%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP262-1 : 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 12:33:15 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 48
% Syntax : Number of formulae : 274 ( 17 unt; 19 def)
% Number of atoms : 1052 ( 312 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1490 ( 712 ~; 759 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 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_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f33,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f37,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f60,f63]) ).
fof(f67,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f60,f67]) ).
fof(f71,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f60,f71]) ).
fof(f75,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f60,f75]) ).
fof(f79,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f60,f79]) ).
fof(f83,definition,
( sQ6_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ6_spl
| inverse(sk_c1) != sk_c7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f83,f63]) ).
fof(f87,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f83,f67]) ).
fof(f88,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f40,f83,f71]) ).
fof(f89,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f41,f83,f75]) ).
fof(f90,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f42,f83,f79]) ).
fof(f91,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f91,f63]) ).
fof(f95,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f91,f67]) ).
fof(f96,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f91,f71]) ).
fof(f97,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f91,f75]) ).
fof(f98,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f91,f79]) ).
fof(f99,definition,
( sQ8_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f99,f63]) ).
fof(f103,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f99,f67]) ).
fof(f104,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f99,f71]) ).
fof(f105,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f99,f75]) ).
fof(f106,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f99,f79]) ).
fof(f107,definition,
( sQ9_spl
<=> multiply(sk_c5,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f109,plain,
( sQ9_spl
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f107,f63]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f67]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f71]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f75]) ).
fof(f114,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f107,f79]) ).
fof(f115,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f125,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f115,f118,f107,f63,f121,f124]) ).
fof(f128,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f125,f80]) ).
fof(f130,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f76,f128]) ).
fof(f131,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f122,f72]) ).
fof(f134,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| sk_c5 != sk_c7
| inverse(sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f92,f122]) ).
fof(f136,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f133]) ).
fof(f137,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f136]) ).
fof(f138,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f144,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f80,f32]) ).
fof(f147,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c6) != sk_c5 ),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f150,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f92,f147]) ).
fof(f151,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f155,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f68,f31]) ).
fof(f157,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f158,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f157]) ).
fof(f159,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f162,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f155,f32]) ).
fof(f163,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f162]) ).
fof(f173,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f158,f158]) ).
fof(f174,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f31,f158]) ).
fof(f175,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f30,f158]) ).
fof(f177,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f61,f158]) ).
fof(f179,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f158]) ).
fof(f180,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f158]) ).
fof(f182,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f84,f177]) ).
fof(f183,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f179]) ).
fof(f184,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f76,f180]) ).
fof(f190,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f175,f158]) ).
fof(f192,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f182,f158]) ).
fof(f194,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f192]) ).
fof(f196,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(resolution,[status(thm)],[f116,f84]) ).
fof(f197,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sk_c6 != sk_c7
| multiply(sk_c4,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f76,f116]) ).
fof(f200,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f61,f196]) ).
fof(f201,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f200]) ).
fof(f202,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f203,definition,
( sQ14_spl
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ14_spl
| multiply(sk_c4,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ15_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ15_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f197,f203,f206,f115,f75]) ).
fof(f213,definition,
( sQ17_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ17_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f217,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f215]) ).
fof(f218,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f287,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f31,f190]) ).
fof(f312,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f183,f159]) ).
fof(f318,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f184,f312]) ).
fof(f321,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f173,f174]) ).
fof(f323,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f31,f173]) ).
fof(f335,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f318,f109]) ).
fof(f336,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c5) ),
inference(paramodulation,[status(thm)],[f318,f144]) ).
fof(f337,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f318,f158]) ).
fof(f339,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f64,f336]) ).
fof(f340,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f339]) ).
fof(f341,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f337]) ).
fof(f342,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f335]) ).
fof(f343,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f344,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f318,f108]) ).
fof(f345,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f341,f287]) ).
fof(f351,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f341,f30]) ).
fof(f352,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f341,f345]) ).
fof(f370,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f344,f208]) ).
fof(f372,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f344,f76]) ).
fof(f374,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c1,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f344,f61]) ).
fof(f376,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f344,f72]) ).
fof(f377,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f344,f80]) ).
fof(f380,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f341,f321]) ).
fof(f381,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(inverse(X0)) = multiply(X0,sk_c7) ),
inference(paramodulation,[status(thm)],[f173,f380]) ).
fof(f388,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(inverse(X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f380,f381]) ).
fof(f392,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f351,f163]) ).
fof(f402,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c4 ),
inference(paramodulation,[status(thm)],[f372,f388]) ).
fof(f404,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c3 ),
inference(paramodulation,[status(thm)],[f68,f388]) ).
fof(f406,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f352,f404]) ).
fof(f424,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f406,f352]) ).
fof(f425,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f406,f380]) ).
fof(f426,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f406,f370]) ).
fof(f428,plain,
( sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c1) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f406,f85]) ).
fof(f430,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f406,f424]) ).
fof(f445,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c1,sk_c3) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f406,f374]) ).
fof(f446,plain,
( sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c5) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f448,f428]) ).
fof(f448,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f425,f445]) ).
fof(f449,plain,
( sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c4 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f402,f446]) ).
fof(f452,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f392,f376]) ).
fof(f453,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f406,f452]) ).
fof(f454,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f426]) ).
fof(f455,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f462,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c3) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f453,f402]) ).
fof(f463,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f453,f372]) ).
fof(f464,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f453,f344]) ).
fof(f465,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f430,f462]) ).
fof(f466,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sQ6_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f449]) ).
fof(f467,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f466]) ).
fof(f538,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c3) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f453,f377]) ).
fof(f539,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f425,f538]) ).
fof(f541,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f547,f453]) ).
fof(f542,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| X0 = multiply(X0,sk_c4) ),
inference(backward_demodulation,[status(thm)],[f547,f425]) ).
fof(f546,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f547,f406]) ).
fof(f547,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f453,f539]) ).
fof(f549,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f547,f464]) ).
fof(f592,definition,
( sQ19_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ19_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f594,plain,
( sQ19_spl
| inverse(sk_c2) != sk_c7 ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,definition,
( sQ20_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ20_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f134,f592,f595,f121,f91]) ).
fof(f604,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(X0,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f194,f321]) ).
fof(f609,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c6) = identity ),
inference(forward_demodulation,[status(thm)],[f194,f287]) ).
fof(f610,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f194,f609]) ).
fof(f612,plain,
( sQ19_spl
| ~ sQ8_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f100,f594]) ).
fof(f613,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(X0,inverse(X0)) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f194,f323]) ).
fof(f617,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(paramodulation,[status(thm)],[f100,f613]) ).
fof(f621,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f604,f617]) ).
fof(f623,plain,
( sQ19_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f621,f612]) ).
fof(f624,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| inverse(sk_c6) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f621,f610]) ).
fof(f625,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| X0 = multiply(X0,sk_c2) ),
inference(backward_demodulation,[status(thm)],[f621,f604]) ).
fof(f628,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f621,f194]) ).
fof(f630,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f621,f624]) ).
fof(f632,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c2) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f621,f92]) ).
fof(f636,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c7) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f621,f108]) ).
fof(f639,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f640,f632]) ).
fof(f640,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f628,f30]) ).
fof(f644,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c7) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f639,f636]) ).
fof(f645,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f639,f597]) ).
fof(f646,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f640,f644]) ).
fof(f647,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f623]) ).
fof(f648,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f647]) ).
fof(f649,plain,
( ~ sQ19_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f630,f593]) ).
fof(f650,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f645]) ).
fof(f651,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f673,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f621,f65]) ).
fof(f674,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f640,f673]) ).
fof(f675,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ19_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f649,f674]) ).
fof(f676,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ7_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f639,f675]) ).
fof(f677,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f676]) ).
fof(f678,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f757,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f621,f125]) ).
fof(f758,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c2) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f639,f757]) ).
fof(f759,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| X0 != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f625,f758]) ).
fof(f760,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| X0 != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f621,f759]) ).
fof(f761,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c2) != sk_c2 ),
inference(destructive_equality_resolution,[status(thm)],[f760]) ).
fof(f762,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f761,f630]) ).
fof(f763,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f762]) ).
fof(f775,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f547,f463]) ).
fof(f812,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f549,f119]) ).
fof(f813,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| X0 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f542,f812]) ).
fof(f814,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| X0 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f541,f813]) ).
fof(f815,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| X0 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f549,f814]) ).
fof(f816,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) != sk_c4 ),
inference(destructive_equality_resolution,[status(thm)],[f815]) ).
fof(f817,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f816,f775]) ).
fof(f818,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f817]) ).
fof(f819,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c4,sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f546,f205]) ).
fof(f820,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f542,f819]) ).
fof(f821,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f549,f820]) ).
fof(f822,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f821]) ).
fof(f823,plain,
( sQ14_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f822]) ).
fof(f824,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f78,f82,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f127,f132,f138,f152,f202,f209,f218,f343,f455,f467,f598,f648,f651,f678,f763,f818,f823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP262-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:03:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.056537 seconds
% 0.11/0.43 % CPU time: 0.212340 seconds
% 0.11/0.43 % Total memory used: 101.688 MB
% 0.11/0.43 % Net memory used: 101.382 MB
%------------------------------------------------------------------------------