%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP289-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:19 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.33s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 47
% Syntax : Number of formulae : 250 ( 10 unt; 20 def)
% Number of atoms : 948 ( 290 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1342 ( 644 ~; 678 |; 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 : 57 ( 57 !; 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_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = 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
| inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
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_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = 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
| ! [X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ) ) ) ),
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
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c5 ),
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(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(f83,definition,
( sQ6_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = 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_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
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_c2,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
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_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c2) = 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
| sQ11_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f60,f115,f118,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(f136,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| sk_c5 != sk_c7
| inverse(sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f100,f122]) ).
fof(f137,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f68,f133]) ).
fof(f138,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f138]) ).
fof(f142,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f72,f32]) ).
fof(f148,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c6) != sk_c5 ),
inference(resolution,[status(thm)],[f119,f108]) ).
fof(f151,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f100,f148]) ).
fof(f152,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f151]) ).
fof(f153,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f76,f31]) ).
fof(f156,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f68,f31]) ).
fof(f157,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f92,f31]) ).
fof(f159,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f31,f32]) ).
fof(f160,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f30,f159]) ).
fof(f164,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f156,f32]) ).
fof(f165,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f164]) ).
fof(f183,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f72,f160]) ).
fof(f184,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f80,f160]) ).
fof(f185,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f84,f160]) ).
fof(f187,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f183]) ).
fof(f188,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f76,f184]) ).
fof(f189,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f92,f185]) ).
fof(f198,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(resolution,[status(thm)],[f116,f92]) ).
fof(f199,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,
( ~ sQ2_spl
| ~ sQ10_spl
| sk_c7 != sk_c7
| multiply(sk_c3,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f68,f116]) ).
fof(f203,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f84,f198]) ).
fof(f204,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f203]) ).
fof(f205,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,definition,
( sQ14_spl
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ14_spl
| multiply(sk_c4,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
( sQ15_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ15_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f199,f206,f209,f115,f75]) ).
fof(f213,definition,
( sQ16_spl
<=> multiply(sk_c3,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f216,definition,
( sQ17_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ17_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f200,f213,f216,f115,f67]) ).
fof(f225,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f218]) ).
fof(f226,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f246,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c6) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f188,f142]) ).
fof(f248,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f142]) ).
fof(f252,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c3,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f61,f246]) ).
fof(f253,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c3,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f187,f248]) ).
fof(f263,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c7,sk_c5) ),
inference(paramodulation,[status(thm)],[f252,f165]) ).
fof(f270,plain,
( sQ14_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c7) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f286,f208]) ).
fof(f277,plain,
( sQ15_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f286,f211]) ).
fof(f281,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f286,f155]) ).
fof(f283,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f286,f76]) ).
fof(f284,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f286,f72]) ).
fof(f285,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f286,f80]) ).
fof(f286,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f252,f253]) ).
fof(f288,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f252,f284]) ).
fof(f289,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f288,f277]) ).
fof(f290,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f293,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f286,f119]) ).
fof(f294,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f286,f293]) ).
fof(f303,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f288,f263]) ).
fof(f304,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f303,f160]) ).
fof(f306,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f304]) ).
fof(f309,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f306,f30]) ).
fof(f327,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f285,f32]) ).
fof(f329,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| X0 = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f309,f327]) ).
fof(f330,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f309,f329]) ).
fof(f335,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f309,f281]) ).
fof(f340,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f344,f283]) ).
fof(f341,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f344,f288]) ).
fof(f344,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f306,f335]) ).
fof(f352,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f344,f294]) ).
fof(f353,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f344,f352]) ).
fof(f354,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f344,f353]) ).
fof(f355,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f354,f340]) ).
fof(f359,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f330,f355]) ).
fof(f360,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f359]) ).
fof(f361,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ14_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f330,f270]) ).
fof(f363,plain,
( sQ14_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f341,f362]) ).
fof(f364,plain,
( sQ14_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f344,f363]) ).
fof(f365,plain,
( sQ14_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ14_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f367,definition,
( sQ19_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ19_spl
| inverse(sk_c2) != sk_c7 ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,definition,
( sQ20_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( sQ20_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f136,f367,f370,f121,f99]) ).
fof(f382,plain,
( sQ19_spl
| ~ sQ9_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f108,f369]) ).
fof(f402,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f100,f160]) ).
fof(f404,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f108,f402]) ).
fof(f408,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f189,f61]) ).
fof(f409,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f372]) ).
fof(f410,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f408,f84]) ).
fof(f414,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f408,f157]) ).
fof(f416,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f408,f382]) ).
fof(f418,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f408,f92]) ).
fof(f425,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f404,f160]) ).
fof(f427,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f31,f425]) ).
fof(f428,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f427,f31]) ).
fof(f431,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f427,f30]) ).
fof(f434,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f408,f65]) ).
fof(f435,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f404,f434]) ).
fof(f440,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c5 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f412,f160]) ).
fof(f442,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f418,f440]) ).
fof(f443,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f431,f442]) ).
fof(f444,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f416]) ).
fof(f445,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f444]) ).
fof(f455,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f443,f108]) ).
fof(f457,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f443,f435]) ).
fof(f458,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f457]) ).
fof(f459,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f458]) ).
fof(f469,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f443,f125]) ).
fof(f470,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f443,f469]) ).
fof(f471,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c5,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f455,f160]) ).
fof(f472,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f431,f471]) ).
fof(f477,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f431,f414]) ).
fof(f478,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f484,f455]) ).
fof(f480,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f484,f431]) ).
fof(f482,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f484,f418]) ).
fof(f484,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f427,f477]) ).
fof(f489,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f484,f428]) ).
fof(f490,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c2) = sk_c1 ),
inference(paramodulation,[status(thm)],[f478,f489]) ).
fof(f493,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f480,f490]) ).
fof(f501,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f493,f484]) ).
fof(f504,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f493,f482]) ).
fof(f505,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f493,f504]) ).
fof(f518,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f501,f470]) ).
fof(f519,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c2) != sk_c5
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f501,f518]) ).
fof(f520,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f501,f519]) ).
fof(f521,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f520,f505]) ).
fof(f523,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f472,f521]) ).
fof(f524,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f523]) ).
fof(f525,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f557,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c6) ),
inference(paramodulation,[status(thm)],[f253,f160]) ).
fof(f559,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f68,f557]) ).
fof(f560,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f62]) ).
fof(f561,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f562,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,f127,f132,f139,f153,f205,f212,f219,f226,f290,f361,f366,f373,f410,f445,f459,f525,f561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP289-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Sun Sep 20 20:08:21 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 % Drodi V4.1.1
% 0.08/0.33 % Refutation found
% 0.08/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.34 % Elapsed time: 0.039217 seconds
% 0.08/0.34 % CPU time: 0.103060 seconds
% 0.08/0.34 % Total memory used: 103.635 MB
% 0.08/0.34 % Net memory used: 103.369 MB
%------------------------------------------------------------------------------