = X0 )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f670,f91]) ).
fof(f680,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| a = X0 )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f675,f69]) ).
fof(f696,plain,
( product(g1,b,d2,d3)
| ~ spl0_8 ),
inference(superposition,[],[f50,f91]) ).
fof(f698,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_8 ),
inference(superposition,[],[f51,f91]) ).
fof(f705,plain,
( a = c
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f680,f28]) ).
fof(f706,plain,
( $false
| spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f705,f442]) ).
fof(f707,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f712,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),f)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f617,f74]) ).
fof(f719,plain,
( ~ product(g2,an_isomorphism(d1),h,f)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f712,f46]) ).
fof(f723,plain,
( ~ product(g2,an_isomorphism(b),h,f)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f719,f91]) ).
fof(f725,plain,
( ~ product(g2,g,h,f)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f723,f44]) ).
fof(f728,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f725,f38]) ).
fof(f729,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f728]) ).
fof(f731,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f127,f78]) ).
fof(f736,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| d3 = X0 )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f731,f91]) ).
fof(f741,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| b = X0 )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f736,f65]) ).
fof(f766,plain,
( b = c
| ~ spl0_2
| ~ spl0_5
| ~ spl0_8 ),
inference(resolution,[],[f741,f28]) ).
fof(f767,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f766,f493]) ).
fof(f768,plain,
( ~ spl0_2
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f767]) ).
fof(f770,plain,
( ! [X0] :
( ~ product(g1,d1,c,X0)
| d3 = X0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f127,f74]) ).
fof(f777,plain,
( ! [X0] :
( ~ product(g1,b,c,X0)
| d3 = X0 )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f770,f91]) ).
fof(f782,plain,
( ! [X0] :
( ~ product(g1,b,c,X0)
| b = X0 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f777,f65]) ).
fof(f797,plain,
( a = b
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(resolution,[],[f782,f29]) ).
fof(f800,plain,
( $false
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f797,f579]) ).
fof(f801,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f800]) ).
fof(f807,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(c))
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f698,f61]) ).
fof(f808,plain,
( product(g1,b,d2,c)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f696,f61]) ).
fof(f812,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(d2),h)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f807,f46]) ).
fof(f816,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(b),h)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f812,f78]) ).
fof(f817,plain,
( ~ product(g2,g,g,h)
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f816,f44]) ).
fof(f818,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f817,f37]) ).
fof(f819,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f818]) ).
fof(f824,plain,
( product(g1,b,c,c)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f808,f74]) ).
fof(f857,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_9 ),
inference(superposition,[],[f51,f95]) ).
fof(f858,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(c))
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f857,f61]) ).
fof(f860,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),h)
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f858,f46]) ).
fof(f862,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(c),h)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f860,f74]) ).
fof(f863,plain,
( ~ product(g2,an_isomorphism(a),h,h)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f862,f46]) ).
fof(f864,plain,
( ~ product(g2,f,h,h)
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f863,f42]) ).
fof(f865,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f864,f35]) ).
fof(f866,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f865]) ).
fof(f868,plain,
( a = c
| ~ spl0_1
| ~ spl0_4
| ~ spl0_8 ),
inference(resolution,[],[f824,f123]) ).
fof(f872,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f868,f397]) ).
fof(f873,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f872]) ).
fof(f875,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f127,f78]) ).
fof(f880,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| d3 = X0 )
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f875,f95]) ).
fof(f885,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| c = X0 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f880,f61]) ).
fof(f905,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_9 ),
inference(superposition,[],[f51,f95]) ).
fof(f913,plain,
( b = c
| ~ spl0_1
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[],[f885,f24]) ).
fof(f914,plain,
( $false
| ~ spl0_1
| spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f913,f184]) ).
fof(f915,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f914]) ).
fof(f922,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f905,f65]) ).
fof(f927,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),g)
| ~ spl0_2
| ~ spl0_9 ),
inference(forward_demodulation,[],[f922,f44]) ).
fof(f930,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(b),g)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f927,f78]) ).
fof(f932,plain,
( ~ product(g2,an_isomorphism(a),g,g)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f930,f44]) ).
fof(f935,plain,
( ~ product(g2,f,g,g)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f932,f42]) ).
fof(f936,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f935,f33]) ).
fof(f937,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f936]) ).
fof(f939,plain,
( ! [X0] :
( ~ product(g1,d1,c,X0)
| d3 = X0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f127,f74]) ).
fof(f944,plain,
( ! [X0] :
( ~ product(g1,a,c,X0)
| d3 = X0 )
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f939,f95]) ).
fof(f947,plain,
( ! [X0] :
( ~ product(g1,a,c,X0)
| b = X0 )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[],[f944,f65]) ).
fof(f972,plain,
( b = c
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(resolution,[],[f947,f26]) ).
fof(f973,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_5
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f972,f639]) ).
fof(f974,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_5
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f973]) ).
fof(f978,plain,
( ! [X0] :
( ~ product(g1,c,c,X0)
| d3 = X0 )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f939,f87]) ).
fof(f983,plain,
( ! [X0] :
( ~ product(g1,c,c,X0)
| c = X0 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f978,f61]) ).
fof(f1010,plain,
( b = c
| ~ spl0_1
| ~ spl0_4
| ~ spl0_7 ),
inference(resolution,[],[f983,f31]) ).
fof(f1013,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1010,f533]) ).
fof(f1014,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1013]) ).
fof(f1019,plain,
( ! [X0] :
( ~ product(g1,c,c,X0)
| a = X0 )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f978,f69]) ).
fof(f1049,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(d3))
| ~ spl0_5 ),
inference(superposition,[],[f51,f78]) ).
fof(f1050,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(a))
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1049,f69]) ).
fof(f1056,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),f)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1050,f42]) ).
fof(f1058,plain,
( ~ product(g2,an_isomorphism(d1),g,f)
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f1056,f44]) ).
fof(f1059,plain,
( ~ product(g2,an_isomorphism(c),g,f)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1058,f87]) ).
fof(f1060,plain,
( ~ product(g2,h,g,f)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1059,f46]) ).
fof(f1061,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1060,f39]) ).
fof(f1062,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1061]) ).
fof(f1064,plain,
( a = b
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(resolution,[],[f1019,f31]) ).
fof(f1065,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1064,f367]) ).
fof(f1066,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1065]) ).
fof(f1068,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f127,f78]) ).
fof(f1074,plain,
( ! [X0] :
( ~ product(g1,c,b,X0)
| d3 = X0 )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1068,f87]) ).
fof(f1079,plain,
( ! [X0] :
( ~ product(g1,c,b,X0)
| c = X0 )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1074,f61]) ).
fof(f1105,plain,
( a = c
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f1079,f30]) ).
fof(f1106,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1105,f397]) ).
fof(f1107,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f1106]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f70]) ).
cnf(s2,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f83]) ).
cnf(s3,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f96]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f111]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f241]) ).
cnf(s6,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f305]) ).
cnf(s8,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f322]) ).
cnf(s9,plain,
( ~ spl0_2
| spl0_5
| ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f353]) ).
cnf(s10,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f396]) ).
cnf(s12,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f418]) ).
cnf(s16,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f475]) ).
cnf(s18,plain,
( ~ spl0_3
| spl0_5
| ~ spl0_6
| ~ spl0_8 ),
inference(sat_conversion,[],[f508]) ).
cnf(s20,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f513]) ).
cnf(s21,plain,
( ~ spl0_1
| ~ spl0_6
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f546]) ).
cnf(s22,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f573]) ).
cnf(s26,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f638]) ).
cnf(s27,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f667]) ).
cnf(s28,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f707]) ).
cnf(s30,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f729]) ).
cnf(s31,plain,
( ~ spl0_2
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f768]) ).
cnf(s33,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f801]) ).
cnf(s34,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_8 ),
inference(sat_conversion,[],[f819]) ).
cnf(s35,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f866]) ).
cnf(s36,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f873]) ).
cnf(s37,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f915]) ).
cnf(s39,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f937]) ).
cnf(s40,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_5
| ~ spl0_9 ),
inference(sat_conversion,[],[f974]) ).
cnf(s42,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f1014]) ).
cnf(s45,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f1062]) ).
cnf(s46,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f1066]) ).
cnf(s47,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f1107]) ).
cnf(s48,plain,
( spl0_5
| spl0_4
| ~ spl0_3 ),
inference(rat,[],[s3,s10,s18,s16,s2]) ).
cnf(s49,plain,
( ~ spl0_5
| spl0_2
| spl0_1 ),
inference(rat,[],[s26,s3,s20,s28,s45,s1]) ).
cnf(s50,plain,
( spl0_2
| spl0_1 ),
inference(rat,[],[s3,s46,s27,s30,s48,s49,s1]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_3
| spl0_1 ),
inference(rat,[],[s3,s28,s39,s45,s50]) ).
cnf(s52,plain,
( ~ spl0_3
| spl0_1 ),
inference(rat,[],[s3,s27,s4,s30,s48,s51,s50]) ).
cnf(s53,plain,
( ~ spl0_6
| spl0_5
| ~ spl0_2 ),
inference(rat,[],[s3,s6,s8,s9]) ).
cnf(s54,plain,
( spl0_5
| spl0_4
| ~ spl0_2 ),
inference(rat,[],[s53,s2]) ).
cnf(s55,plain,
( ~ spl0_5
| ~ spl0_2 ),
inference(rat,[],[s31,s3,s5,s39]) ).
cnf(s56,plain,
spl0_1,
inference(rat,[],[s3,s40,s33,s4,s54,s55,s52,s50]) ).
cnf(s57,plain,
( ~ spl0_9
| spl0_5 ),
inference(rat,[],[s22,s2,s35,s56]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_8 ),
inference(rat,[],[s36,s30,s56]) ).
cnf(s59,plain,
( spl0_7
| spl0_5 ),
inference(rat,[],[s58,s2,s21,s3,s57,s56]) ).
cnf(s60,plain,
( spl0_5
| spl0_2 ),
inference(rat,[],[s2,s42,s12,s59,s56]) ).
cnf(s61,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s47,s45,s56]) ).
cnf(s62,plain,
~ spl0_5,
inference(rat,[],[s37,s35,s3,s61,s34,s56]) ).
cnf(s64,plain,
spl0_7,
inference(rat,[],[s59,s62]) ).
cnf(s65,plain,
spl0_2,
inference(rat,[],[s60,s62]) ).
cnf(s67,plain,
~ spl0_4,
inference(rat,[],[s4,s65,s64]) ).
cnf(s68,plain,
$false,
inference(rat,[],[s54,s62,s65,s67]) ).
fof(f1108,plain,
$false,
inference(avatar_sat_refutation,[],[s68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:14:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.29/1.60 % (1755912)Input is clausal, will run a generic CNF schedule.
% 1.29/1.60 % (1755944)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2421359052:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.29/1.60 % (1755951)dis-21_1_sil=8000:lcm=predicate:random_seed=525317745:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.29/1.60 % (1755949)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4010950004:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.29/1.60 % (1755946)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=846992231:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.29/1.60 % (1755945)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1158096931:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.29/1.60 % (1755948)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3268335727:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.29/1.60 % (1755947)lrs+10_1_sil=8000:sp=occurrence:random_seed=1702459947:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.29/1.60 % (1755947)First to succeed.
% 1.29/1.60 % (1755947)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1755912"
% 1.29/1.60 % (1755951)Instruction limit reached!
% 1.29/1.60 % (1755951)------------------------------
% 1.29/1.60 % (1755951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/1.60 % (1755951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/1.60 % (1755951)CaDiCaL version: 2.1.3
% 1.29/1.60 % (1755951)Termination reason: Instruction limit
% 1.29/1.60 % (1755951)Termination phase: Saturation
% 1.29/1.60 % (1755951)Time elapsed: 0.103 s
% 1.29/1.60 % (1755951)Peak memory usage: 88 MB
% 1.29/1.60 % (1755951)Instructions burned: 118 (million)
% 1.29/1.60 % (1755948)Instruction limit reached!
% 1.29/1.60 % (1755948)------------------------------
% 1.29/1.60 % (1755948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/1.60 % (1755948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/1.60 % (1755948)CaDiCaL version: 2.1.3
% 1.29/1.60 % (1755948)Termination reason: Instruction limit
% 1.29/1.60 % (1755948)Termination phase: Saturation
% 1.29/1.60 % (1755948)Time elapsed: 0.108 s
% 1.29/1.60 % (1755948)Peak memory usage: 89 MB
% 1.29/1.60 % (1755948)Instructions burned: 115 (million)
% 1.29/1.60 % (1755949)Also succeeded, but the first one will report.
% 1.29/1.60 % (1755964)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1458526024:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.29/1.60 % (1755965)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=252261722:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 1.29/1.60 % (1755947)Refutation found. Thanks to Tanya!
% 1.29/1.60 % SZS status Unsatisfiable for theBenchmark
% 1.29/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.00/1.85 % (1755947)------------------------------
% 5.00/1.85 % (1755947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.85 % (1755947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.85 % (1755947)CaDiCaL version: 2.1.3
% 5.00/1.85 % (1755947)Termination reason: Refutation
% 5.00/1.85 % (1755947)Time elapsed: 0.028 s
% 5.00/1.85 % (1755947)Peak memory usage: 89 MB
% 5.00/1.85 % (1755947)Instructions burned: 31 (million)
% 5.00/1.85 % (1755947)------------------------------
% 5.00/1.85 % (1755947)------------------------------
% 5.00/1.85 % (1755912)Success in time 0.595 s
% 5.00/1.85 % Vampire exiting
%------------------------------------------------------------------------------