%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP278-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:33:17 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 42
% Syntax : Number of formulae : 264 ( 13 unt; 18 def)
% Number of atoms : 937 ( 287 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 1282 ( 609 ~; 655 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 67 ( 67 !; 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_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,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
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c5
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f48,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
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| ! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5 ) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f49,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
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ1_spl
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( sQ1_spl
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f28,f50,f53]) ).
fof(f57,definition,
( sQ2_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f50,f57]) ).
fof(f61,definition,
( sQ3_spl
<=> multiply(sk_c2,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ3_spl
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f50,f61]) ).
fof(f65,definition,
( sQ4_spl
<=> inverse(sk_c3) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c5 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f50,f65]) ).
fof(f69,definition,
( sQ5_spl
<=> multiply(sk_c3,sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f50,f69]) ).
fof(f73,definition,
( sQ6_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ6_spl
| inverse(sk_c1) != sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f33,f73,f53]) ).
fof(f77,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f34,f73,f57]) ).
fof(f78,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f35,f73,f61]) ).
fof(f79,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f36,f73,f65]) ).
fof(f80,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f37,f73,f69]) ).
fof(f81,definition,
( sQ7_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ7_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f83,plain,
( sQ7_spl
| inverse(sk_c4) != sk_c5 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f38,f81,f53]) ).
fof(f85,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f39,f81,f57]) ).
fof(f86,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f81,f61]) ).
fof(f87,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f81,f65]) ).
fof(f88,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f81,f69]) ).
fof(f89,definition,
( sQ8_spl
<=> multiply(sk_c6,sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( sQ8_spl
| multiply(sk_c6,sk_c4) != sk_c5 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f43,f89,f53]) ).
fof(f93,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f89,f57]) ).
fof(f94,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f89,f61]) ).
fof(f95,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f89,f65]) ).
fof(f96,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f89,f69]) ).
fof(f97,definition,
! [X0] :
( sQ9_spl
<=> ( inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ9_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
! [X1] :
( sQ10_spl
<=> ( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0] :
( ~ sQ10_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
! [X2] :
( sQ11_spl
<=> ( multiply(X2,sk_c4) != sk_c5
| inverse(X2) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f104,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c4) != sk_c5
| inverse(X0) != sk_c5 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ11_spl
| sQ10_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f49,f97,f81,f89,f53,f100,f103]) ).
fof(f108,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c5,X0) = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f51,f27]) ).
fof(f113,plain,
( ~ sQ7_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f82,f26]) ).
fof(f114,plain,
( ~ sQ2_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f58,f26]) ).
fof(f115,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f66,f26]) ).
fof(f116,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f74,f26]) ).
fof(f117,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f118,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f117]) ).
fof(f119,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f62,f27]) ).
fof(f120,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c5 ),
inference(resolution,[status(thm)],[f104,f70]) ).
fof(f122,plain,
( ~ sQ11_spl
| sk_c4 != sk_c5
| inverse(identity) != sk_c5 ),
inference(paramodulation,[status(thm)],[f25,f104]) ).
fof(f125,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f66,f120]) ).
fof(f126,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f125]) ).
fof(f127,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f128,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f90,f27]) ).
fof(f129,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f113,f27]) ).
fof(f130,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c5,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f129]) ).
fof(f133,plain,
! [X0] :
( ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f116,f27]) ).
fof(f134,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c6,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f133]) ).
fof(f135,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f101,f62]) ).
fof(f138,plain,
( ~ sQ10_spl
| sk_c5 != sk_c6
| inverse(identity) != sk_c6 ),
inference(paramodulation,[status(thm)],[f25,f101]) ).
fof(f140,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f58,f135]) ).
fof(f141,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f140]) ).
fof(f142,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f143,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f98,f51]) ).
fof(f148,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f143]) ).
fof(f149,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f150,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,definition,
( sQ12_spl
<=> identity = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ12_spl
| identity = sk_c5 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f158,definition,
( sQ14_spl
<=> sk_c6 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ14_spl
| sk_c6 = sk_c5 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f160,plain,
( sQ14_spl
| sk_c6 != sk_c5 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,definition,
( sQ15_spl
<=> inverse(identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ15_spl
| inverse(identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f165,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| inverse(sk_c5) != sk_c6
| sk_c4 != sk_c5 ),
inference(paramodulation,[status(thm)],[f54,f98]) ).
fof(f167,definition,
( sQ16_spl
<=> sk_c4 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ16_spl
| sk_c4 = sk_c5 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f169,plain,
( sQ16_spl
| sk_c4 != sk_c5 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,definition,
( sQ17_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ17_spl
| inverse(sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f165,f167,f170,f97,f53]) ).
fof(f186,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c3) = multiply(sk_c2,identity) ),
inference(paramodulation,[status(thm)],[f115,f119]) ).
fof(f250,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f138,f161,f158,f100]) ).
fof(f252,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(paramodulation,[status(thm)],[f51,f134]) ).
fof(f260,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c5) = multiply(sk_c1,sk_c6) ),
inference(paramodulation,[status(thm)],[f252,f108]) ).
fof(f262,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c5,multiply(sk_c1,X0)) = multiply(sk_c1,X0) ),
inference(paramodulation,[status(thm)],[f134,f108]) ).
fof(f263,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c5,multiply(sk_c4,X0)) = multiply(sk_c1,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f128,f108]) ).
fof(f264,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c2) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f114,f108]) ).
fof(f266,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c4) = multiply(sk_c1,sk_c5) ),
inference(paramodulation,[status(thm)],[f90,f108]) ).
fof(f269,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f51,f260]) ).
fof(f270,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| X0 = multiply(sk_c1,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f130,f263]) ).
fof(f273,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(sk_c1,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f113,f266]) ).
fof(f282,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c4,X0) = multiply(sk_c1,X0) ),
inference(paramodulation,[status(thm)],[f130,f270]) ).
fof(f285,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c5,X0) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f270,f134]) ).
fof(f290,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| X0 = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(backward_demodulation,[status(thm)],[f282,f270]) ).
fof(f291,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(backward_demodulation,[status(thm)],[f282,f108]) ).
fof(f294,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(sk_c4,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f282,f273]) ).
fof(f296,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c5,multiply(sk_c1,X0)) = multiply(sk_c4,X0) ),
inference(backward_demodulation,[status(thm)],[f282,f262]) ).
fof(f306,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c4,X0)) ),
inference(backward_demodulation,[status(thm)],[f285,f128]) ).
fof(f308,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f285,f116]) ).
fof(f309,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f285,f90]) ).
fof(f374,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f309,f113]) ).
fof(f448,definition,
( sQ26_spl
<=> inverse(identity) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ26_spl
| inverse(identity) != sk_c5 ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f122,f448,f167,f103]) ).
fof(f457,plain,
( sQ15_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f152,f163]) ).
fof(f464,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f152,f25]) ).
fof(f465,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f464,f308]) ).
fof(f467,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ12_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f152,f465]) ).
fof(f468,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ12_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f464,f309]) ).
fof(f474,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f168,f82]) ).
fof(f483,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| X0 = multiply(sk_c5,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f168,f290]) ).
fof(f484,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f168,f291]) ).
fof(f485,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c5,X0) = multiply(sk_c5,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f159,f484]) ).
fof(f488,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f483,f485]) ).
fof(f493,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f374,f151,f73,f50,f89,f81]) ).
fof(f502,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| identity = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f168,f294]) ).
fof(f503,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ14_spl
| identity = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f488,f502]) ).
fof(f514,plain,
( sQ26_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f503,f450]) ).
fof(f515,plain,
( sQ26_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f474,f514]) ).
fof(f516,plain,
( sQ26_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f515]) ).
fof(f517,plain,
( sQ26_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f531,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f118,f118]) ).
fof(f532,plain,
( ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c4) ),
inference(paramodulation,[status(thm)],[f54,f118]) ).
fof(f533,plain,
( ~ sQ5_spl
| sk_c4 = multiply(inverse(sk_c3),sk_c5) ),
inference(paramodulation,[status(thm)],[f70,f118]) ).
fof(f534,plain,
( ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f62,f118]) ).
fof(f535,plain,
( ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c5) ),
inference(paramodulation,[status(thm)],[f51,f118]) ).
fof(f538,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f66,f533]) ).
fof(f543,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f58,f534]) ).
fof(f598,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f25,f118]) ).
fof(f603,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f26,f118]) ).
fof(f605,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f608,f186]) ).
fof(f606,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c2) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f608,f264]) ).
fof(f608,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f531,f603]) ).
fof(f614,plain,
( ~ sQ2_spl
| sk_c2 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f114,f118]) ).
fof(f618,plain,
( ~ sQ2_spl
| sk_c2 = inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f608,f614]) ).
fof(f641,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f130,f306]) ).
fof(f642,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f643,f51]) ).
fof(f643,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c1,X0) = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f641,f296]) ).
fof(f654,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c5) ),
inference(backward_demodulation,[status(thm)],[f467,f535]) ).
fof(f656,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ12_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f468,f167,f151,f73,f81,f50,f89]) ).
fof(f695,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f618,f118]) ).
fof(f696,plain,
( ~ sQ4_spl
| sk_c3 = multiply(inverse(sk_c5),identity) ),
inference(paramodulation,[status(thm)],[f115,f118]) ).
fof(f698,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(backward_demodulation,[status(thm)],[f699,f532]) ).
fof(f699,plain,
( ~ sQ4_spl
| sk_c3 = inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f608,f696]) ).
fof(f701,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c2 = inverse(sk_c5) ),
inference(backward_demodulation,[status(thm)],[f717,f618]) ).
fof(f703,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c1) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f717,f75]) ).
fof(f706,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(sk_c2,multiply(sk_c5,X0)) ),
inference(backward_demodulation,[status(thm)],[f717,f695]) ).
fof(f707,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f717,f114]) ).
fof(f709,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c6,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f717,f543]) ).
fof(f717,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f70,f698]) ).
fof(f724,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f699,f701]) ).
fof(f727,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f119,f706]) ).
fof(f731,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f717,f727]) ).
fof(f732,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c1),X0) ),
inference(backward_demodulation,[status(thm)],[f736,f598]) ).
fof(f733,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| X0 = multiply(X0,sk_c1) ),
inference(backward_demodulation,[status(thm)],[f736,f608]) ).
fof(f736,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f606,f707]) ).
fof(f740,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f717,f709]) ).
fof(f741,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f742,f83]) ).
fof(f742,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f538,f740]) ).
fof(f770,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c3 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f699,f741]) ).
fof(f771,plain,
( sQ7_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f724,f770]) ).
fof(f782,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c1 ),
inference(paramodulation,[status(thm)],[f732,f733]) ).
fof(f790,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c1 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f782,f703]) ).
fof(f792,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ0_spl
| sk_c5 = sk_c1 ),
inference(paramodulation,[status(thm)],[f731,f733]) ).
fof(f803,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f792,f790]) ).
fof(f804,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f803]) ).
fof(f805,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f804]) ).
fof(f825,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f742,f169]) ).
fof(f826,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f825]) ).
fof(f827,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f889,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f717,f91]) ).
fof(f890,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f731,f889]) ).
fof(f891,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f742,f890]) ).
fof(f892,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f891]) ).
fof(f893,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f892]) ).
fof(f894,plain,
( sQ15_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f474,f457]) ).
fof(f900,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f474,f172]) ).
fof(f903,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| multiply(sk_c5,sk_c5) = identity ),
inference(forward_demodulation,[status(thm)],[f168,f113]) ).
fof(f907,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f269,f903]) ).
fof(f910,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(inverse(sk_c5),X0) ),
inference(forward_demodulation,[status(thm)],[f907,f598]) ).
fof(f917,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f474,f910]) ).
fof(f922,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f907,f26]) ).
fof(f923,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f917,f55]) ).
fof(f924,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c6 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f168,f923]) ).
fof(f943,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f168,f642]) ).
fof(f944,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f917,f943]) ).
fof(f945,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ15_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f944,f894]) ).
fof(f946,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sQ15_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f945]) ).
fof(f953,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f922,f654]) ).
fof(f981,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f953,f160]) ).
fof(f982,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f981]) ).
fof(f983,plain,
( sQ14_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f1005,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f924,f158,f73,f50,f167,f81,f53]) ).
fof(f1028,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c3) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f717,f605]) ).
fof(f1029,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f731,f1028]) ).
fof(f1030,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f731,f115]) ).
fof(f1032,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(X0,sk_c2) ),
inference(backward_demodulation,[status(thm)],[f1035,f608]) ).
fof(f1035,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f1029,f1030]) ).
fof(f1115,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = sk_c2 ),
inference(paramodulation,[status(thm)],[f731,f1032]) ).
fof(f1122,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1115,f771]) ).
fof(f1123,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1122]) ).
fof(f1131,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f717,f900]) ).
fof(f1132,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1131]) ).
fof(f1133,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1132]) ).
fof(f1134,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f60,f64,f68,f72,f76,f77,f78,f79,f80,f84,f85,f86,f87,f88,f92,f93,f94,f95,f96,f106,f127,f142,f150,f173,f250,f451,f493,f517,f656,f805,f827,f893,f946,f983,f1005,f1123,f1133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP278-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:08:05 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % 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: 0.070792 seconds
% 0.14/0.44 % CPU time: 0.274203 seconds
% 0.14/0.44 % Total memory used: 105.500 MB
% 0.14/0.44 % Net memory used: 105.153 MB
%------------------------------------------------------------------------------