%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 44
% Syntax : Number of formulae : 253 ( 11 unt; 17 def)
% Number of atoms : 1047 ( 286 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 1518 ( 724 ~; 777 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 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,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X2,X1,X3] :
( multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ),
file('/export/starexec/sandbox2/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_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f38,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c5
| inverse(sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f58,plain,
! [X3] :
( multiply(X3,sk_c4) != sk_c5
| inverse(X3) != sk_c5
| ! [X1] :
( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| ! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f59,plain,
! [X0,X1,X2] :
( multiply(X2,sk_c4) != sk_c5
| inverse(X2) != sk_c5
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ0_spl
| multiply(sk_c6,sk_c5) != sk_c4 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ1_spl
| multiply(sk_c5,sk_c6) != sk_c4 ),
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_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c6 ),
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_c2,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| multiply(sk_c2,sk_c5) = sk_c6 ),
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_c3) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c5 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f79,definition,
( sQ5_spl
<=> multiply(sk_c3,sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f83,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ6_spl
| multiply(sk_c5,sk_c4) != sk_c6 ),
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
<=> inverse(sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f93,plain,
( sQ7_spl
| inverse(sk_c6) != sk_c4 ),
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
<=> multiply(sk_c1,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f101,plain,
( sQ8_spl
| multiply(sk_c1,sk_c6) != sk_c4 ),
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
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c1) = 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_c6
| multiply(X0,sk_c6) != sk_c4 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c4 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
! [X1] :
( sQ11_spl
<=> ( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
! [X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c4) != sk_c5
| inverse(X2) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f122,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c4) != sk_c5
| inverse(X0) != sk_c5 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ12_spl
| sQ11_spl
| ~ sQ1_spl
| sQ10_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f60,f83,f91,f115,f63,f118,f121]) ).
fof(f125,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c5 ),
inference(resolution,[status(thm)],[f122,f80]) ).
fof(f126,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| sk_c6 != sk_c5
| inverse(sk_c5) != sk_c5 ),
inference(paramodulation,[status(thm)],[f84,f122]) ).
fof(f128,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f76,f125]) ).
fof(f129,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f128]) ).
fof(f130,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c4 != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f61,f119]) ).
fof(f137,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f116,f100]) ).
fof(f139,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f108,f137]) ).
fof(f140,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f140]) ).
fof(f145,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f72,f32]) ).
fof(f150,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f76,f31]) ).
fof(f152,plain,
( ~ sQ9_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f108,f31]) ).
fof(f153,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f154,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f153]) ).
fof(f155,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c4,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f64,f32]) ).
fof(f167,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f30,f154]) ).
fof(f175,plain,
( ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f72,f154]) ).
fof(f176,plain,
( ~ sQ5_spl
| sk_c4 = multiply(inverse(sk_c3),sk_c5) ),
inference(paramodulation,[status(thm)],[f80,f154]) ).
fof(f178,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f68,f175]) ).
fof(f179,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f76,f176]) ).
fof(f219,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c5) = multiply(sk_c2,sk_c4) ),
inference(paramodulation,[status(thm)],[f179,f145]) ).
fof(f221,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c2,sk_c4) ),
inference(paramodulation,[status(thm)],[f64,f145]) ).
fof(f226,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| sk_c4 = multiply(sk_c2,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f61,f219]) ).
fof(f227,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c2,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f178,f221]) ).
fof(f246,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f253,f150]) ).
fof(f247,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f253,f64]) ).
fof(f248,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f253,f76]) ).
fof(f251,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f253,f72]) ).
fof(f253,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f226,f227]) ).
fof(f255,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f226,f251]) ).
fof(f260,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f255,f93]) ).
fof(f261,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c4) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f255,f101]) ).
fof(f266,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f255,f247]) ).
fof(f267,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = multiply(inverse(sk_c4),sk_c4) ),
inference(paramodulation,[status(thm)],[f266,f154]) ).
fof(f269,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f267]) ).
fof(f272,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f269,f30]) ).
fof(f285,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f272,f246]) ).
fof(f289,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f295,f260]) ).
fof(f290,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f295,f269]) ).
fof(f291,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f295,f248]) ).
fof(f292,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f295,f255]) ).
fof(f293,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f295,f253]) ).
fof(f295,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f269,f285]) ).
fof(f296,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f295,f289]) ).
fof(f304,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f296]) ).
fof(f305,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f315,plain,
( ~ sQ7_spl
| multiply(sk_c4,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f92,f31]) ).
fof(f321,plain,
( ~ sQ9_spl
| sk_c1 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f152,f154]) ).
fof(f323,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| sk_c1 = multiply(sk_c4,identity) ),
inference(forward_demodulation,[status(thm)],[f92,f321]) ).
fof(f351,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f227,f154]) ).
fof(f353,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f68,f351]) ).
fof(f364,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c6) = multiply(sk_c5,sk_c5) ),
inference(paramodulation,[status(thm)],[f178,f155]) ).
fof(f366,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c1) = multiply(sk_c5,identity) ),
inference(paramodulation,[status(thm)],[f152,f155]) ).
fof(f369,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| identity = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f315,f364]) ).
fof(f370,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f179,f369]) ).
fof(f378,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f370,f31]) ).
fof(f379,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f370,f30]) ).
fof(f384,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f379,f323]) ).
fof(f385,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f395,f379]) ).
fof(f395,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c1 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f370,f384]) ).
fof(f505,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f385,f261]) ).
fof(f506,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c1 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f395,f505]) ).
fof(f507,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f395,f506]) ).
fof(f508,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
fof(f509,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f517,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f353,f62]) ).
fof(f518,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f517]) ).
fof(f519,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,definition,
( sQ13_spl
<=> inverse(sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ13_spl
| inverse(sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ14_spl
<=> sk_c4 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ14_spl
| sk_c4 != sk_c6 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f132,f520,f523,f118,f60]) ).
fof(f528,plain,
( sQ13_spl
| ~ sQ7_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f92,f522]) ).
fof(f529,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f154,f167]) ).
fof(f542,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c4) ),
inference(paramodulation,[status(thm)],[f100,f154]) ).
fof(f544,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f108,f542]) ).
fof(f547,plain,
( ~ sQ0_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c4) ),
inference(paramodulation,[status(thm)],[f61,f154]) ).
fof(f549,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c5 = multiply(sk_c4,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f92,f547]) ).
fof(f564,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c4 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f544,f154]) ).
fof(f566,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f564]) ).
fof(f572,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f566,f529]) ).
fof(f576,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c4,sk_c6) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f581,f65]) ).
fof(f578,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f581,f61]) ).
fof(f581,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f572,f549]) ).
fof(f582,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f572,f576]) ).
fof(f583,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f544,f578]) ).
fof(f584,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f525]) ).
fof(f585,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f587,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f582,f523,f107,f99,f91,f60,f63]) ).
fof(f588,plain,
( sQ13_spl
| ~ sQ7_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f528,f523,f91,f520]) ).
fof(f596,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| sk_c1 = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f572,f366]) ).
fof(f597,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 = multiply(sk_c4,identity) ),
inference(forward_demodulation,[status(thm)],[f581,f596]) ).
fof(f598,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f572,f597]) ).
fof(f599,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c1 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f566,f598]) ).
fof(f602,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c4,sk_c6) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f581,f64]) ).
fof(f603,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f572,f602]) ).
fof(f762,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f583,f92]) ).
fof(f797,definition,
( sQ15_spl
<=> inverse(sk_c5) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f799,plain,
( sQ15_spl
| inverse(sk_c5) != sk_c5 ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f800,definition,
( sQ16_spl
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f802,plain,
( sQ16_spl
| sk_c6 != sk_c5 ),
inference(component_clause,[status(thm)],[f800]) ).
fof(f803,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f126,f797,f800,f121,f83]) ).
fof(f807,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f581,f799]) ).
fof(f808,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f581,f807]) ).
fof(f810,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c5 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f599,f581]) ).
fof(f813,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f599,f603]) ).
fof(f822,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c1) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f599,f762]) ).
fof(f823,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f599,f822]) ).
fof(f836,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c1) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f599,f808]) ).
fof(f837,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c1 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f823,f836]) ).
fof(f838,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f599,f837]) ).
fof(f839,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f838]) ).
fof(f840,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f839]) ).
fof(f841,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f842,f525]) ).
fof(f842,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f290,f370]) ).
fof(f850,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f292,f841]) ).
fof(f851,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f850]) ).
fof(f852,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f851]) ).
fof(f853,plain,
( sQ16_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f813,f802]) ).
fof(f856,plain,
( sQ16_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f810,f853]) ).
fof(f857,plain,
( sQ16_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f856]) ).
fof(f858,plain,
( sQ16_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f871,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f292,f92]) ).
fof(f872,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f842,f871]) ).
fof(f876,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f842,f379]) ).
fof(f880,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f842,f378]) ).
fof(f961,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c3) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f292,f116]) ).
fof(f962,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f842,f961]) ).
fof(f963,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f292,f962]) ).
fof(f964,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(inverse(sk_c3)) != sk_c3 ),
inference(resolution,[status(thm)],[f963,f880]) ).
fof(f969,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f872,f964]) ).
fof(f970,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f872,f969]) ).
fof(f971,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f970]) ).
fof(f972,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f971]) ).
fof(f973,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f293,f85]) ).
fof(f974,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f876,f973]) ).
fof(f975,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f842,f974]) ).
fof(f976,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f292,f975]) ).
fof(f977,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f976]) ).
fof(f978,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f979,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f86,f87,f88,f89,f90,f94,f95,f96,f97,f98,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f124,f130,f141,f305,f509,f519,f526,f585,f587,f588,f803,f840,f852,f858,f972,f978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:11:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.069067 seconds
% 0.14/0.44 % CPU time: 0.237034 seconds
% 0.14/0.44 % Total memory used: 105.420 MB
% 0.14/0.44 % Net memory used: 105.025 MB
%------------------------------------------------------------------------------