%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP300-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:33:21 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 36
% Syntax : Number of formulae : 171 ( 11 unt; 12 def)
% Number of atoms : 522 ( 207 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 647 ( 296 ~; 339 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 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_c5,sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c4
| multiply(sk_c4,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
! [X2,X1,X3] :
( inverse(X3) != sk_c4
| multiply(X3,sk_c4) != sk_c5
| inverse(sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c4,sk_c6) != sk_c5
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f30,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f38,plain,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
( multiply(sk_c5,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f45,plain,
( multiply(sk_c2,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f46,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
( multiply(sk_c5,sk_c4) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f51,plain,
( multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f53,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f56,plain,
! [X3] :
( inverse(X3) != sk_c4
| multiply(X3,sk_c4) != sk_c5
| inverse(sk_c6) != sk_c4
| ! [X1] :
( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c4,sk_c6) != sk_c5
| ! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c4 ) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f57,plain,
! [X0,X1,X2] :
( inverse(X2) != sk_c4
| multiply(X2,sk_c4) != sk_c5
| inverse(sk_c6) != sk_c4
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c4,sk_c6) != sk_c5
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c4 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f60,plain,
( sQ0_spl
| multiply(sk_c6,sk_c5) != sk_c4 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> multiply(sk_c5,sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f63,plain,
( sQ1_spl
| multiply(sk_c5,sk_c4) != sk_c6 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f58,f61]) ).
fof(f65,definition,
( sQ2_spl
<=> multiply(sk_c2,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ2_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f58,f65]) ).
fof(f69,definition,
( sQ3_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ3_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f58,f69]) ).
fof(f73,definition,
( sQ4_spl
<=> inverse(sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ4_spl
| inverse(sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ4_spl
| inverse(sk_c6) != sk_c4 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f58,f73]) ).
fof(f77,definition,
( sQ5_spl
<=> multiply(sk_c3,sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ5_spl
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f81,definition,
( sQ6_spl
<=> inverse(sk_c3) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ6_spl
| inverse(sk_c3) = sk_c4 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f85,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f38,f85,f61]) ).
fof(f89,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f39,f85,f65]) ).
fof(f90,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f40,f85,f69]) ).
fof(f91,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f85,f73]) ).
fof(f92,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f85,f77]) ).
fof(f93,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f85,f81]) ).
fof(f94,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c6 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f94,f61]) ).
fof(f98,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f94,f65]) ).
fof(f99,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f94,f69]) ).
fof(f100,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f94,f73]) ).
fof(f101,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f94,f77]) ).
fof(f102,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f94,f81]) ).
fof(f103,definition,
( sQ9_spl
<=> multiply(sk_c4,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ9_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f103,f61]) ).
fof(f107,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f103,f65]) ).
fof(f108,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f103,f69]) ).
fof(f109,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f103,f73]) ).
fof(f112,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f113,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
! [X2] :
( sQ11_spl
<=> ( inverse(X2) != sk_c4
| multiply(X2,sk_c4) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f116,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c5 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ11_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ9_spl
| sQ10_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f58,f112,f103,f61,f73,f115]) ).
fof(f119,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c4 ),
inference(resolution,[status(thm)],[f116,f78]) ).
fof(f121,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f82,f119]) ).
fof(f122,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f121]) ).
fof(f123,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f113,f66]) ).
fof(f126,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f113,f86]) ).
fof(f130,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f70,f125]) ).
fof(f131,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f130]) ).
fof(f132,plain,
( ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f95,f126]) ).
fof(f134,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f137,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f104,f31]) ).
fof(f146,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f74,f30]) ).
fof(f147,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f95,f30]) ).
fof(f148,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f149,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f104,f146]) ).
fof(f150,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f29,f148]) ).
fof(f152,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f149,f29]) ).
fof(f153,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f152,f62]) ).
fof(f157,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f153,f104]) ).
fof(f161,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ9_spl
| multiply(sk_c4,sk_c5) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f153,f60]) ).
fof(f183,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ4_spl
| X0 = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f152,f137]) ).
fof(f184,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ1_spl
| X0 = multiply(sk_c4,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f153,f183]) ).
fof(f188,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c4,sk_c5) ),
inference(paramodulation,[status(thm)],[f157,f184]) ).
fof(f191,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f161]) ).
fof(f192,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f197,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f104,f31]) ).
fof(f210,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f29,f150]) ).
fof(f211,plain,
( ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f66,f150]) ).
fof(f213,plain,
( ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c5) ),
inference(paramodulation,[status(thm)],[f86,f150]) ).
fof(f220,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f70,f211]) ).
fof(f222,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f95,f213]) ).
fof(f223,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f59,f222]) ).
fof(f360,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f223,f95]) ).
fof(f368,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f152,f63]) ).
fof(f369,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f223,f368]) ).
fof(f370,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f369]) ).
fof(f371,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f376,plain,
( sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f223,f75]) ).
fof(f377,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f150,f210]) ).
fof(f383,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f223,f104]) ).
fof(f386,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f223,f147]) ).
fof(f390,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f223,f86]) ).
fof(f394,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f223,f59]) ).
fof(f399,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f223,f137]) ).
fof(f401,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c4) ),
inference(paramodulation,[status(thm)],[f394,f399]) ).
fof(f406,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f383,f401]) ).
fof(f421,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f406,f150]) ).
fof(f423,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f30,f421]) ).
fof(f426,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| multiply(sk_c4,sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f423,f386]) ).
fof(f427,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f423,f377]) ).
fof(f462,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c4,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f427,f197]) ).
fof(f463,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c4,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f223,f462]) ).
fof(f465,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c1 = multiply(sk_c4,sk_c5) ),
inference(paramodulation,[status(thm)],[f426,f463]) ).
fof(f472,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c1 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f394,f465]) ).
fof(f480,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c1) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f472,f390]) ).
fof(f482,plain,
( sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c4) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f472,f376]) ).
fof(f484,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f472,f360]) ).
fof(f490,plain,
( sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f472,f482]) ).
fof(f494,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f490]) ).
fof(f495,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f653,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c1) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f472,f116]) ).
fof(f654,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f472,f653]) ).
fof(f655,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c1) != sk_c5 ),
inference(resolution,[status(thm)],[f654,f484]) ).
fof(f657,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f480,f655]) ).
fof(f658,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f657]) ).
fof(f659,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f658]) ).
fof(f678,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f220,f150]) ).
fof(f680,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f74,f678]) ).
fof(f681,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f146,f680]) ).
fof(f682,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f681,f146]) ).
fof(f686,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f682,f103,f69,f65,f73]) ).
fof(f687,plain,
$false,
inference(sat_refutation,[status(thm)],[f64,f68,f72,f76,f88,f89,f90,f91,f92,f93,f97,f98,f99,f100,f101,f102,f106,f107,f108,f109,f118,f123,f132,f135,f192,f371,f495,f659,f686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP300-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n011.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:08:30 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.15/5.40 % Drodi V4.1.1
% 0.15/5.41 % Refutation found
% 0.15/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.44 % Elapsed time: 0.056359 seconds
% 0.15/5.44 % CPU time: 0.137553 seconds
% 0.15/5.44 % Total memory used: 26.712 MB
% 0.15/5.44 % Net memory used: 26.673 MB
%------------------------------------------------------------------------------