%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP113-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 12:32:32 PM UTC 2026
% Result : Unsatisfiable 2.00s 0.88s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 95
% Syntax : Number of formulae : 569 ( 45 unt; 79 def)
% Number of atoms : 1624 ( 628 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 1801 ( 746 ~; 976 |; 0 &)
% ( 79 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 81 ( 79 usr; 80 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : multiply(X,inverse(X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [X] :
( X = identity
| X = c
| X = b
| X = a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
a != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
b != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
c != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(c,c) != identity
| multiply(b,b) != identity
| multiply(a,a) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(a,multiply(a,multiply(a,a))) != identity
| multiply(a,multiply(a,a)) != c
| multiply(a,a) != b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(b,multiply(b,multiply(b,b))) != identity
| multiply(b,multiply(b,b)) != a
| multiply(b,b) != c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(c,multiply(c,multiply(c,c))) != identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0] :
( X0 = identity
| X0 = c
| X0 = b
| X0 = a ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
a != c,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
a != identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
b != c,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
b != identity,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
c != identity,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
( multiply(c,c) != identity
| multiply(b,b) != identity
| multiply(a,a) != identity ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
( multiply(a,multiply(a,multiply(a,a))) != identity
| multiply(a,multiply(a,a)) != c
| multiply(a,a) != b ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
( multiply(b,multiply(b,multiply(b,b))) != identity
| multiply(b,multiply(b,b)) != a
| multiply(b,b) != c ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
( multiply(c,multiply(c,multiply(c,c))) != identity
| multiply(c,multiply(c,c)) != b
| multiply(c,c) != a ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
( sQ0_spl
<=> multiply(a,a) = identity ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( ~ sQ0_spl
| multiply(a,a) = identity ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ1_spl
<=> multiply(b,b) = identity ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ1_spl
| multiply(b,b) = identity ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ2_spl
<=> multiply(c,c) = identity ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ2_spl
| multiply(c,c) = identity ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f41,plain,
( sQ2_spl
| multiply(c,c) != identity ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f33,f36,f39]) ).
fof(f43,definition,
( sQ3_spl
<=> multiply(a,a) = b ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ3_spl
| multiply(a,a) = b ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f45,plain,
( sQ3_spl
| multiply(a,a) != b ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,definition,
( sQ4_spl
<=> multiply(a,multiply(a,a)) = c ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ4_spl
| multiply(a,multiply(a,a)) = c ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f48,plain,
( sQ4_spl
| multiply(a,multiply(a,a)) != c ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ5_spl
<=> multiply(a,multiply(a,multiply(a,a))) = identity ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( sQ5_spl
| multiply(a,multiply(a,multiply(a,a))) != identity ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f30,f43,f46,f49]) ).
fof(f53,definition,
( sQ6_spl
<=> multiply(b,b) = c ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ6_spl
| multiply(b,b) = c ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( sQ6_spl
| multiply(b,b) != c ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ7_spl
<=> multiply(b,multiply(b,b)) = a ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ7_spl
| multiply(b,multiply(b,b)) != a ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ8_spl
<=> multiply(b,multiply(b,multiply(b,b))) = identity ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ8_spl
| multiply(b,multiply(b,multiply(b,b))) = identity ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f61,plain,
( sQ8_spl
| multiply(b,multiply(b,multiply(b,b))) != identity ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f31,f53,f56,f59]) ).
fof(f63,definition,
( sQ9_spl
<=> multiply(c,c) = a ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ9_spl
| multiply(c,c) = a ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ9_spl
| multiply(c,c) != a ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ10_spl
<=> multiply(c,multiply(c,c)) = b ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ10_spl
| multiply(c,multiply(c,c)) = b ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ10_spl
| multiply(c,multiply(c,c)) != b ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ11_spl
<=> multiply(c,multiply(c,multiply(c,c))) = identity ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ11_spl
| multiply(c,multiply(c,multiply(c,c))) = identity ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f71,plain,
( sQ11_spl
| multiply(c,multiply(c,multiply(c,c))) != identity ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f32,f63,f66,f69]) ).
fof(f82,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f20,f18]) ).
fof(f84,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f85,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f84]) ).
fof(f87,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(paramodulation,[status(thm)],[f19,f21]) ).
fof(f92,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f21,f19]) ).
fof(f93,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f17,f92]) ).
fof(f94,plain,
( b = identity
| b = b
| b = a ),
inference(resolution,[status(thm)],[f22,f26]) ).
fof(f95,plain,
( a = identity
| a = b
| a = a ),
inference(resolution,[status(thm)],[f22,f24]) ).
fof(f96,plain,
( sQ6_spl
| multiply(b,b) = identity
| multiply(b,b) = b
| multiply(b,b) = a ),
inference(resolution,[status(thm)],[f22,f55]) ).
fof(f97,plain,
( identity = identity
| identity = b
| identity = a ),
inference(resolution,[status(thm)],[f22,f28]) ).
fof(f98,plain,
! [X0,X1] :
( X1 = identity
| X1 = b
| X1 = a
| X0 = identity
| X0 = X1
| X0 = b
| X0 = a ),
inference(paramodulation,[status(thm)],[f22,f22]) ).
fof(f106,plain,
! [X0] :
( sQ9_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(c,X0) != a ),
inference(paramodulation,[status(thm)],[f22,f65]) ).
fof(f109,plain,
! [X0] :
( X0 = b
| c != b
| X0 = identity
| X0 = a ),
inference(equality_factoring,[status(thm)],[f22]) ).
fof(f111,definition,
( sQ12_spl
<=> b = a ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ12_spl
| b = a ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
( sQ13_spl
<=> b = b ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f117,definition,
( sQ14_spl
<=> b = identity ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ14_spl
| b = identity ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f111,f114,f117]) ).
fof(f121,definition,
( sQ15_spl
<=> a = a ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f124,definition,
( sQ16_spl
<=> a = identity ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ16_spl
| a = identity ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ16_spl
| sQ12_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f95,f121,f111,f124]) ).
fof(f128,definition,
( sQ17_spl
<=> multiply(b,b) = a ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ17_spl
| multiply(b,b) = a ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,definition,
( sQ18_spl
<=> multiply(b,b) = b ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ18_spl
| multiply(b,b) = b ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ6_spl
| sQ1_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f96,f128,f131,f36,f53]) ).
fof(f135,definition,
( sQ19_spl
<=> identity = identity ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ19_spl
| sQ14_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f97,f124,f117,f135]) ).
fof(f139,definition,
! [X0] :
( sQ20_spl
<=> ( X0 = a
| X0 = identity
| X0 = b ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ20_spl
| X0 = a
| X0 = identity
| X0 = b ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
( sQ21_spl
<=> c = a ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ21_spl
| c = a ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f146,definition,
( sQ22_spl
<=> c = b ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( ~ sQ22_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f109,f139,f146]) ).
fof(f150,definition,
( sQ23_spl
<=> c = identity ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ23_spl
| c = identity ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f154,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f27]) ).
fof(f155,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f25]) ).
fof(f157,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f23]) ).
fof(f159,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f174,plain,
( ~ sQ20_spl
| c = a
| c = identity ),
inference(resolution,[status(thm)],[f140,f26]) ).
fof(f184,definition,
( sQ24_spl
<=> multiply(a,a) = a ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ24_spl
| multiply(a,a) = a ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f186,plain,
( sQ24_spl
| multiply(a,a) != a ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f188,definition,
( sQ25_spl
<=> multiply(c,multiply(c,c)) = identity ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ25_spl
| multiply(c,multiply(c,c)) = identity ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ26_spl
<=> multiply(c,multiply(c,c)) = a ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ26_spl
| multiply(c,multiply(c,c)) = a ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f196,plain,
( ~ sQ20_spl
| sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f174,f150,f142,f139]) ).
fof(f197,definition,
! [X0] :
( sQ27_spl
<=> ( X0 = identity
| X0 = a ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f198,plain,
! [X0] :
( ~ sQ27_spl
| X0 = identity
| X0 = a ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f208,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f28]) ).
fof(f209,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f210,plain,
( ~ sQ3_spl
| ~ sQ24_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f185,f44]) ).
fof(f211,plain,
( ~ sQ3_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f23]) ).
fof(f212,plain,
( ~ sQ3_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f224,plain,
( sQ8_spl
| ~ sQ1_spl
| multiply(b,multiply(b,identity)) != identity ),
inference(backward_demodulation,[status(thm)],[f37,f61]) ).
fof(f228,plain,
( sQ8_spl
| ~ sQ1_spl
| multiply(b,b) != identity ),
inference(forward_demodulation,[status(thm)],[f20,f224]) ).
fof(f229,plain,
( sQ8_spl
| ~ sQ1_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f37,f228]) ).
fof(f230,plain,
( sQ8_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f229]) ).
fof(f231,plain,
( sQ8_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f238,plain,
( ~ sQ27_spl
| b = identity ),
inference(resolution,[status(thm)],[f198,f23]) ).
fof(f248,plain,
( ~ sQ27_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f238,f117,f197]) ).
fof(f260,plain,
( sQ4_spl
| multiply(a,multiply(a,a)) = identity
| multiply(a,multiply(a,a)) = b
| multiply(a,multiply(a,a)) = a ),
inference(resolution,[status(thm)],[f22,f48]) ).
fof(f265,plain,
! [X0] :
( sQ2_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(c,X0) != identity ),
inference(paramodulation,[status(thm)],[f22,f41]) ).
fof(f266,plain,
! [X0] :
( sQ2_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(X0,c) != identity ),
inference(paramodulation,[status(thm)],[f22,f41]) ).
fof(f275,definition,
( sQ29_spl
<=> multiply(a,multiply(a,a)) = a ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ29_spl
| multiply(a,multiply(a,a)) = a ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f277,plain,
( sQ29_spl
| multiply(a,multiply(a,a)) != a ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,definition,
( sQ30_spl
<=> multiply(a,multiply(a,a)) = b ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( ~ sQ30_spl
| multiply(a,multiply(a,a)) = b ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,definition,
( sQ31_spl
<=> multiply(a,multiply(a,a)) = identity ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ31_spl
| multiply(a,multiply(a,a)) = identity ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( sQ4_spl
| sQ31_spl
| sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f260,f275,f278,f281,f46]) ).
fof(f300,plain,
( sQ5_spl
| ~ sQ4_spl
| multiply(a,c) != identity ),
inference(backward_demodulation,[status(thm)],[f47,f51]) ).
fof(f318,plain,
! [X0] :
( ~ sQ3_spl
| multiply(b,X0) = multiply(a,multiply(a,X0)) ),
inference(paramodulation,[status(thm)],[f44,f19]) ).
fof(f322,plain,
( ~ sQ11_spl
| multiply(c,multiply(c,c)) = identity
| multiply(c,multiply(c,c)) = b
| multiply(c,multiply(c,c)) = a
| multiply(c,c) = identity ),
inference(paramodulation,[status(thm)],[f22,f70]) ).
fof(f324,plain,
( ~ sQ11_spl
| multiply(c,c) = identity
| multiply(c,c) = b
| multiply(c,c) = a
| multiply(c,multiply(c,c)) = identity ),
inference(paramodulation,[status(thm)],[f22,f70]) ).
fof(f327,plain,
! [X0] :
( ~ sQ11_spl
| multiply(identity,X0) = multiply(c,multiply(multiply(c,multiply(c,c)),X0)) ),
inference(paramodulation,[status(thm)],[f70,f19]) ).
fof(f331,definition,
( sQ33_spl
<=> multiply(c,multiply(c,multiply(c,c))) = b ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ33_spl
| multiply(c,multiply(c,multiply(c,c))) = b ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f335,plain,
( ~ sQ11_spl
| sQ25_spl
| sQ10_spl
| sQ26_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f322,f39,f191,f66,f188,f69]) ).
fof(f336,definition,
( sQ34_spl
<=> multiply(c,c) = b ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ34_spl
| multiply(c,c) = b ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f338,plain,
( sQ34_spl
| multiply(c,c) != b ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,plain,
( ~ sQ11_spl
| sQ2_spl
| sQ34_spl
| sQ9_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f324,f188,f63,f336,f39,f69]) ).
fof(f340,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(c,multiply(multiply(c,multiply(c,c)),X0)) ),
inference(forward_demodulation,[status(thm)],[f17,f327]) ).
fof(f341,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(c,multiply(c,multiply(multiply(c,c),X0))) ),
inference(forward_demodulation,[status(thm)],[f19,f340]) ).
fof(f342,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(c,multiply(c,multiply(c,multiply(c,X0)))) ),
inference(forward_demodulation,[status(thm)],[f19,f341]) ).
fof(f350,plain,
! [X0] :
( ~ sQ34_spl
| multiply(b,X0) = multiply(c,multiply(c,X0)) ),
inference(paramodulation,[status(thm)],[f337,f19]) ).
fof(f358,definition,
( sQ35_spl
<=> multiply(c,b) = a ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ35_spl
| multiply(c,b) = a ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,definition,
( sQ36_spl
<=> multiply(c,b) = b ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ36_spl
| multiply(c,b) = b ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
( sQ37_spl
<=> multiply(c,b) = identity ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( ~ sQ37_spl
| multiply(c,b) = identity ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f373,definition,
( sQ38_spl
<=> multiply(a,b) = a ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( ~ sQ38_spl
| multiply(a,b) = a ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f387,plain,
( ~ sQ34_spl
| c = multiply(inverse(c),b) ),
inference(paramodulation,[status(thm)],[f337,f85]) ).
fof(f388,plain,
( ~ sQ17_spl
| b = multiply(inverse(b),a) ),
inference(paramodulation,[status(thm)],[f129,f85]) ).
fof(f390,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f85]) ).
fof(f401,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f20,f390]) ).
fof(f444,definition,
( sQ41_spl
<=> c = c ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f447,definition,
( sQ42_spl
<=> multiply(inverse(c),b) = a ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ42_spl
| multiply(inverse(c),b) = a ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,definition,
( sQ43_spl
<=> multiply(inverse(c),b) = b ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ43_spl
| multiply(inverse(c),b) = b ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f457,definition,
( sQ45_spl
<=> c = multiply(c,b) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ45_spl
| c = multiply(c,b) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f459,plain,
( sQ45_spl
| c != multiply(c,b) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ46_spl
<=> inverse(c) = a ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ46_spl
| inverse(c) = a ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,definition,
( sQ47_spl
<=> inverse(c) = b ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ47_spl
| inverse(c) = b ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ48_spl
<=> inverse(c) = identity ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ48_spl
| inverse(c) = identity ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f478,plain,
( ~ sQ42_spl
| ~ sQ43_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f451,f448]) ).
fof(f479,plain,
( ~ sQ42_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f23]) ).
fof(f480,plain,
( ~ sQ42_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f488,plain,
( ~ sQ45_spl
| b = multiply(inverse(c),c) ),
inference(paramodulation,[status(thm)],[f458,f85]) ).
fof(f491,plain,
( ~ sQ45_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f18,f488]) ).
fof(f492,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f27]) ).
fof(f493,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f502,plain,
( ~ sQ35_spl
| b = multiply(inverse(c),a) ),
inference(paramodulation,[status(thm)],[f359,f85]) ).
fof(f507,plain,
( sQ11_spl
| multiply(c,multiply(c,c)) = identity
| multiply(c,multiply(c,c)) = b
| multiply(c,multiply(c,c)) = a
| multiply(c,c) != identity ),
inference(paramodulation,[status(thm)],[f22,f71]) ).
fof(f509,plain,
( sQ11_spl
| multiply(c,c) = identity
| multiply(c,c) = b
| multiply(c,c) = a
| multiply(c,multiply(c,c)) != identity ),
inference(paramodulation,[status(thm)],[f22,f71]) ).
fof(f513,plain,
( sQ11_spl
| sQ25_spl
| sQ10_spl
| sQ26_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f507,f39,f191,f66,f188,f69]) ).
fof(f514,plain,
( sQ11_spl
| sQ2_spl
| sQ34_spl
| sQ9_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f509,f188,f63,f336,f39,f69]) ).
fof(f519,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| a = identity ),
inference(forward_demodulation,[status(thm)],[f64,f40]) ).
fof(f520,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f25]) ).
fof(f521,plain,
( ~ sQ2_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f524,plain,
( ~ sQ29_spl
| ~ sQ3_spl
| multiply(a,b) = a ),
inference(backward_demodulation,[status(thm)],[f44,f276]) ).
fof(f537,plain,
( ~ sQ10_spl
| ~ sQ34_spl
| multiply(b,c) = b ),
inference(forward_demodulation,[status(thm)],[f350,f67]) ).
fof(f540,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f337,f40]) ).
fof(f541,plain,
( ~ sQ2_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f27]) ).
fof(f542,plain,
( ~ sQ2_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| multiply(c,identity) = identity ),
inference(backward_demodulation,[status(thm)],[f40,f189]) ).
fof(f550,plain,
( ~ sQ26_spl
| ~ sQ2_spl
| multiply(c,identity) = a ),
inference(forward_demodulation,[status(thm)],[f40,f192]) ).
fof(f551,plain,
( ~ sQ26_spl
| ~ sQ2_spl
| c = a ),
inference(forward_demodulation,[status(thm)],[f20,f550]) ).
fof(f552,plain,
( ~ sQ26_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f24]) ).
fof(f553,plain,
( ~ sQ26_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f579,plain,
( ~ sQ10_spl
| ~ sQ34_spl
| c = multiply(inverse(b),b) ),
inference(paramodulation,[status(thm)],[f537,f85]) ).
fof(f581,definition,
( sQ49_spl
<=> multiply(b,c) = a ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( ~ sQ49_spl
| multiply(b,c) = a ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f583,plain,
( sQ49_spl
| multiply(b,c) != a ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f587,definition,
( sQ51_spl
<=> multiply(b,c) = identity ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( ~ sQ51_spl
| multiply(b,c) = identity ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f589,plain,
( sQ51_spl
| multiply(b,c) != identity ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f591,plain,
( ~ sQ10_spl
| ~ sQ34_spl
| c = identity ),
inference(forward_demodulation,[status(thm)],[f18,f579]) ).
fof(f592,plain,
( ~ sQ10_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f28]) ).
fof(f593,plain,
( ~ sQ10_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f615,plain,
( ~ sQ9_spl
| c = multiply(inverse(c),a) ),
inference(paramodulation,[status(thm)],[f64,f85]) ).
fof(f616,plain,
! [X0] :
( ~ sQ9_spl
| multiply(a,X0) = multiply(c,multiply(c,X0)) ),
inference(paramodulation,[status(thm)],[f64,f19]) ).
fof(f620,plain,
( ~ sQ49_spl
| c = multiply(inverse(b),a) ),
inference(paramodulation,[status(thm)],[f582,f85]) ).
fof(f623,plain,
( ~ sQ49_spl
| ~ sQ17_spl
| c = b ),
inference(forward_demodulation,[status(thm)],[f388,f620]) ).
fof(f624,plain,
( ~ sQ49_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f26]) ).
fof(f625,plain,
( ~ sQ49_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f633,plain,
( sQ45_spl
| multiply(c,b) = identity
| multiply(c,b) = b
| multiply(c,b) = a ),
inference(resolution,[status(thm)],[f459,f22]) ).
fof(f636,plain,
( sQ45_spl
| sQ37_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f633,f358,f361,f364,f457]) ).
fof(f640,plain,
( ~ sQ35_spl
| ~ sQ9_spl
| b = c ),
inference(forward_demodulation,[status(thm)],[f615,f502]) ).
fof(f641,plain,
( ~ sQ35_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f26]) ).
fof(f642,plain,
( ~ sQ35_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f641]) ).
fof(f650,definition,
( sQ52_spl
<=> multiply(c,a) = a ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( ~ sQ52_spl
| multiply(c,a) = a ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,definition,
( sQ53_spl
<=> multiply(c,a) = b ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( ~ sQ53_spl
| multiply(c,a) = b ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f656,definition,
( sQ54_spl
<=> multiply(c,a) = identity ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f657,plain,
( ~ sQ54_spl
| multiply(c,a) = identity ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f671,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| multiply(c,identity) = identity ),
inference(forward_demodulation,[status(thm)],[f189,f70]) ).
fof(f672,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| c = identity ),
inference(forward_demodulation,[status(thm)],[f20,f671]) ).
fof(f673,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f28]) ).
fof(f674,plain,
( ~ sQ11_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f675,plain,
( ~ sQ53_spl
| ~ sQ54_spl
| identity = b ),
inference(forward_demodulation,[status(thm)],[f657,f654]) ).
fof(f676,plain,
( ~ sQ53_spl
| ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f27]) ).
fof(f677,plain,
( ~ sQ53_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f710,plain,
! [X0] :
( ~ sQ2_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(X0,c) = identity ),
inference(paramodulation,[status(thm)],[f22,f40]) ).
fof(f712,plain,
( ~ sQ2_spl
| c = multiply(inverse(c),identity) ),
inference(paramodulation,[status(thm)],[f40,f85]) ).
fof(f713,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(c,multiply(c,X0)) ),
inference(paramodulation,[status(thm)],[f40,f19]) ).
fof(f718,plain,
( ~ sQ2_spl
| c = inverse(c) ),
inference(forward_demodulation,[status(thm)],[f20,f712]) ).
fof(f722,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(c,multiply(c,X0)) ),
inference(forward_demodulation,[status(thm)],[f17,f713]) ).
fof(f729,plain,
( ~ sQ2_spl
| inverse(c) = identity
| inverse(c) = b
| inverse(c) = a
| c = c ),
inference(paramodulation,[status(thm)],[f22,f718]) ).
fof(f736,plain,
( ~ sQ2_spl
| sQ48_spl
| sQ47_spl
| sQ46_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f729,f444,f460,f463,f466,f39]) ).
fof(f743,plain,
( ~ sQ18_spl
| b = multiply(inverse(b),b) ),
inference(paramodulation,[status(thm)],[f132,f85]) ).
fof(f746,plain,
( ~ sQ18_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f18,f743]) ).
fof(f747,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f746,f27]) ).
fof(f748,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f747]) ).
fof(f759,plain,
( ~ sQ37_spl
| b = multiply(inverse(c),identity) ),
inference(paramodulation,[status(thm)],[f365,f85]) ).
fof(f762,plain,
( ~ sQ37_spl
| b = inverse(c) ),
inference(forward_demodulation,[status(thm)],[f20,f759]) ).
fof(f763,plain,
( ~ sQ37_spl
| ~ sQ2_spl
| b = c ),
inference(forward_demodulation,[status(thm)],[f718,f762]) ).
fof(f764,plain,
( ~ sQ37_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f763,f26]) ).
fof(f765,plain,
( ~ sQ37_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f764]) ).
fof(f773,plain,
( ~ sQ25_spl
| ~ sQ34_spl
| multiply(b,c) = identity ),
inference(forward_demodulation,[status(thm)],[f350,f189]) ).
fof(f774,plain,
( ~ sQ25_spl
| ~ sQ34_spl
| sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f773,f589]) ).
fof(f775,plain,
( ~ sQ25_spl
| ~ sQ34_spl
| sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f778,plain,
( sQ10_spl
| ~ sQ9_spl
| multiply(c,a) != b ),
inference(backward_demodulation,[status(thm)],[f64,f68]) ).
fof(f791,definition,
( sQ55_spl
<=> multiply(b,a) = a ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f792,plain,
( ~ sQ55_spl
| multiply(b,a) = a ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f793,plain,
( sQ55_spl
| multiply(b,a) != a ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f794,definition,
( sQ56_spl
<=> multiply(b,a) = b ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f795,plain,
( ~ sQ56_spl
| multiply(b,a) = b ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f796,plain,
( sQ56_spl
| multiply(b,a) != b ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f797,definition,
( sQ57_spl
<=> multiply(b,a) = identity ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f798,plain,
( ~ sQ57_spl
| multiply(b,a) = identity ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f799,plain,
( sQ57_spl
| multiply(b,a) != identity ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f848,plain,
( ~ sQ3_spl
| a = multiply(inverse(a),b) ),
inference(paramodulation,[status(thm)],[f44,f85]) ).
fof(f854,plain,
( ~ sQ47_spl
| c = inverse(b) ),
inference(paramodulation,[status(thm)],[f464,f401]) ).
fof(f857,plain,
( ~ sQ47_spl
| multiply(b,c) = identity ),
inference(paramodulation,[status(thm)],[f464,f18]) ).
fof(f859,plain,
( ~ sQ17_spl
| ~ sQ47_spl
| b = multiply(c,a) ),
inference(backward_demodulation,[status(thm)],[f854,f388]) ).
fof(f861,plain,
( ~ sQ47_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f857,f587,f463]) ).
fof(f866,plain,
( ~ sQ37_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f762,f463,f364]) ).
fof(f902,plain,
( ~ sQ1_spl
| b = multiply(inverse(b),identity) ),
inference(paramodulation,[status(thm)],[f37,f85]) ).
fof(f905,plain,
( ~ sQ1_spl
| b = inverse(b) ),
inference(forward_demodulation,[status(thm)],[f20,f902]) ).
fof(f916,definition,
( sQ58_spl
<=> inverse(b) = a ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f917,plain,
( ~ sQ58_spl
| inverse(b) = a ),
inference(component_clause,[status(thm)],[f916]) ).
fof(f919,definition,
( sQ59_spl
<=> inverse(b) = b ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f920,plain,
( ~ sQ59_spl
| inverse(b) = b ),
inference(component_clause,[status(thm)],[f919]) ).
fof(f929,plain,
( ~ sQ58_spl
| ~ sQ59_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f920,f917]) ).
fof(f930,plain,
( ~ sQ58_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f929,f23]) ).
fof(f931,plain,
( ~ sQ58_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f930]) ).
fof(f944,plain,
( ~ sQ35_spl
| ~ sQ48_spl
| b = multiply(identity,a) ),
inference(backward_demodulation,[status(thm)],[f467,f502]) ).
fof(f957,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| multiply(b,multiply(b,identity)) = identity ),
inference(backward_demodulation,[status(thm)],[f37,f60]) ).
fof(f958,plain,
( ~ sQ1_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f905,f919,f36]) ).
fof(f973,plain,
( ~ sQ35_spl
| ~ sQ48_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f17,f944]) ).
fof(f974,plain,
( ~ sQ35_spl
| ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f973,f23]) ).
fof(f975,plain,
( ~ sQ35_spl
| ~ sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f974]) ).
fof(f980,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| multiply(b,b) = identity ),
inference(forward_demodulation,[status(thm)],[f20,f957]) ).
fof(f995,plain,
( ~ sQ59_spl
| ~ sQ47_spl
| c = b ),
inference(forward_demodulation,[status(thm)],[f854,f920]) ).
fof(f996,plain,
( ~ sQ59_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f995,f26]) ).
fof(f997,plain,
( ~ sQ59_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f996]) ).
fof(f1014,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| b = multiply(inverse(b),identity) ),
inference(paramodulation,[status(thm)],[f980,f85]) ).
fof(f1017,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| b = inverse(b) ),
inference(forward_demodulation,[status(thm)],[f20,f1014]) ).
fof(f1033,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f24]) ).
fof(f1034,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1033]) ).
fof(f1055,plain,
! [X0,X1] :
( multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity
| multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = b
| multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = a
| c = identity ),
inference(paramodulation,[status(thm)],[f22,f87]) ).
fof(f1079,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f87,f85]) ).
fof(f1081,definition,
! [X0,X1] :
( sQ61_spl
<=> ( multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity
| multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = b
| multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = a ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1084,plain,
( sQ61_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1055,f150,f1081]) ).
fof(f1110,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f20,f1079]) ).
fof(f1128,plain,
( sQ2_spl
| inverse(c) = identity
| inverse(c) = b
| inverse(c) = a ),
inference(resolution,[status(thm)],[f266,f18]) ).
fof(f1134,plain,
( sQ2_spl
| sQ48_spl
| sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f1128,f460,f463,f466,f39]) ).
fof(f1150,plain,
( ~ sQ35_spl
| ~ sQ2_spl
| b = multiply(c,a) ),
inference(backward_demodulation,[status(thm)],[f718,f502]) ).
fof(f1154,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| c = b ),
inference(forward_demodulation,[status(thm)],[f722,f67]) ).
fof(f1155,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1154,f26]) ).
fof(f1156,plain,
( ~ sQ10_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1155]) ).
fof(f1175,plain,
( ~ sQ46_spl
| c = inverse(a) ),
inference(paramodulation,[status(thm)],[f461,f401]) ).
fof(f1177,plain,
( ~ sQ46_spl
| multiply(c,a) = identity ),
inference(paramodulation,[status(thm)],[f461,f21]) ).
fof(f1180,plain,
( ~ sQ46_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1177,f656,f460]) ).
fof(f1188,definition,
( sQ63_spl
<=> inverse(a) = a ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1189,plain,
( ~ sQ63_spl
| inverse(a) = a ),
inference(component_clause,[status(thm)],[f1188]) ).
fof(f1190,plain,
( sQ63_spl
| inverse(a) != a ),
inference(component_clause,[status(thm)],[f1188]) ).
fof(f1191,definition,
( sQ64_spl
<=> inverse(a) = b ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1192,plain,
( ~ sQ64_spl
| inverse(a) = b ),
inference(component_clause,[status(thm)],[f1191]) ).
fof(f1194,definition,
( sQ65_spl
<=> inverse(a) = identity ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1236,plain,
( ~ sQ47_spl
| multiply(b,c) = identity ),
inference(paramodulation,[status(thm)],[f854,f21]) ).
fof(f1240,plain,
( ~ sQ17_spl
| b = multiply(inverse(b),a) ),
inference(paramodulation,[status(thm)],[f129,f85]) ).
fof(f1256,plain,
( ~ sQ51_spl
| c = multiply(inverse(b),identity) ),
inference(paramodulation,[status(thm)],[f588,f85]) ).
fof(f1259,plain,
( ~ sQ51_spl
| c = inverse(b) ),
inference(forward_demodulation,[status(thm)],[f20,f1256]) ).
fof(f1272,plain,
! [X0] :
( sQ34_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(c,c) = identity
| multiply(c,c) = X0
| multiply(c,c) = a ),
inference(resolution,[status(thm)],[f98,f338]) ).
fof(f1278,plain,
! [X0] :
( X0 = identity
| X0 = b
| X0 = a
| c = identity
| c = X0
| c = a ),
inference(resolution,[status(thm)],[f98,f26]) ).
fof(f1329,plain,
! [X0] :
( X0 = b
| b != b
| X0 = identity
| X0 = a
| X0 = identity
| X0 = X0
| X0 = a ),
inference(equality_factoring,[status(thm)],[f98]) ).
fof(f1338,definition,
! [X0] :
( sQ66_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| multiply(c,c) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1339,plain,
! [X0] :
( ~ sQ66_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(c,c) = X0 ),
inference(component_clause,[status(thm)],[f1338]) ).
fof(f1341,plain,
( sQ34_spl
| sQ2_spl
| sQ66_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1272,f63,f1338,f39,f336]) ).
fof(f1343,definition,
! [X0] :
( sQ67_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| a = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1344,plain,
! [X0] :
( ~ sQ67_spl
| X0 = identity
| X0 = b
| X0 = a
| a = X0 ),
inference(component_clause,[status(thm)],[f1343]) ).
fof(f1348,definition,
! [X0] :
( sQ68_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| identity = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1349,plain,
! [X0] :
( ~ sQ68_spl
| X0 = identity
| X0 = b
| X0 = a
| identity = X0 ),
inference(component_clause,[status(thm)],[f1348]) ).
fof(f1353,definition,
! [X0] :
( sQ69_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| c = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1356,plain,
( sQ23_spl
| sQ69_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1278,f142,f1353,f150]) ).
fof(f1398,definition,
! [X0] :
( sQ71_spl
<=> ( X0 = a
| X0 = identity
| X0 = b
| X0 = identity
| X0 = X0
| X0 = a ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
( ~ sQ13_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f1329,f1398,f114]) ).
fof(f1404,definition,
! [X0] :
( sQ72_spl
<=> ( b = X0
| X0 != X0
| X0 = identity
| X0 = a ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
! [X0] :
( ~ sQ72_spl
| b = X0
| X0 != X0
| X0 = identity
| X0 = a ),
inference(component_clause,[status(thm)],[f1404]) ).
fof(f1454,definition,
! [X0] :
( sQ76_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| multiply(c,b) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1455,plain,
! [X0] :
( ~ sQ76_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(c,b) = X0 ),
inference(component_clause,[status(thm)],[f1454]) ).
fof(f1468,definition,
! [X0] :
( sQ77_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| multiply(c,a) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1469,plain,
! [X0] :
( ~ sQ77_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(c,a) = X0 ),
inference(component_clause,[status(thm)],[f1468]) ).
fof(f1492,plain,
( ~ sQ43_spl
| ~ sQ34_spl
| c = b ),
inference(forward_demodulation,[status(thm)],[f387,f451]) ).
fof(f1493,plain,
( ~ sQ43_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1492,f26]) ).
fof(f1494,plain,
( ~ sQ43_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1493]) ).
fof(f1506,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| c = identity ),
inference(forward_demodulation,[status(thm)],[f20,f544]) ).
fof(f1507,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1506,f28]) ).
fof(f1508,plain,
( ~ sQ25_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1507]) ).
fof(f1545,plain,
! [X0] :
( ~ sQ2_spl
| X0 = identity
| X0 = b
| X0 = a
| inverse(c) = identity
| inverse(c) = X0
| inverse(c) = a
| c = b ),
inference(paramodulation,[status(thm)],[f98,f718]) ).
fof(f1554,definition,
! [X0] :
( sQ79_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| inverse(c) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1555,plain,
! [X0] :
( ~ sQ79_spl
| X0 = identity
| X0 = b
| X0 = a
| inverse(c) = X0 ),
inference(component_clause,[status(thm)],[f1554]) ).
fof(f1557,plain,
( ~ sQ2_spl
| sQ48_spl
| sQ79_spl
| sQ46_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f1545,f146,f460,f1554,f466,f39]) ).
fof(f1562,plain,
( ~ sQ54_spl
| ~ sQ35_spl
| ~ sQ2_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f1150,f657]) ).
fof(f1563,plain,
( ~ sQ54_spl
| ~ sQ35_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1562,f27]) ).
fof(f1564,plain,
( ~ sQ54_spl
| ~ sQ35_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1563]) ).
fof(f1605,plain,
( ~ sQ35_spl
| ~ sQ2_spl
| multiply(c,a) = identity
| multiply(c,a) = b
| multiply(c,a) = a
| b = c ),
inference(paramodulation,[status(thm)],[f22,f1150]) ).
fof(f1609,plain,
( ~ sQ35_spl
| ~ sQ2_spl
| sQ54_spl
| sQ53_spl
| sQ52_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f1605,f146,f650,f653,f656,f39,f358]) ).
fof(f1611,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ sQ2_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f1150,f651]) ).
fof(f1612,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1611,f23]) ).
fof(f1613,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1612]) ).
fof(f1617,plain,
( ~ sQ35_spl
| b = multiply(inverse(c),a) ),
inference(paramodulation,[status(thm)],[f359,f85]) ).
fof(f1666,plain,
( sQ29_spl
| ~ sQ0_spl
| multiply(a,identity) != a ),
inference(forward_demodulation,[status(thm)],[f34,f277]) ).
fof(f1667,plain,
( sQ29_spl
| ~ sQ0_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f20,f1666]) ).
fof(f1668,plain,
( sQ29_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1667]) ).
fof(f1669,plain,
( sQ29_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1668]) ).
fof(f1737,plain,
( ~ sQ17_spl
| ~ sQ51_spl
| b = multiply(c,a) ),
inference(forward_demodulation,[status(thm)],[f1259,f1240]) ).
fof(f1758,plain,
( ~ sQ51_spl
| b = inverse(c) ),
inference(paramodulation,[status(thm)],[f1259,f401]) ).
fof(f1761,plain,
( ~ sQ51_spl
| multiply(c,b) = identity ),
inference(paramodulation,[status(thm)],[f1259,f18]) ).
fof(f1763,plain,
( ~ sQ51_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f1758,f463,f587]) ).
fof(f1773,plain,
( ~ sQ51_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1761,f364,f587]) ).
fof(f1776,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ2_spl
| X0 = identity
| X0 = b
| X0 = a
| identity = X0 ),
inference(forward_demodulation,[status(thm)],[f40,f1339]) ).
fof(f1777,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ2_spl
| X0 = b
| X0 = a
| identity = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f1776]) ).
fof(f1778,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ35_spl
| ~ sQ2_spl
| X0 = identity
| X0 = b
| X0 = a
| b = X0 ),
inference(forward_demodulation,[status(thm)],[f1150,f1469]) ).
fof(f1779,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ35_spl
| ~ sQ2_spl
| X0 = identity
| X0 = a
| b = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f1778]) ).
fof(f1780,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ35_spl
| X0 = identity
| X0 = b
| X0 = a
| a = X0 ),
inference(forward_demodulation,[status(thm)],[f359,f1455]) ).
fof(f1781,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ35_spl
| X0 = identity
| X0 = b
| a = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f1780]) ).
fof(f1782,plain,
! [X0] :
( ~ sQ72_spl
| b = X0
| X0 = identity
| X0 = a ),
inference(trivial_equality_resolution,[status(thm)],[f1405]) ).
fof(f1783,plain,
( ~ sQ33_spl
| ~ sQ2_spl
| multiply(c,c) = b ),
inference(forward_demodulation,[status(thm)],[f722,f332]) ).
fof(f1784,plain,
( ~ sQ33_spl
| ~ sQ2_spl
| identity = b ),
inference(forward_demodulation,[status(thm)],[f40,f1783]) ).
fof(f1785,plain,
( ~ sQ33_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1784,f27]) ).
fof(f1786,plain,
( ~ sQ33_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1785]) ).
fof(f1787,plain,
! [X0] :
( ~ sQ68_spl
| X0 = b
| X0 = a
| identity = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f1349]) ).
fof(f1788,plain,
! [X0] :
( ~ sQ67_spl
| X0 = identity
| X0 = b
| a = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f1344]) ).
fof(f1793,plain,
( ~ sQ29_spl
| ~ sQ3_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f524,f373,f43,f275]) ).
fof(f1799,plain,
( ~ sQ72_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1782,f139,f1404]) ).
fof(f1838,plain,
( ~ sQ66_spl
| ~ sQ2_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1777,f139,f39,f1338]) ).
fof(f1841,plain,
( ~ sQ76_spl
| ~ sQ35_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1781,f139,f358,f1454]) ).
fof(f1863,plain,
( ~ sQ17_spl
| ~ sQ47_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f859,f653,f463,f128]) ).
fof(f1886,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f778,f653,f63,f66]) ).
fof(f2028,plain,
! [X0] :
( sQ56_spl
| X0 = identity
| X0 = b
| X0 = a
| multiply(b,a) = identity
| multiply(b,a) = X0
| multiply(b,a) = a ),
inference(resolution,[status(thm)],[f98,f796]) ).
fof(f2092,definition,
! [X0] :
( sQ86_spl
<=> ( X0 = identity
| X0 = b
| X0 = a
| multiply(b,a) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f2095,plain,
( sQ56_spl
| sQ57_spl
| sQ86_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f2028,f791,f2092,f797,f794]) ).
fof(f2167,plain,
( ~ sQ57_spl
| a = multiply(inverse(b),identity) ),
inference(paramodulation,[status(thm)],[f798,f85]) ).
fof(f2171,plain,
( ~ sQ57_spl
| a = inverse(b) ),
inference(forward_demodulation,[status(thm)],[f20,f2167]) ).
fof(f2172,plain,
( ~ sQ57_spl
| ~ sQ51_spl
| a = c ),
inference(forward_demodulation,[status(thm)],[f1259,f2171]) ).
fof(f2173,plain,
( ~ sQ57_spl
| ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2172,f24]) ).
fof(f2174,plain,
( ~ sQ57_spl
| ~ sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f2173]) ).
fof(f2194,definition,
! [X0,X1] :
( sQ88_spl
<=> ( X1 = identity
| X1 = b
| X1 = a
| multiply(X0,c) = identity
| multiply(X0,c) = X1
| multiply(X0,c) = a
| X0 = identity
| X0 = b
| X0 = a ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f2237,plain,
( ~ sQ55_spl
| a = multiply(inverse(b),a) ),
inference(paramodulation,[status(thm)],[f792,f85]) ).
fof(f2241,plain,
( ~ sQ55_spl
| ~ sQ51_spl
| a = multiply(c,a) ),
inference(forward_demodulation,[status(thm)],[f1259,f2237]) ).
fof(f2250,plain,
( ~ sQ56_spl
| a = multiply(inverse(b),b) ),
inference(paramodulation,[status(thm)],[f795,f85]) ).
fof(f2254,plain,
( ~ sQ56_spl
| a = identity ),
inference(forward_demodulation,[status(thm)],[f18,f2250]) ).
fof(f2255,plain,
( ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2254,f25]) ).
fof(f2256,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f2255]) ).
fof(f2269,plain,
( sQ2_spl
| multiply(inverse(c),identity) = identity
| multiply(inverse(c),identity) = b
| multiply(inverse(c),identity) = a ),
inference(resolution,[status(thm)],[f265,f93]) ).
fof(f2286,definition,
( sQ94_spl
<=> multiply(inverse(c),identity) = a ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f2287,plain,
( ~ sQ94_spl
| multiply(inverse(c),identity) = a ),
inference(component_clause,[status(thm)],[f2286]) ).
fof(f2289,definition,
( sQ95_spl
<=> multiply(inverse(c),identity) = b ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f2290,plain,
( ~ sQ95_spl
| multiply(inverse(c),identity) = b ),
inference(component_clause,[status(thm)],[f2289]) ).
fof(f2292,definition,
( sQ96_spl
<=> multiply(inverse(c),identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f2295,plain,
( sQ2_spl
| sQ96_spl
| sQ95_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f2269,f2286,f2289,f2292,f39]) ).
fof(f2319,plain,
( ~ sQ94_spl
| inverse(c) = a ),
inference(forward_demodulation,[status(thm)],[f20,f2287]) ).
fof(f2325,plain,
( ~ sQ95_spl
| inverse(c) = b ),
inference(forward_demodulation,[status(thm)],[f20,f2290]) ).
fof(f2419,plain,
( ~ sQ17_spl
| ~ sQ51_spl
| multiply(a,inverse(b)) = inverse(c) ),
inference(paramodulation,[status(thm)],[f1737,f1110]) ).
fof(f2423,plain,
( ~ sQ17_spl
| multiply(b,inverse(a)) = inverse(b) ),
inference(paramodulation,[status(thm)],[f129,f1110]) ).
fof(f2452,plain,
( ~ sQ17_spl
| ~ sQ51_spl
| multiply(a,c) = inverse(c) ),
inference(forward_demodulation,[status(thm)],[f1259,f2419]) ).
fof(f2489,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ47_spl
| X0 = identity
| X0 = b
| X0 = a
| b = X0 ),
inference(forward_demodulation,[status(thm)],[f464,f1555]) ).
fof(f2490,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ47_spl
| X0 = identity
| X0 = a
| b = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f2489]) ).
fof(f2494,plain,
( ~ sQ68_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1787,f139,f1348]) ).
fof(f2495,plain,
( ~ sQ67_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1788,f139,f1343]) ).
fof(f2496,plain,
( ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ47_spl
| multiply(a,c) = b ),
inference(forward_demodulation,[status(thm)],[f464,f2452]) ).
fof(f2526,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ47_spl
| multiply(b,X0) = multiply(a,multiply(c,X0)) ),
inference(paramodulation,[status(thm)],[f2496,f19]) ).
fof(f2529,plain,
( ~ sQ38_spl
| b = multiply(inverse(a),a) ),
inference(paramodulation,[status(thm)],[f374,f85]) ).
fof(f2536,plain,
( ~ sQ38_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f18,f2529]) ).
fof(f2537,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2536,f27]) ).
fof(f2538,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f2537]) ).
fof(f2617,plain,
( ~ sQ63_spl
| multiply(a,a) = identity ),
inference(paramodulation,[status(thm)],[f1189,f21]) ).
fof(f2621,plain,
( ~ sQ63_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f2617,f33,f1188]) ).
fof(f2669,plain,
( sQ11_spl
| ~ sQ9_spl
| multiply(a,multiply(c,c)) != identity ),
inference(forward_demodulation,[status(thm)],[f616,f71]) ).
fof(f2670,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ47_spl
| multiply(b,c) != identity ),
inference(forward_demodulation,[status(thm)],[f2526,f2669]) ).
fof(f2671,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ47_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f1236,f2670]) ).
fof(f2672,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2671]) ).
fof(f2673,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f2672]) ).
fof(f2753,plain,
( ~ sQ6_spl
| b = multiply(inverse(b),c) ),
inference(paramodulation,[status(thm)],[f54,f85]) ).
fof(f2754,plain,
! [X0] :
( ~ sQ6_spl
| multiply(c,X0) = multiply(b,multiply(b,X0)) ),
inference(paramodulation,[status(thm)],[f54,f19]) ).
fof(f2762,plain,
( ~ sQ6_spl
| ~ sQ51_spl
| b = multiply(c,c) ),
inference(forward_demodulation,[status(thm)],[f1259,f2753]) ).
fof(f2763,plain,
( ~ sQ6_spl
| ~ sQ51_spl
| ~ sQ9_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f64,f2762]) ).
fof(f2764,plain,
( ~ sQ6_spl
| ~ sQ51_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2763,f23]) ).
fof(f2765,plain,
( ~ sQ6_spl
| ~ sQ51_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f2764]) ).
fof(f2798,plain,
( ~ sQ55_spl
| ~ sQ51_spl
| multiply(a,inverse(a)) = inverse(c) ),
inference(paramodulation,[status(thm)],[f2241,f1110]) ).
fof(f2802,plain,
( ~ sQ55_spl
| ~ sQ51_spl
| identity = inverse(c) ),
inference(forward_demodulation,[status(thm)],[f21,f2798]) ).
fof(f2803,plain,
( ~ sQ55_spl
| ~ sQ51_spl
| ~ sQ47_spl
| identity = b ),
inference(forward_demodulation,[status(thm)],[f464,f2802]) ).
fof(f2804,plain,
( ~ sQ55_spl
| ~ sQ51_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2803,f27]) ).
fof(f2805,plain,
( ~ sQ55_spl
| ~ sQ51_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f2804]) ).
fof(f2819,plain,
( ~ sQ30_spl
| multiply(a,a) = multiply(inverse(a),b) ),
inference(paramodulation,[status(thm)],[f279,f85]) ).
fof(f2846,definition,
( sQ102_spl
<=> multiply(b,identity) = a ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f2847,plain,
( ~ sQ102_spl
| multiply(b,identity) = a ),
inference(component_clause,[status(thm)],[f2846]) ).
fof(f2852,definition,
( sQ104_spl
<=> multiply(b,identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f2853,plain,
( ~ sQ104_spl
| multiply(b,identity) = identity ),
inference(component_clause,[status(thm)],[f2852]) ).
fof(f2868,plain,
( ~ sQ104_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f20,f2853]) ).
fof(f2869,plain,
( ~ sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2868,f27]) ).
fof(f2870,plain,
~ sQ104_spl,
inference(contradiction_clause,[status(thm)],[f2869]) ).
fof(f2871,plain,
( ~ sQ102_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f20,f2847]) ).
fof(f2872,plain,
( ~ sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2871,f23]) ).
fof(f2873,plain,
~ sQ102_spl,
inference(contradiction_clause,[status(thm)],[f2872]) ).
fof(f2876,plain,
( ~ sQ95_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f2325,f463,f2289]) ).
fof(f2885,plain,
( ~ sQ55_spl
| ~ sQ8_spl
| ~ sQ1_spl
| a = multiply(b,a) ),
inference(forward_demodulation,[status(thm)],[f1017,f2237]) ).
fof(f2981,plain,
( ~ sQ46_spl
| multiply(a,c) = identity ),
inference(paramodulation,[status(thm)],[f1175,f21]) ).
fof(f2990,plain,
( ~ sQ55_spl
| ~ sQ8_spl
| ~ sQ1_spl
| multiply(a,inverse(a)) = inverse(b) ),
inference(paramodulation,[status(thm)],[f2885,f1110]) ).
fof(f2993,plain,
( ~ sQ55_spl
| ~ sQ8_spl
| ~ sQ1_spl
| identity = inverse(b) ),
inference(forward_demodulation,[status(thm)],[f21,f2990]) ).
fof(f2994,plain,
( ~ sQ55_spl
| ~ sQ8_spl
| ~ sQ1_spl
| identity = b ),
inference(forward_demodulation,[status(thm)],[f1017,f2993]) ).
fof(f2995,plain,
( ~ sQ55_spl
| ~ sQ8_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2994,f27]) ).
fof(f2996,plain,
( ~ sQ55_spl
| ~ sQ8_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f2995]) ).
fof(f2998,plain,
( ~ sQ57_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f2171,f916,f797]) ).
fof(f3109,plain,
( ~ sQ36_spl
| multiply(b,inverse(b)) = inverse(c) ),
inference(paramodulation,[status(thm)],[f362,f1110]) ).
fof(f3115,plain,
( ~ sQ36_spl
| identity = inverse(c) ),
inference(forward_demodulation,[status(thm)],[f21,f3109]) ).
fof(f3122,plain,
( ~ sQ35_spl
| ~ sQ46_spl
| b = multiply(a,a) ),
inference(forward_demodulation,[status(thm)],[f461,f502]) ).
fof(f3123,plain,
( ~ sQ35_spl
| ~ sQ46_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3122,f45]) ).
fof(f3124,plain,
( ~ sQ35_spl
| ~ sQ46_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f3123]) ).
fof(f3138,plain,
( sQ29_spl
| ~ sQ3_spl
| multiply(b,a) != a ),
inference(forward_demodulation,[status(thm)],[f318,f277]) ).
fof(f3144,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(b,a) = c ),
inference(forward_demodulation,[status(thm)],[f318,f47]) ).
fof(f3145,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ46_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f2981,f300]) ).
fof(f3146,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ46_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3145]) ).
fof(f3147,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f3146]) ).
fof(f3149,plain,
( ~ sQ31_spl
| ~ sQ3_spl
| multiply(b,a) = identity ),
inference(forward_demodulation,[status(thm)],[f318,f282]) ).
fof(f3150,plain,
( ~ sQ31_spl
| ~ sQ3_spl
| sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3149,f799]) ).
fof(f3151,plain,
( ~ sQ31_spl
| ~ sQ3_spl
| sQ57_spl ),
inference(contradiction_clause,[status(thm)],[f3150]) ).
fof(f3154,plain,
( ~ sQ17_spl
| ~ sQ46_spl
| multiply(b,c) = inverse(b) ),
inference(forward_demodulation,[status(thm)],[f1175,f2423]) ).
fof(f3167,plain,
( sQ49_spl
| ~ sQ17_spl
| ~ sQ46_spl
| inverse(b) != a ),
inference(forward_demodulation,[status(thm)],[f3154,f583]) ).
fof(f3168,plain,
( sQ49_spl
| ~ sQ17_spl
| ~ sQ46_spl
| ~ sQ58_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f917,f3167]) ).
fof(f3169,plain,
( sQ49_spl
| ~ sQ17_spl
| ~ sQ46_spl
| ~ sQ58_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3168]) ).
fof(f3170,plain,
( sQ49_spl
| ~ sQ17_spl
| ~ sQ46_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f3169]) ).
fof(f3175,plain,
( ~ sQ6_spl
| ~ sQ58_spl
| b = multiply(a,c) ),
inference(forward_demodulation,[status(thm)],[f917,f2753]) ).
fof(f3176,plain,
( ~ sQ6_spl
| ~ sQ58_spl
| ~ sQ46_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f2981,f3175]) ).
fof(f3177,plain,
( ~ sQ6_spl
| ~ sQ58_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3176,f27]) ).
fof(f3178,plain,
( ~ sQ6_spl
| ~ sQ58_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f3177]) ).
fof(f3180,plain,
( ~ sQ94_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f2319,f460,f2286]) ).
fof(f3216,plain,
( ~ sQ36_spl
| c = inverse(identity) ),
inference(paramodulation,[status(thm)],[f3115,f401]) ).
fof(f3240,plain,
( ~ sQ36_spl
| c = identity ),
inference(forward_demodulation,[status(thm)],[f82,f3216]) ).
fof(f3241,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3240,f28]) ).
fof(f3242,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f3241]) ).
fof(f3453,plain,
( sQ56_spl
| multiply(b,a) = identity
| multiply(b,a) = a
| multiply(b,a) = identity
| multiply(b,a) = multiply(b,a)
| multiply(b,a) = a ),
inference(resolution,[status(thm)],[f796,f98]) ).
fof(f3464,definition,
( sQ108_spl
<=> multiply(b,a) = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f3467,plain,
( sQ56_spl
| sQ57_spl
| sQ108_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f3453,f791,f3464,f797,f794]) ).
fof(f3539,plain,
( sQ9_spl
| multiply(inverse(c),a) = identity
| multiply(inverse(c),a) = b
| multiply(inverse(c),a) = a ),
inference(resolution,[status(thm)],[f106,f93]) ).
fof(f3550,definition,
( sQ116_spl
<=> multiply(inverse(c),a) = a ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f3551,plain,
( ~ sQ116_spl
| multiply(inverse(c),a) = a ),
inference(component_clause,[status(thm)],[f3550]) ).
fof(f3553,definition,
( sQ117_spl
<=> multiply(inverse(c),a) = b ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f3554,plain,
( ~ sQ117_spl
| multiply(inverse(c),a) = b ),
inference(component_clause,[status(thm)],[f3553]) ).
fof(f3556,definition,
( sQ118_spl
<=> multiply(inverse(c),a) = identity ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f3557,plain,
( ~ sQ118_spl
| multiply(inverse(c),a) = identity ),
inference(component_clause,[status(thm)],[f3556]) ).
fof(f3559,plain,
( sQ9_spl
| sQ118_spl
| sQ117_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f3539,f3550,f3553,f3556,f63]) ).
fof(f3574,plain,
( ~ sQ79_spl
| ~ sQ47_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f2490,f139,f463,f1554]) ).
fof(f3577,plain,
( ~ sQ118_spl
| ~ sQ47_spl
| multiply(b,a) = identity ),
inference(forward_demodulation,[status(thm)],[f464,f3557]) ).
fof(f3578,plain,
( ~ sQ118_spl
| ~ sQ47_spl
| sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3577,f799]) ).
fof(f3579,plain,
( ~ sQ118_spl
| ~ sQ47_spl
| sQ57_spl ),
inference(contradiction_clause,[status(thm)],[f3578]) ).
fof(f3580,plain,
( ~ sQ116_spl
| ~ sQ47_spl
| multiply(b,a) = a ),
inference(forward_demodulation,[status(thm)],[f464,f3551]) ).
fof(f3581,plain,
( ~ sQ116_spl
| ~ sQ47_spl
| sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3580,f793]) ).
fof(f3582,plain,
( ~ sQ116_spl
| ~ sQ47_spl
| sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f3581]) ).
fof(f3584,plain,
( ~ sQ117_spl
| ~ sQ47_spl
| multiply(b,a) = b ),
inference(forward_demodulation,[status(thm)],[f464,f3554]) ).
fof(f3585,plain,
( ~ sQ117_spl
| ~ sQ47_spl
| sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3584,f796]) ).
fof(f3586,plain,
( ~ sQ117_spl
| ~ sQ47_spl
| sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f3585]) ).
fof(f3592,plain,
( ~ sQ77_spl
| ~ sQ35_spl
| ~ sQ2_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1779,f139,f39,f358,f1468]) ).
fof(f3603,plain,
( sQ8_spl
| ~ sQ6_spl
| multiply(c,multiply(b,b)) != identity ),
inference(forward_demodulation,[status(thm)],[f2754,f61]) ).
fof(f3604,plain,
( sQ8_spl
| ~ sQ6_spl
| multiply(c,c) != identity ),
inference(forward_demodulation,[status(thm)],[f54,f3603]) ).
fof(f3617,plain,
( ~ sQ35_spl
| ~ sQ118_spl
| b = identity ),
inference(forward_demodulation,[status(thm)],[f3557,f1617]) ).
fof(f3618,plain,
( ~ sQ35_spl
| ~ sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3617,f27]) ).
fof(f3619,plain,
( ~ sQ35_spl
| ~ sQ118_spl ),
inference(contradiction_clause,[status(thm)],[f3618]) ).
fof(f3641,plain,
( ~ sQ2_spl
| sQ8_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f3604]) ).
fof(f3642,plain,
( ~ sQ2_spl
| sQ8_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f3641]) ).
fof(f3646,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ2_spl
| X0 = multiply(c,multiply(c,X0)) ),
inference(backward_demodulation,[status(thm)],[f722,f342]) ).
fof(f3664,plain,
( ~ sQ116_spl
| ~ sQ2_spl
| multiply(c,a) = a ),
inference(forward_demodulation,[status(thm)],[f718,f3551]) ).
fof(f3665,plain,
( ~ sQ116_spl
| ~ sQ2_spl
| ~ sQ35_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f1150,f3664]) ).
fof(f3666,plain,
( ~ sQ116_spl
| ~ sQ2_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3665,f23]) ).
fof(f3667,plain,
( ~ sQ116_spl
| ~ sQ2_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f3666]) ).
fof(f3705,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| multiply(c,a) = b ),
inference(forward_demodulation,[status(thm)],[f718,f3554]) ).
fof(f3747,plain,
( sQ29_spl
| ~ sQ3_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f3138,f791,f43,f275]) ).
fof(f3749,plain,
( ~ sQ3_spl
| ~ sQ30_spl
| a = multiply(a,a) ),
inference(forward_demodulation,[status(thm)],[f2819,f848]) ).
fof(f3750,plain,
( ~ sQ3_spl
| ~ sQ30_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3749,f186]) ).
fof(f3751,plain,
( ~ sQ3_spl
| ~ sQ30_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f3750]) ).
fof(f3762,plain,
( sQ7_spl
| ~ sQ6_spl
| multiply(c,b) != a ),
inference(forward_demodulation,[status(thm)],[f2754,f58]) ).
fof(f3763,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ35_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f359,f3762]) ).
fof(f3764,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ35_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3763]) ).
fof(f3765,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f3764]) ).
fof(f3826,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| multiply(a,inverse(b)) = inverse(c) ),
inference(paramodulation,[status(thm)],[f3705,f1110]) ).
fof(f3835,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| multiply(a,inverse(b)) = c ),
inference(forward_demodulation,[status(thm)],[f718,f3826]) ).
fof(f3845,plain,
( ~ sQ35_spl
| multiply(b,inverse(a)) = inverse(c) ),
inference(paramodulation,[status(thm)],[f359,f1110]) ).
fof(f3848,plain,
( ~ sQ35_spl
| ~ sQ17_spl
| inverse(b) = inverse(c) ),
inference(forward_demodulation,[status(thm)],[f2423,f3845]) ).
fof(f3856,plain,
( ~ sQ35_spl
| ~ sQ17_spl
| ~ sQ2_spl
| inverse(b) = c ),
inference(forward_demodulation,[status(thm)],[f718,f3848]) ).
fof(f3886,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ1_spl
| multiply(a,b) = c ),
inference(backward_demodulation,[status(thm)],[f1017,f3835]) ).
fof(f3999,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ1_spl
| multiply(b,inverse(c)) = inverse(a) ),
inference(paramodulation,[status(thm)],[f3886,f1110]) ).
fof(f4000,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ1_spl
| b = multiply(inverse(a),c) ),
inference(paramodulation,[status(thm)],[f3886,f85]) ).
fof(f4002,plain,
( sQ51_spl
| ~ sQ117_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ1_spl
| inverse(a) != identity ),
inference(backward_demodulation,[status(thm)],[f4003,f589]) ).
fof(f4003,plain,
( ~ sQ117_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ1_spl
| multiply(b,c) = inverse(a) ),
inference(forward_demodulation,[status(thm)],[f718,f3999]) ).
fof(f4047,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| a = multiply(inverse(b),c) ),
inference(paramodulation,[status(thm)],[f3144,f85]) ).
fof(f4052,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ1_spl
| a = multiply(b,c) ),
inference(forward_demodulation,[status(thm)],[f1017,f4047]) ).
fof(f4053,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ117_spl
| ~ sQ2_spl
| a = inverse(a) ),
inference(forward_demodulation,[status(thm)],[f4003,f4052]) ).
fof(f4054,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ117_spl
| ~ sQ2_spl
| sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4053,f1190]) ).
fof(f4055,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ117_spl
| ~ sQ2_spl
| sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f4054]) ).
fof(f4239,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = identity
| X1 = b
| X1 = a
| multiply(X0,c) = identity
| multiply(X0,c) = X1
| multiply(X0,c) = a
| X0 = identity
| X0 = b
| X0 = a
| b = identity ),
inference(paramodulation,[status(thm)],[f98,f710]) ).
fof(f4252,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| c = identity
| c = b
| c = a
| c = multiply(c,identity) ),
inference(paramodulation,[status(thm)],[f710,f3646]) ).
fof(f4261,plain,
( ~ sQ2_spl
| sQ88_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f4239,f117,f2194,f39]) ).
fof(f4279,definition,
( sQ124_spl
<=> c = multiply(c,identity) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f4282,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f4252,f4279,f142,f146,f150,f69,f39]) ).
fof(f4293,plain,
( ~ sQ2_spl
| ~ sQ117_spl
| ~ sQ8_spl
| ~ sQ1_spl
| inverse(a) = identity
| inverse(a) = b
| inverse(a) = a
| b = identity ),
inference(paramodulation,[status(thm)],[f710,f4000]) ).
fof(f4312,plain,
( ~ sQ2_spl
| ~ sQ117_spl
| ~ sQ8_spl
| ~ sQ1_spl
| sQ65_spl
| sQ64_spl
| sQ63_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f4293,f117,f1188,f1191,f1194,f36,f59,f3553,f39]) ).
fof(f4319,plain,
( sQ51_spl
| ~ sQ117_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f4002,f1194,f36,f59,f39,f3553,f587]) ).
fof(f4347,plain,
( ~ sQ64_spl
| a = inverse(b) ),
inference(paramodulation,[status(thm)],[f1192,f401]) ).
fof(f4370,plain,
( ~ sQ64_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f4347,f916,f1191]) ).
fof(f4390,plain,
( ~ sQ35_spl
| ~ sQ17_spl
| ~ sQ2_spl
| multiply(b,c) = identity ),
inference(paramodulation,[status(thm)],[f3856,f21]) ).
fof(f4406,plain,
( ~ sQ35_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f4390,f587,f39,f128,f358]) ).
fof(f4410,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f52,f62,f72,f120,f127,f134,f138,f149,f155,f157,f159,f196,f209,f212,f231,f248,f284,f335,f339,f480,f493,f513,f514,f521,f542,f553,f593,f625,f636,f642,f674,f677,f736,f748,f765,f775,f861,f866,f931,f958,f975,f997,f1034,f1084,f1134,f1156,f1180,f1341,f1356,f1402,f1494,f1508,f1557,f1564,f1609,f1613,f1669,f1763,f1773,f1786,f1793,f1799,f1838,f1841,f1863,f1886,f2095,f2174,f2256,f2295,f2494,f2495,f2538,f2621,f2673,f2765,f2805,f2870,f2873,f2876,f2996,f2998,f3124,f3147,f3151,f3170,f3178,f3180,f3242,f3467,f3559,f3574,f3579,f3582,f3586,f3592,f3619,f3642,f3667,f3747,f3751,f3765,f4055,f4261,f4282,f4312,f4319,f4370,f4406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP113-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 19:58:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 2.00/0.88 % Refutation found
% 2.00/0.88 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.00/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.00/0.90 % Elapsed time: 0.538755 seconds
% 2.00/0.90 % CPU time: 3.681214 seconds
% 2.00/0.90 % Total memory used: 141.301 MB
% 2.00/0.90 % Net memory used: 137.432 MB
%------------------------------------------------------------------------------