%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:15 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 40
% Syntax : Number of formulae : 175 ( 12 unt; 16 def)
% Number of atoms : 511 ( 217 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 620 ( 284 ~; 320 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 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_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [X2,X3,X4,X5,X1] :
( inverse(sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X5) != sk_c7
| multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != sk_c6
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f50,plain,
( inverse(sk_c6) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X5] :
( inverse(X5) != sk_c7
| ! [X4] :
( multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( inverse(sk_c6) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> multiply(sk_c5,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f52,f55]) ).
fof(f59,definition,
( sQ2_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ2_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f52,f59]) ).
fof(f63,definition,
( sQ3_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| inverse(sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ3_spl
| inverse(sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f52,f63]) ).
fof(f67,definition,
( sQ4_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ4_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f32,f67,f55]) ).
fof(f71,plain,
( sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f33,f67,f59]) ).
fof(f72,plain,
( sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f34,f67,f63]) ).
fof(f73,definition,
( sQ5_spl
<=> multiply(sk_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ5_spl
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f35,f73,f55]) ).
fof(f77,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f36,f73,f59]) ).
fof(f79,definition,
( sQ6_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ6_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f79,f55]) ).
fof(f83,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f79,f59]) ).
fof(f84,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f40,f79,f63]) ).
fof(f85,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f41,f85,f55]) ).
fof(f89,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f85,f59]) ).
fof(f90,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f85,f63]) ).
fof(f91,definition,
( sQ8_spl
<=> multiply(sk_c3,sk_c7) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ8_spl
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f91,f55]) ).
fof(f95,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f91,f59]) ).
fof(f96,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f91,f63]) ).
fof(f97,definition,
( sQ9_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ9_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f47,f97,f55]) ).
fof(f101,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f48,f97,f59]) ).
fof(f102,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f49,f97,f63]) ).
fof(f103,definition,
! [X0] :
( sQ10_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f104,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
! [X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f107,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
! [X2,X3] :
( sQ12_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f110,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( ~ sQ3_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f51,f103,f106,f109,f63]) ).
fof(f113,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f110]) ).
fof(f119,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f56,f28]) ).
fof(f129,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7
| multiply(sk_c7,sk_c4) != sk_c6 ),
inference(paramodulation,[status(thm)],[f92,f113]) ).
fof(f130,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f129,f85,f97,f109,f91]) ).
fof(f131,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f107,f74]) ).
fof(f134,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f131]) ).
fof(f135,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f134]) ).
fof(f136,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f64,f27]) ).
fof(f142,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f143,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f142]) ).
fof(f144,plain,
! [X0] :
( ~ sQ3_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f138,f28]) ).
fof(f145,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f26,f144]) ).
fof(f167,plain,
( ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f53,f143]) ).
fof(f171,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f56,f143]) ).
fof(f174,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f68,f167]) ).
fof(f176,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f60,f171]) ).
fof(f185,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f174,f143]) ).
fof(f188,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f185]) ).
fof(f196,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f104,f53]) ).
fof(f197,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f104,f56]) ).
fof(f201,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f68,f196]) ).
fof(f202,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f201]) ).
fof(f203,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f60,f197]) ).
fof(f205,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f204]) ).
fof(f206,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f207,definition,
( sQ13_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ13_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f211,plain,
( sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f209]) ).
fof(f212,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f216,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f217,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f143,f216]) ).
fof(f221,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f188,f27]) ).
fof(f355,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f64,f107]) ).
fof(f358,definition,
( sQ14_spl
<=> multiply(sk_c6,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( sQ14_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,definition,
( sQ15_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ15_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f355,f358,f361,f106,f63]) ).
fof(f399,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c5,sk_c8) ),
inference(paramodulation,[status(thm)],[f176,f119]) ).
fof(f404,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f56,f399]) ).
fof(f416,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f404,f143]) ).
fof(f419,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f416]) ).
fof(f420,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f419,f27]) ).
fof(f424,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f419,f217]) ).
fof(f426,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c6,X0) ),
inference(backward_demodulation,[status(thm)],[f424,f145]) ).
fof(f432,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f426,f360]) ).
fof(f438,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(paramodulation,[status(thm)],[f64,f420]) ).
fof(f442,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f424,f438]) ).
fof(f443,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f363]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f432,f361,f59,f55,f63,f358]) ).
fof(f447,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f424,f113]) ).
fof(f459,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f442,f64]) ).
fof(f460,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f442,f447]) ).
fof(f461,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f442,f460]) ).
fof(f488,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f459,f461]) ).
fof(f492,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f426,f488]) ).
fof(f493,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f492]) ).
fof(f494,plain,
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f499,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f188,f217]) ).
fof(f503,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f98,f143]) ).
fof(f504,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f499,f503]) ).
fof(f512,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f517,f65]) ).
fof(f514,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f517,f499]) ).
fof(f517,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c7 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f504,f92]) ).
fof(f518,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f517,f221]) ).
fof(f549,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f517,f86]) ).
fof(f551,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c4) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f553,f512]) ).
fof(f552,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c2) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f553,f80]) ).
fof(f553,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f514,f549]) ).
fof(f555,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c2) = sk_c4 ),
inference(paramodulation,[status(thm)],[f552,f518]) ).
fof(f557,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sk_c2 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f514,f555]) ).
fof(f559,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f557,f552]) ).
fof(f560,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f551]) ).
fof(f561,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ4_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f562,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f62,f66,f70,f71,f72,f76,f77,f82,f83,f84,f88,f89,f90,f94,f95,f96,f100,f101,f102,f112,f130,f136,f203,f206,f212,f364,f444,f446,f494,f561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP267-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:05:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.056455 seconds
% 0.14/0.42 % CPU time: 0.176135 seconds
% 0.14/0.42 % Total memory used: 103.706 MB
% 0.14/0.42 % Net memory used: 103.414 MB
%------------------------------------------------------------------------------