%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 10:16:24 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 41
% Syntax : Number of formulae : 364 ( 37 unt; 12 def)
% Number of atoms : 1140 ( 148 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1557 ( 781 ~; 764 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-1 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : group_member(identity_for(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP006-0.ax',identity_in_group) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP006-0.ax',right_identity) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2,X3)
| ~ product(X0,X1,X2,X4)
| X4 = X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP006-0.ax',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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',a_times_a_is_a) ).
fof(f24,axiom,
product(g1,a,b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_b) ).
fof(f25,axiom,
product(g1,b,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_is_b) ).
fof(f26,axiom,
product(g1,a,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_c) ).
fof(f28,axiom,
product(g1,b,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_b_is_c) ).
fof(f29,axiom,
product(g1,b,c,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_c_is_a) ).
fof(f30,axiom,
product(g1,c,b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_b_is_a) ).
fof(f31,axiom,
product(g1,c,c,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_c_is_b) ).
fof(f32,axiom,
product(g2,f,f,f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_times_f_is_f) ).
fof(f33,axiom,
product(g2,f,g,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_times_g_is_g) ).
fof(f34,axiom,
product(g2,g,f,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_times_f_is_g) ).
fof(f35,axiom,
product(g2,f,h,h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_times_h_is_h) ).
fof(f36,axiom,
product(g2,h,f,h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_f_is_h) ).
fof(f37,axiom,
product(g2,g,g,h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_times_g_is_h) ).
fof(f38,axiom,
product(g2,g,h,f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_times_h_is_f) ).
fof(f39,axiom,
product(g2,h,g,f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_g_is_f) ).
fof(f40,axiom,
product(g2,h,h,g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_h_is_g) ).
fof(f41,axiom,
an_isomorphism(a) = f,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d1_in_group1) ).
fof(f48,axiom,
group_member(d2,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_in_group1) ).
fof(f49,axiom,
group_member(d3,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_in_group1) ).
fof(f50,axiom,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox2/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/sandbox2/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(f58,plain,
( a = identity_for(g1)
| b = identity_for(g1)
| c = identity_for(g1) ),
inference(resolution,[],[f20,f1]) ).
fof(f61,definition,
( spl0_1
<=> c = identity_for(g1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f62,plain,
( c != identity_for(g1)
| spl0_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( c = identity_for(g1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f65,definition,
( spl0_2
<=> b = identity_for(g1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f67,plain,
( b = identity_for(g1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f69,definition,
( spl0_3
<=> a = identity_for(g1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f71,plain,
( a = identity_for(g1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f58,f69,f65,f61]) ).
fof(f74,definition,
( spl0_4
<=> c = d3 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f75,plain,
( c != d3
| spl0_4 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( c = d3
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_5
<=> b = d3 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f79,plain,
( b != d3
| spl0_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( b = d3
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_6
<=> a = d3 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f83,plain,
( a != d3
| spl0_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( a = d3
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f57,f82,f78,f74]) ).
fof(f87,definition,
( spl0_7
<=> c = d2 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f88,plain,
( c != d2
| spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( c = d2
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl0_8
<=> b = d2 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f93,plain,
( b = d2
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f95,definition,
( spl0_9
<=> a = d2 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f96,plain,
( a != d2
| spl0_9 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( a = d2
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f56,f95,f91,f87]) ).
fof(f100,definition,
( spl0_10
<=> c = d1 ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f101,plain,
( c != d1
| spl0_10 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
( c = d1
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f104,definition,
( spl0_11
<=> b = d1 ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f105,plain,
( b != d1
| spl0_11 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( b = d1
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl0_12
<=> a = d1 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f109,plain,
( a != d1
| spl0_12 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( a = d1
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f55,f108,f104,f100]) ).
fof(f137,plain,
! [X0] :
( ~ product(g1,a,b,X0)
| b = X0 ),
inference(resolution,[],[f10,f24]) ).
fof(f138,plain,
! [X0] :
( ~ product(g1,a,c,X0)
| c = X0 ),
inference(resolution,[],[f10,f26]) ).
fof(f140,plain,
! [X0] :
( ~ product(g1,b,b,X0)
| c = X0 ),
inference(resolution,[],[f10,f28]) ).
fof(f141,plain,
! [X0] :
( ~ product(g1,b,c,X0)
| a = X0 ),
inference(resolution,[],[f10,f29]) ).
fof(f144,plain,
! [X0] :
( ~ product(g1,c,c,X0)
| b = X0 ),
inference(resolution,[],[f10,f31]) ).
fof(f145,plain,
! [X0] :
( ~ product(g1,d1,d2,X0)
| d3 = X0 ),
inference(resolution,[],[f10,f50]) ).
fof(f237,plain,
( ! [X0] : product(g1,X0,b,X0)
| ~ spl0_2 ),
inference(superposition,[],[f3,f67]) ).
fof(f271,plain,
( a = b
| ~ spl0_2 ),
inference(resolution,[],[f237,f137]) ).
fof(f272,plain,
( b = c
| ~ spl0_2 ),
inference(resolution,[],[f237,f140]) ).
fof(f298,plain,
( a = c
| ~ spl0_2 ),
inference(forward_demodulation,[],[f272,f271]) ).
fof(f388,plain,
( a != d2
| ~ spl0_2
| spl0_7 ),
inference(forward_demodulation,[],[f88,f298]) ).
fof(f389,plain,
( a = d2
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f93,f271]) ).
fof(f395,plain,
( ~ spl0_9
| ~ spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f388,f87,f65,f95]) ).
fof(f396,plain,
( spl0_9
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f389,f91,f65,f95]) ).
fof(f400,plain,
( a = d2
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f89,f298]) ).
fof(f401,plain,
( a != d1
| ~ spl0_2
| spl0_10 ),
inference(forward_demodulation,[],[f101,f298]) ).
fof(f402,plain,
( a = d1
| ~ spl0_2
| ~ spl0_11 ),
inference(forward_demodulation,[],[f106,f271]) ).
fof(f403,plain,
( spl0_9
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f400,f87,f65,f95]) ).
fof(f404,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f401,f100,f65,f108]) ).
fof(f405,plain,
( spl0_12
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f402,f104,f65,f108]) ).
fof(f414,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_5 ),
inference(superposition,[],[f51,f80]) ).
fof(f415,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),g)
| ~ spl0_5 ),
inference(forward_demodulation,[],[f414,f44]) ).
fof(f422,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_6 ),
inference(superposition,[],[f51,f84]) ).
fof(f423,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f)
| ~ spl0_6 ),
inference(forward_demodulation,[],[f422,f42]) ).
fof(f439,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(d3))
| ~ spl0_8 ),
inference(superposition,[],[f51,f93]) ).
fof(f447,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(c))
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f439,f76]) ).
fof(f449,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(b),h)
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f447,f46]) ).
fof(f450,plain,
( ~ product(g2,an_isomorphism(d1),g,h)
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f449,f44]) ).
fof(f472,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(d2),g)
| ~ spl0_5
| ~ spl0_11 ),
inference(superposition,[],[f415,f106]) ).
fof(f473,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(d2),f)
| ~ spl0_6
| ~ spl0_11 ),
inference(superposition,[],[f423,f106]) ).
fof(f475,plain,
( ~ product(g2,an_isomorphism(b),g,h)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(superposition,[],[f450,f106]) ).
fof(f478,plain,
( ~ product(g2,g,g,h)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f475,f44]) ).
fof(f480,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(c),f)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f473,f89]) ).
fof(f485,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f478,f37]) ).
fof(f486,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f487,plain,
( ~ product(g2,an_isomorphism(b),h,f)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f480,f46]) ).
fof(f492,plain,
( ~ product(g2,g,h,f)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f487,f44]) ).
fof(f496,plain,
( $false
| ~ spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f492,f38]) ).
fof(f497,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f496]) ).
fof(f500,plain,
( a != c
| spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f88,f97]) ).
fof(f503,plain,
( ~ product(g2,an_isomorphism(b),an_isomorphism(a),g)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f472,f97]) ).
fof(f508,plain,
( ~ product(g2,an_isomorphism(b),f,g)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f503,f42]) ).
fof(f512,plain,
( ~ product(g2,g,f,g)
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f508,f44]) ).
fof(f515,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f512,f34]) ).
fof(f516,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f518,plain,
( product(g1,c,d2,d3)
| ~ spl0_10 ),
inference(superposition,[],[f50,f102]) ).
fof(f519,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_10 ),
inference(superposition,[],[f51,f102]) ).
fof(f530,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(c))
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f519,f76]) ).
fof(f537,plain,
( ~ product(g2,h,an_isomorphism(d2),h)
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f530,f46]) ).
fof(f542,plain,
( ~ product(g2,h,an_isomorphism(a),h)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f537,f97]) ).
fof(f545,plain,
( ~ product(g2,h,f,h)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f542,f42]) ).
fof(f546,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f545,f36]) ).
fof(f547,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f548,plain,
( b != c
| spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f75,f80]) ).
fof(f563,plain,
( b != c
| ~ spl0_10
| spl0_11 ),
inference(forward_demodulation,[],[f105,f102]) ).
fof(f568,plain,
( ! [X0] : product(g1,X0,c,X0)
| ~ spl0_1 ),
inference(superposition,[],[f3,f63]) ).
fof(f578,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),an_isomorphism(d3))
| ~ spl0_7 ),
inference(superposition,[],[f51,f89]) ).
fof(f583,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),an_isomorphism(b))
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f578,f80]) ).
fof(f587,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),g)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f583,f44]) ).
fof(f591,plain,
( ~ product(g2,an_isomorphism(d1),h,g)
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f587,f46]) ).
fof(f594,plain,
( ~ product(g2,an_isomorphism(c),h,g)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f591,f102]) ).
fof(f595,plain,
( ~ product(g2,h,h,g)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f594,f46]) ).
fof(f596,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f595,f40]) ).
fof(f597,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f598,plain,
( a != b
| spl0_5
| ~ spl0_6 ),
inference(forward_demodulation,[],[f79,f84]) ).
fof(f599,plain,
( a != c
| spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f75,f84]) ).
fof(f601,plain,
( product(g1,c,d2,a)
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f518,f84]) ).
fof(f605,plain,
( product(g1,c,c,a)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f601,f89]) ).
fof(f637,plain,
( a = c
| ~ spl0_1 ),
inference(resolution,[],[f568,f138]) ).
fof(f638,plain,
( a = b
| ~ spl0_1 ),
inference(resolution,[],[f568,f141]) ).
fof(f639,plain,
( b = c
| ~ spl0_1 ),
inference(resolution,[],[f568,f144]) ).
fof(f643,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f639,f563]) ).
fof(f644,plain,
( ~ spl0_1
| ~ spl0_10
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f643]) ).
fof(f647,plain,
( $false
| ~ spl0_1
| spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f637,f599]) ).
fof(f648,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f647]) ).
fof(f650,plain,
( a != c
| spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f62,f71]) ).
fof(f653,plain,
( ! [X0] : product(g1,X0,a,X0)
| ~ spl0_3 ),
inference(superposition,[],[f3,f71]) ).
fof(f656,plain,
( a = b
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(resolution,[],[f605,f144]) ).
fof(f660,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f656,f598]) ).
fof(f661,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f660]) ).
fof(f664,plain,
( product(g1,a,d2,d3)
| ~ spl0_12 ),
inference(superposition,[],[f50,f110]) ).
fof(f673,plain,
( product(g1,a,d2,a)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f664,f84]) ).
fof(f678,plain,
( product(g1,a,c,a)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f673,f89]) ).
fof(f726,plain,
( a = c
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(resolution,[],[f678,f138]) ).
fof(f730,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f726,f599]) ).
fof(f731,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f730]) ).
fof(f735,plain,
( ! [X0] :
( a = X0
| ~ product(g1,d1,d2,X0) )
| ~ spl0_6 ),
inference(forward_demodulation,[],[f145,f84]) ).
fof(f746,plain,
( a != b
| ~ spl0_8
| spl0_9 ),
inference(forward_demodulation,[],[f96,f93]) ).
fof(f749,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_10 ),
inference(superposition,[],[f51,f102]) ).
fof(f755,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f749,f84]) ).
fof(f760,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(d2),f)
| ~ spl0_6
| ~ spl0_10 ),
inference(forward_demodulation,[],[f755,f42]) ).
fof(f763,plain,
( ~ product(g2,an_isomorphism(c),an_isomorphism(b),f)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f760,f93]) ).
fof(f766,plain,
( ~ product(g2,an_isomorphism(c),g,f)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f763,f44]) ).
fof(f767,plain,
( ~ product(g2,h,g,f)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f766,f46]) ).
fof(f768,plain,
( $false
| ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f767,f39]) ).
fof(f769,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f768]) ).
fof(f802,plain,
( ! [X0] :
( ~ product(g1,d1,a,X0)
| a = X0 )
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f735,f97]) ).
fof(f803,plain,
( ! [X0] :
( ~ product(g1,c,a,X0)
| a = X0 )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f802,f102]) ).
fof(f807,plain,
( a = c
| ~ spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(resolution,[],[f803,f653]) ).
fof(f810,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f807,f500]) ).
fof(f811,plain,
( ~ spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f810]) ).
fof(f815,plain,
( ! [X0] :
( ~ product(g1,d1,a,X0)
| d3 = X0 )
| ~ spl0_9 ),
inference(forward_demodulation,[],[f145,f97]) ).
fof(f820,plain,
( ! [X0] :
( ~ product(g1,c,a,X0)
| d3 = X0 )
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f815,f102]) ).
fof(f838,plain,
( a != b
| ~ spl0_5
| spl0_6 ),
inference(forward_demodulation,[],[f83,f80]) ).
fof(f839,plain,
( ! [X0] :
( ~ product(g1,c,a,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f820,f80]) ).
fof(f841,plain,
( b = c
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10 ),
inference(resolution,[],[f839,f653]) ).
fof(f844,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f841,f563]) ).
fof(f845,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f844]) ).
fof(f849,plain,
( ! [X0] :
( ~ product(g1,c,d2,X0)
| d3 = X0 )
| ~ spl0_10 ),
inference(forward_demodulation,[],[f145,f102]) ).
fof(f854,plain,
( ! [X0] :
( b = X0
| ~ product(g1,c,d2,X0) )
| ~ spl0_5
| ~ spl0_10 ),
inference(forward_demodulation,[],[f849,f80]) ).
fof(f871,plain,
( ! [X0] :
( ~ product(g1,c,b,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f854,f93]) ).
fof(f872,plain,
( a = b
| ~ spl0_5
| ~ spl0_8
| ~ spl0_10 ),
inference(resolution,[],[f871,f30]) ).
fof(f875,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f872,f746]) ).
fof(f876,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f875]) ).
fof(f885,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_12 ),
inference(superposition,[],[f51,f110]) ).
fof(f890,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(b))
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f885,f80]) ).
fof(f894,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),g)
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f890,f44]) ).
fof(f896,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(b),g)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f894,f93]) ).
fof(f897,plain,
( ~ product(g2,an_isomorphism(a),g,g)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f896,f44]) ).
fof(f898,plain,
( ~ product(g2,f,g,g)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f897,f42]) ).
fof(f899,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f898,f33]) ).
fof(f900,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f899]) ).
fof(f901,plain,
( ! [X0] :
( ~ product(g1,a,d2,X0)
| d3 = X0 )
| ~ spl0_12 ),
inference(forward_demodulation,[],[f145,f110]) ).
fof(f905,plain,
( ! [X0] :
( b = X0
| ~ product(g1,a,d2,X0) )
| ~ spl0_5
| ~ spl0_12 ),
inference(forward_demodulation,[],[f901,f80]) ).
fof(f921,plain,
( ! [X0] :
( ~ product(g1,a,c,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f905,f89]) ).
fof(f922,plain,
( b = c
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(resolution,[],[f921,f26]) ).
fof(f928,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f922,f548]) ).
fof(f929,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f928]) ).
fof(f978,plain,
( ! [X0] :
( ~ product(g1,a,a,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f905,f97]) ).
fof(f979,plain,
( a = b
| ~ spl0_5
| ~ spl0_9
| ~ spl0_12 ),
inference(resolution,[],[f978,f23]) ).
fof(f989,plain,
( $false
| ~ spl0_5
| spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f979,f838]) ).
fof(f990,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f989]) ).
fof(f992,plain,
( ! [X0] :
( b = X0
| ~ product(g1,d1,d2,X0) )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f145,f80]) ).
fof(f1018,plain,
( a != b
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f109,f106]) ).
fof(f1019,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_8 ),
inference(forward_demodulation,[],[f992,f93]) ).
fof(f1020,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1019,f106]) ).
fof(f1021,plain,
( b = c
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11 ),
inference(resolution,[],[f1020,f28]) ).
fof(f1025,plain,
( $false
| spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1021,f548]) ).
fof(f1026,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1025]) ).
fof(f1028,plain,
( ! [X0] :
( ~ product(g1,b,d2,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f992,f106]) ).
fof(f1050,plain,
( ! [X0] :
( ~ product(g1,b,c,X0)
| b = X0 )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1028,f89]) ).
fof(f1051,plain,
( a = b
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(resolution,[],[f1050,f29]) ).
fof(f1054,plain,
( $false
| ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1051,f838]) ).
fof(f1055,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1054]) ).
fof(f1057,plain,
( ! [X0] :
( ~ product(g1,d1,c,X0)
| d3 = X0 )
| ~ spl0_7 ),
inference(forward_demodulation,[],[f145,f89]) ).
fof(f1062,plain,
( ! [X0] :
( ~ product(g1,b,c,X0)
| d3 = X0 )
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1057,f106]) ).
fof(f1096,plain,
( b != c
| ~ spl0_4
| spl0_5 ),
inference(forward_demodulation,[],[f79,f76]) ).
fof(f1097,plain,
( a != c
| ~ spl0_4
| spl0_6 ),
inference(forward_demodulation,[],[f83,f76]) ).
fof(f1104,plain,
( ! [X0] :
( ~ product(g1,b,c,X0)
| c = X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1062,f76]) ).
fof(f1105,plain,
( a = c
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11 ),
inference(resolution,[],[f1104,f29]) ).
fof(f1108,plain,
( $false
| spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1105,f650]) ).
fof(f1109,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1108]) ).
fof(f1112,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f638,f1018]) ).
fof(f1113,plain,
( ~ spl0_1
| ~ spl0_11
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f1112]) ).
fof(f1117,plain,
( ! [X0] :
( ~ product(g1,b,d2,X0)
| d3 = X0 )
| ~ spl0_11 ),
inference(forward_demodulation,[],[f145,f106]) ).
fof(f1122,plain,
( ! [X0] :
( c = X0
| ~ product(g1,b,d2,X0) )
| ~ spl0_4
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1117,f76]) ).
fof(f1140,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| c = X0 )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1122,f97]) ).
fof(f1141,plain,
( b = c
| ~ spl0_4
| ~ spl0_9
| ~ spl0_11 ),
inference(resolution,[],[f1140,f25]) ).
fof(f1147,plain,
( $false
| ~ spl0_4
| spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1141,f1096]) ).
fof(f1148,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1147]) ).
fof(f1152,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| d3 = X0 )
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1117,f97]) ).
fof(f1173,plain,
( ! [X0] :
( ~ product(g1,b,a,X0)
| a = X0 )
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1152,f84]) ).
fof(f1174,plain,
( a = b
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11 ),
inference(resolution,[],[f1173,f25]) ).
fof(f1180,plain,
( $false
| ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f1174,f1018]) ).
fof(f1181,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f1180]) ).
fof(f1186,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3))
| ~ spl0_12 ),
inference(superposition,[],[f51,f110]) ).
fof(f1189,plain,
( ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(a))
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1186,f84]) ).
fof(f1191,plain,
( ~ product(g2,f,an_isomorphism(d2),f)
| ~ spl0_6
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1189,f42]) ).
fof(f1193,plain,
( ~ product(g2,f,an_isomorphism(a),f)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1191,f97]) ).
fof(f1194,plain,
( ~ product(g2,f,f,f)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1193,f42]) ).
fof(f1195,plain,
( $false
| ~ spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1194,f32]) ).
fof(f1196,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1195]) ).
fof(f1199,plain,
( ! [X0] :
( a = X0
| ~ product(g1,b,d2,X0) )
| ~ spl0_6
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1117,f84]) ).
fof(f1223,plain,
( ! [X0] :
( ~ product(g1,b,b,X0)
| a = X0 )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1199,f93]) ).
fof(f1224,plain,
( a = c
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(resolution,[],[f1223,f28]) ).
fof(f1228,plain,
( $false
| spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f1224,f599]) ).
fof(f1229,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f1228]) ).
fof(f1231,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f145,f93]) ).
fof(f1236,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| d3 = X0 )
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1231,f110]) ).
fof(f1240,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| a = X0 )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1236,f84]) ).
fof(f1243,plain,
( a = b
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(resolution,[],[f1240,f24]) ).
fof(f1249,plain,
( $false
| spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1243,f598]) ).
fof(f1250,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1249]) ).
fof(f1252,plain,
( ! [X0] :
( ~ product(g1,a,d2,X0)
| d3 = X0 )
| ~ spl0_12 ),
inference(forward_demodulation,[],[f145,f110]) ).
fof(f1282,plain,
( ! [X0] :
( ~ product(g1,a,a,X0)
| d3 = X0 )
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1252,f97]) ).
fof(f1283,plain,
( ! [X0] :
( ~ product(g1,a,a,X0)
| c = X0 )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1282,f76]) ).
fof(f1284,plain,
( a = c
| ~ spl0_4
| ~ spl0_9
| ~ spl0_12 ),
inference(resolution,[],[f1283,f23]) ).
fof(f1294,plain,
( $false
| ~ spl0_4
| spl0_7
| ~ spl0_9
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1284,f500]) ).
fof(f1295,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_9
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1294]) ).
fof(f1302,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),an_isomorphism(d3))
| ~ spl0_7 ),
inference(superposition,[],[f51,f89]) ).
fof(f1307,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(c),an_isomorphism(c))
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1302,f76]) ).
fof(f1312,plain,
( ~ product(g2,an_isomorphism(d1),h,h)
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1307,f46]) ).
fof(f1316,plain,
( ~ product(g2,an_isomorphism(a),h,h)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1312,f110]) ).
fof(f1317,plain,
( ~ product(g2,f,h,h)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1316,f42]) ).
fof(f1318,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1317,f35]) ).
fof(f1319,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1318]) ).
fof(f1320,plain,
( ! [X0] :
( ~ product(g1,d1,c,X0)
| d3 = X0 )
| ~ spl0_7 ),
inference(forward_demodulation,[],[f145,f89]) ).
fof(f1323,plain,
( ! [X0] :
( c = X0
| ~ product(g1,d1,c,X0) )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f1320,f76]) ).
fof(f1339,plain,
( ! [X0] :
( ~ product(g1,c,c,X0)
| c = X0 )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1323,f102]) ).
fof(f1340,plain,
( b = c
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10 ),
inference(resolution,[],[f1339,f31]) ).
fof(f1344,plain,
( $false
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f1340,f1096]) ).
fof(f1345,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f1344]) ).
fof(f1346,plain,
( ! [X0] :
( ~ product(g1,c,d2,X0)
| d3 = X0 )
| ~ spl0_10 ),
inference(forward_demodulation,[],[f145,f102]) ).
fof(f1349,plain,
( ! [X0] :
( c = X0
| ~ product(g1,c,d2,X0) )
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1346,f76]) ).
fof(f1365,plain,
( ! [X0] :
( ~ product(g1,c,b,X0)
| c = X0 )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f1349,f93]) ).
fof(f1366,plain,
( a = c
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(resolution,[],[f1365,f30]) ).
fof(f1369,plain,
( $false
| ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f1366,f1097]) ).
fof(f1370,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f1369]) ).
fof(f1372,plain,
( ! [X0] :
( ~ product(g1,d1,b,X0)
| d3 = X0 )
| ~ spl0_8 ),
inference(forward_demodulation,[],[f145,f93]) ).
fof(f1375,plain,
( ! [X0] :
( c = X0
| ~ product(g1,d1,b,X0) )
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f1372,f76]) ).
fof(f1391,plain,
( ! [X0] :
( ~ product(g1,a,b,X0)
| c = X0 )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1375,f110]) ).
fof(f1392,plain,
( b = c
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12 ),
inference(resolution,[],[f1391,f24]) ).
fof(f1398,plain,
( $false
| ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f1392,f1096]) ).
fof(f1399,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f1398]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f72]) ).
cnf(s2,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f85]) ).
cnf(s3,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f98]) ).
cnf(s4,plain,
( spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
( ~ spl0_2
| spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f395]) ).
cnf(s13,plain,
( ~ spl0_2
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f396]) ).
cnf(s14,plain,
( ~ spl0_2
| ~ spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f403]) ).
cnf(s15,plain,
( ~ spl0_2
| spl0_10
| ~ spl0_12 ),
inference(sat_conversion,[],[f404]) ).
cnf(s16,plain,
( ~ spl0_2
| ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f405]) ).
cnf(s17,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f486]) ).
cnf(s18,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f497]) ).
cnf(s19,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f516]) ).
cnf(s22,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f547]) ).
cnf(s25,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f597]) ).
cnf(s26,plain,
( ~ spl0_1
| ~ spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f644]) ).
cnf(s28,plain,
( ~ spl0_1
| spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f648]) ).
cnf(s29,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f661]) ).
cnf(s33,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f731]) ).
cnf(s37,plain,
( ~ spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f769]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_6
| spl0_7
| ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f811]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f845]) ).
cnf(s42,plain,
( ~ spl0_5
| ~ spl0_8
| spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f876]) ).
cnf(s44,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f900]) ).
cnf(s46,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f929]) ).
cnf(s51,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f990]) ).
cnf(s52,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f1026]) ).
cnf(s53,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f1055]) ).
cnf(s55,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f1109]) ).
cnf(s56,plain,
( ~ spl0_1
| ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f1113]) ).
cnf(s59,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_9
| ~ spl0_11 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s61,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f1181]) ).
cnf(s62,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f1196]) ).
cnf(s63,plain,
( spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_11 ),
inference(sat_conversion,[],[f1229]) ).
cnf(s65,plain,
( spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f1250]) ).
cnf(s68,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_9
| ~ spl0_12 ),
inference(sat_conversion,[],[f1295]) ).
cnf(s72,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(sat_conversion,[],[f1319]) ).
cnf(s73,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f1345]) ).
cnf(s74,plain,
( ~ spl0_4
| spl0_6
| ~ spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f1370]) ).
cnf(s76,plain,
( ~ spl0_4
| spl0_5
| ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f1399]) ).
cnf(s77,plain,
( ~ spl0_9
| spl0_7
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s4,s61,s62,s38]) ).
cnf(s78,plain,
( ~ spl0_8
| spl0_5
| spl0_4 ),
inference(rat,[],[s4,s63,s65,s37,s2]) ).
cnf(s79,plain,
( spl0_7
| spl0_8
| ~ spl0_6
| ~ spl0_3 ),
inference(rat,[],[s3,s77]) ).
cnf(s80,plain,
( spl0_5
| spl0_4
| ~ spl0_3 ),
inference(rat,[],[s4,s33,s29,s18,s79,s78,s2]) ).
cnf(s81,plain,
( spl0_7
| ~ spl0_6
| spl0_4
| ~ spl0_3 ),
inference(rat,[],[s4,s63,s42,s44,s79,s77,s80]) ).
cnf(s82,plain,
( ~ spl0_6
| spl0_4
| ~ spl0_3 ),
inference(rat,[],[s4,s46,s18,s25,s81,s80]) ).
cnf(s83,plain,
( ~ spl0_12
| spl0_7
| spl0_6
| ~ spl0_5 ),
inference(rat,[],[s3,s51,s44]) ).
cnf(s84,plain,
( ~ spl0_11
| spl0_7
| ~ spl0_5
| spl0_4 ),
inference(rat,[],[s3,s52,s19]) ).
cnf(s85,plain,
( spl0_7
| spl0_4
| ~ spl0_3 ),
inference(rat,[],[s3,s42,s40,s4,s84,s83,s80,s82]) ).
cnf(s86,plain,
( spl0_4
| ~ spl0_3 ),
inference(rat,[],[s4,s53,s46,s25,s85,s82,s80]) ).
cnf(s87,plain,
( ~ spl0_11
| spl0_7
| ~ spl0_5
| ~ spl0_4 ),
inference(rat,[],[s3,s17,s19]) ).
cnf(s88,plain,
( spl0_7
| spl0_6
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s3,s42,s40,s4,s87,s83,s86]) ).
cnf(s89,plain,
( spl0_6
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s4,s53,s25,s72,s88,s86]) ).
cnf(s90,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s4,s42,s44,s87,s79,s77,s86,s89]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(rat,[],[s4,s18,s25,s72,s90,s89,s86]) ).
cnf(s92,plain,
( ~ spl0_12
| spl0_7
| ~ spl0_3 ),
inference(rat,[],[s3,s76,s68,s86,s91]) ).
cnf(s93,plain,
( ~ spl0_11
| spl0_7
| ~ spl0_3 ),
inference(rat,[],[s3,s59,s17,s86,s91]) ).
cnf(s94,plain,
( spl0_7
| spl0_6
| ~ spl0_3 ),
inference(rat,[],[s3,s74,s22,s4,s93,s92,s86]) ).
cnf(s95,plain,
( ~ spl0_7
| ~ spl0_3
| spl0_1 ),
inference(rat,[],[s4,s73,s55,s72,s86,s91]) ).
cnf(s96,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s37,s79,s4,s94,s93,s92]) ).
cnf(s97,plain,
( ~ spl0_3
| spl0_1 ),
inference(rat,[],[s96,s95]) ).
cnf(s98,plain,
( spl0_7
| ~ spl0_2 ),
inference(rat,[],[s13,s3,s12]) ).
cnf(s99,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s16,s4,s15]) ).
cnf(s100,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s2,s22,s29,s25,s99,s14]) ).
cnf(s101,plain,
~ spl0_2,
inference(rat,[],[s100,s98]) ).
cnf(s102,plain,
( spl0_4
| ~ spl0_12
| spl0_7 ),
inference(rat,[],[s83,s2,s28,s1,s96,s101]) ).
cnf(s103,plain,
( ~ spl0_4
| ~ spl0_12
| spl0_7 ),
inference(rat,[],[s76,s44,s3,s68]) ).
cnf(s104,plain,
( ~ spl0_12
| spl0_7 ),
inference(rat,[],[s103,s102]) ).
cnf(s105,plain,
( spl0_12
| ~ spl0_1 ),
inference(rat,[],[s26,s4,s56]) ).
cnf(s106,plain,
spl0_7,
inference(rat,[],[s105,s104,s1,s96,s101]) ).
cnf(s107,plain,
( spl0_4
| ~ spl0_12 ),
inference(rat,[],[s2,s46,s33,s106]) ).
cnf(s108,plain,
~ spl0_12,
inference(rat,[],[s107,s72,s106]) ).
cnf(s109,plain,
~ spl0_1,
inference(rat,[],[s105,s108]) ).
cnf(s110,plain,
~ spl0_3,
inference(rat,[],[s97,s109]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s1,s101,s109,s110]) ).
fof(f1401,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n015.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:17:45 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 % (1384323)Will run a generic schedule for satisfiability detection.
% 0.19/0.50 % (1384334)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1691083482:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.50 % (1384329)% WARNING: option uhcvi not known.
% 0.19/0.50 % (1384328)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1555913761_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.50 % (1384330)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3947066623:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.50 % (1384329)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4047138033:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.50 % (1384331)dis+10_1_sil=32000:sp=arity:random_seed=1304524024:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.50 % (1384332)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1462366750:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.50 % (1384333)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=149131144:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.50 % TRYING [1]
% 0.19/0.50 % TRYING [2]
% 0.19/0.50 % TRYING [3]
% 0.19/0.50 % TRYING [4]
% 0.19/0.50 % (1384331) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1384323-1384331"...
% 0.19/0.50 % (1384331)...printing done.
% 0.19/0.50 % (1384331)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (1384331)------------------------------
% 0.19/0.51 % (1384331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.51 % (1384331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.51 % (1384331)CaDiCaL version: 2.1.3
% 0.19/0.51 % (1384331)Termination reason: Refutation
% 0.19/0.51 % (1384331)Time elapsed: 0.028 s
% 0.19/0.51 % (1384331)Peak memory usage: 12 MB
% 0.19/0.51 % (1384331)Instructions burned: 44 (million)
% 0.19/0.51 % (1384323)Success in time 0.062 s
% 0.19/0.51 % Vampire exiting
%------------------------------------------------------------------------------