%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP304-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:33:22 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 42
% Syntax : Number of formulae : 264 ( 14 unt; 20 def)
% Number of atoms : 998 ( 306 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1432 ( 698 ~; 714 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
multiply(sk_c7,sk_c6) = sk_c5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [X2,X1,X3,X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f50,plain,
! [X4] :
( inverse(X4) != sk_c7
| ! [X3] :
( multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| ! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( sQ0_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> multiply(sk_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f52,f55]) ).
fof(f59,definition,
( sQ2_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f52,f59]) ).
fof(f63,definition,
( sQ3_spl
<=> multiply(sk_c7,sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f67,definition,
( sQ4_spl
<=> multiply(sk_c3,sk_c7) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ4_spl
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f71,definition,
( sQ5_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ5_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f75,definition,
( sQ6_spl
<=> inverse(sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ6_spl
| inverse(sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f77,plain,
( sQ6_spl
| inverse(sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f35,f75,f55]) ).
fof(f79,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f36,f75,f59]) ).
fof(f80,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f37,f75,f63]) ).
fof(f81,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f75,f67]) ).
fof(f82,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f75,f71]) ).
fof(f83,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f83,f55]) ).
fof(f87,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f83,f59]) ).
fof(f88,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f83,f63]) ).
fof(f89,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f83,f67]) ).
fof(f90,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f83,f71]) ).
fof(f91,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c6 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f91,f55]) ).
fof(f95,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f91,f59]) ).
fof(f96,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f91,f63]) ).
fof(f97,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f91,f67]) ).
fof(f98,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f91,f71]) ).
fof(f99,definition,
( sQ9_spl
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ9_spl
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f103,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
! [X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f106,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
! [X2,X3] :
( sQ12_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f99,f52,f75,f102,f105,f108]) ).
fof(f112,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f109]) ).
fof(f130,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(paramodulation,[status(thm)],[f53,f112]) ).
fof(f131,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f56,f112]) ).
fof(f133,definition,
( sQ13_spl
<=> multiply(sk_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ13_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ14_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ14_spl
| inverse(sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f130,f133,f136,f108,f52]) ).
fof(f140,definition,
( sQ15_spl
<=> multiply(sk_c7,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ15_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f131,f140,f59,f108,f55]) ).
fof(f145,plain,
( sQ15_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f29,f142]) ).
fof(f146,plain,
( sQ9_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f29,f101]) ).
fof(f147,plain,
( sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f146]) ).
fof(f148,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c6) != sk_c7
| sk_c5 != sk_c6 ),
inference(paramodulation,[status(thm)],[f53,f106]) ).
fof(f151,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c7
| sk_c4 != sk_c6 ),
inference(paramodulation,[status(thm)],[f68,f106]) ).
fof(f152,definition,
( sQ16_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( sQ16_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f150,f152,f136,f105,f52]) ).
fof(f156,definition,
( sQ17_spl
<=> sk_c4 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( ~ sQ17_spl
| sk_c4 = sk_c6 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f158,plain,
( sQ17_spl
| sk_c4 != sk_c6 ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f151,f156,f71,f105,f67]) ).
fof(f162,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f76,f27]) ).
fof(f163,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f92,f27]) ).
fof(f164,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f165,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f164]) ).
fof(f180,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f56,f165]) ).
fof(f188,plain,
( ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f84,f165]) ).
fof(f191,plain,
sk_c6 = multiply(inverse(sk_c7),sk_c5),
inference(paramodulation,[status(thm)],[f29,f165]) ).
fof(f193,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f60,f180]) ).
fof(f194,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f29,f193]) ).
fof(f195,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f92,f188]) ).
fof(f196,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f53,f195]) ).
fof(f199,plain,
( ~ sQ6_spl
| sk_c6 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f76,f191]) ).
fof(f203,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f194,f64]) ).
fof(f205,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f194,f60]) ).
fof(f209,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f194,f84]) ).
fof(f210,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f194,f29]) ).
fof(f212,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f194,f103]) ).
fof(f214,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c6
| multiply(sk_c1,sk_c6) != sk_c5 ),
inference(paramodulation,[status(thm)],[f92,f212]) ).
fof(f215,definition,
( sQ18_spl
<=> multiply(sk_c1,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ18_spl
| multiply(sk_c1,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
( sQ19_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ19_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f214,f215,f218,f59,f55,f102,f91]) ).
fof(f222,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f220]) ).
fof(f223,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f225,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f194,f106]) ).
fof(f226,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f194,f225]) ).
fof(f235,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f196,f163]) ).
fof(f238,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f154]) ).
fof(f239,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f238]) ).
fof(f240,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f241,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c5) ),
inference(forward_demodulation,[status(thm)],[f194,f191]) ).
fof(f242,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f241]) ).
fof(f245,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c5) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f194,f68]) ).
fof(f247,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f194,f72]) ).
fof(f248,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f194,f195]) ).
fof(f249,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f194,f54]) ).
fof(f250,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f242,f27]) ).
fof(f251,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f242,f26]) ).
fof(f266,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c5) ),
inference(paramodulation,[status(thm)],[f209,f165]) ).
fof(f268,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f92,f266]) ).
fof(f269,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f251,f268]) ).
fof(f274,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f269,f251]) ).
fof(f275,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f269,f92]) ).
fof(f281,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f245,f165]) ).
fof(f283,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c5,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f247,f281]) ).
fof(f287,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f275,f165]) ).
fof(f288,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f274,f287]) ).
fof(f292,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f288,f217]) ).
fof(f293,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f269,f292]) ).
fof(f294,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f293]) ).
fof(f295,plain,
( sQ18_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f353,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f251,f249]) ).
fof(f354,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f353]) ).
fof(f355,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f374,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c4 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f283,f165]) ).
fof(f376,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f250,f374]) ).
fof(f377,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f376,f158]) ).
fof(f378,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f385,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f251,f163]) ).
fof(f386,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f242,f385]) ).
fof(f388,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f251,f248]) ).
fof(f397,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f157,f242]) ).
fof(f407,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f386,f388]) ).
fof(f412,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f407,f210]) ).
fof(f413,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c1) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f386,f412]) ).
fof(f414,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f407,f413]) ).
fof(f417,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c1) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f407,f226]) ).
fof(f418,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f386,f417]) ).
fof(f419,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f407,f418]) ).
fof(f428,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f407,f275]) ).
fof(f429,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c1) != sk_c1 ),
inference(resolution,[status(thm)],[f428,f419]) ).
fof(f432,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f414,f429]) ).
fof(f433,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f432]) ).
fof(f434,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f433]) ).
fof(f435,plain,
( sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f145,f152,f140]) ).
fof(f436,plain,
( sQ16_spl
| ~ sQ17_spl
| sk_c5 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f157,f154]) ).
fof(f443,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f397,f26]) ).
fof(f447,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f194,f77]) ).
fof(f455,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f397,f27]) ).
fof(f465,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f194,f29]) ).
fof(f466,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f157,f465]) ).
fof(f480,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f466,f203]) ).
fof(f481,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f157,f480]) ).
fof(f482,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f436]) ).
fof(f483,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f484,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f196,f138]) ).
fof(f490,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f29]) ).
fof(f496,plain,
( sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f490,f135]) ).
fof(f497,plain,
( sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f496]) ).
fof(f498,plain,
( sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f497]) ).
fof(f499,plain,
( sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f498]) ).
fof(f512,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f196,f199]) ).
fof(f513,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f512,f165]) ).
fof(f515,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f513]) ).
fof(f518,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f515,f26]) ).
fof(f522,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f518,f162]) ).
fof(f526,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f529,f76]) ).
fof(f528,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f529,f484]) ).
fof(f529,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f515,f522]) ).
fof(f532,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f526,f528]) ).
fof(f533,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f532]) ).
fof(f534,plain,
( sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f537,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f196,f103]) ).
fof(f538,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f529,f537]) ).
fof(f539,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f196,f538]) ).
fof(f540,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c5) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f196,f84]) ).
fof(f541,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c1,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f529,f540]) ).
fof(f543,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,X0) = multiply(sk_c1,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f541,f28]) ).
fof(f545,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c1,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f518,f543]) ).
fof(f546,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f518,f545]) ).
fof(f562,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f518,f235]) ).
fof(f564,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c5) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f570,f526]) ).
fof(f570,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f515,f562]) ).
fof(f571,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f570,f564]) ).
fof(f585,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c1) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f570,f539]) ).
fof(f586,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f570,f585]) ).
fof(f587,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f570,f586]) ).
fof(f588,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c1) != sk_c1 ),
inference(resolution,[status(thm)],[f587,f571]) ).
fof(f590,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f546,f588]) ).
fof(f591,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f590]) ).
fof(f592,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f595,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f481,f194]) ).
fof(f602,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c3) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f481,f247]) ).
fof(f605,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f481,f447]) ).
fof(f606,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f481,f605]) ).
fof(f607,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c2) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f481,f205]) ).
fof(f618,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ17_spl
| multiply(sk_c4,sk_c2) = sk_c4 ),
inference(paramodulation,[status(thm)],[f607,f455]) ).
fof(f619,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| multiply(sk_c4,sk_c3) = sk_c4 ),
inference(paramodulation,[status(thm)],[f602,f455]) ).
fof(f622,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sk_c2 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f443,f618]) ).
fof(f623,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f443,f619]) ).
fof(f626,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f622,f607]) ).
fof(f627,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f626,f606]) ).
fof(f628,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f627]) ).
fof(f668,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f376,f103]) ).
fof(f669,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f595,f668]) ).
fof(f670,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f376,f669]) ).
fof(f678,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ5_spl
| sk_c7 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f623,f595]) ).
fof(f679,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f623,f376]) ).
fof(f687,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f679,f251]) ).
fof(f692,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f678,f72]) ).
fof(f794,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c3) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f623,f670]) ).
fof(f795,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f623,f794]) ).
fof(f796,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ17_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f623,f795]) ).
fof(f797,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f796,f692]) ).
fof(f799,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ4_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f687,f797]) ).
fof(f800,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f799]) ).
fof(f801,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f800]) ).
fof(f802,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f62,f78,f79,f80,f81,f82,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f111,f139,f143,f148,f155,f159,f221,f223,f240,f295,f355,f378,f434,f435,f483,f499,f534,f592,f628,f801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP304-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:04:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.054462 seconds
% 0.11/0.44 % CPU time: 0.200751 seconds
% 0.11/0.44 % Total memory used: 104.736 MB
% 0.11/0.44 % Net memory used: 104.403 MB
%------------------------------------------------------------------------------