%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:33:16 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 42
% Syntax : Number of formulae : 182 ( 12 unt; 17 def)
% Number of atoms : 550 ( 223 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 680 ( 312 ~; 351 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 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_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c6,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c6,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/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_c6
| multiply(X5,sk_c6) != X4
| multiply(sk_c6,X4) != sk_c7
| inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/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(f37,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
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_c6,sk_c4) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
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_c6
| ! [X4] :
( multiply(X5,sk_c6) != X4
| multiply(sk_c6,X4) != sk_c7
| ! [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_c6
| multiply(X3,sk_c6) != X2
| multiply(sk_c6,X2) != sk_c7
| 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(f78,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f37,f73,f63]) ).
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_c6,sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| multiply(sk_c6,sk_c4) = sk_c7 ),
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_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ8_spl
| multiply(sk_c3,sk_c6) = 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_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ9_spl
| inverse(sk_c3) = sk_c6 ),
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_c6
| multiply(X3,sk_c6) != X2
| multiply(sk_c6,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f110,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != X0
| multiply(sk_c6,X0) != sk_c7 ),
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_c6
| multiply(sk_c6,multiply(X0,sk_c6)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f110]) ).
fof(f131,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6
| multiply(sk_c6,sk_c4) != sk_c7 ),
inference(paramodulation,[status(thm)],[f92,f113]) ).
fof(f136,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f131,f85,f97,f109,f91]) ).
fof(f145,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f64,f27]) ).
fof(f148,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f149,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f148]) ).
fof(f162,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f104,f53]) ).
fof(f163,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f104,f56]) ).
fof(f169,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f68,f162]) ).
fof(f170,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f169]) ).
fof(f171,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f172,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f60,f163]) ).
fof(f173,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f172]) ).
fof(f174,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f182,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f107,f74]) ).
fof(f183,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| inverse(sk_c7) != sk_c6
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f145,f107]) ).
fof(f185,plain,
( ~ sQ11_spl
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f27,f107]) ).
fof(f189,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f80,f182]) ).
fof(f190,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f189]) ).
fof(f191,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f192,definition,
( sQ15_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ15_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ16_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ16_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f183,f192,f195,f106,f63]) ).
fof(f199,definition,
( sQ17_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ17_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f203,definition,
( sQ18_spl
<=> inverse(inverse(sk_c6)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f185,f192,f203,f106]) ).
fof(f215,plain,
( sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f201]) ).
fof(f216,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f224,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f56,f149]) ).
fof(f232,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f26,f149]) ).
fof(f237,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f60,f224]) ).
fof(f244,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f237,f149]) ).
fof(f247,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f244]) ).
fof(f248,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f247,f194]) ).
fof(f249,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f253,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f247,f145]) ).
fof(f255,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f247,f26]) ).
fof(f273,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f279,f255]) ).
fof(f278,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f279,f64]) ).
fof(f279,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f255,f253]) ).
fof(f285,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f273,f113]) ).
fof(f286,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)],[f279,f285]) ).
fof(f287,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f286,f278]) ).
fof(f290,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f273,f287]) ).
fof(f291,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f290]) ).
fof(f292,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f293,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f279,f197]) ).
fof(f294,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f278,f293]) ).
fof(f295,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f294]) ).
fof(f296,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f302,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f92,f149]) ).
fof(f304,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c6,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f98,f302]) ).
fof(f309,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f149,f232]) ).
fof(f323,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f149]) ).
fof(f325,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f80,f323]) ).
fof(f334,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f80,f27]) ).
fof(f346,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f351,f86]) ).
fof(f349,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f351,f65]) ).
fof(f351,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f304]) ).
fof(f352,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f351,f325]) ).
fof(f353,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f352,f149]) ).
fof(f355,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f353]) ).
fof(f360,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f355,f309]) ).
fof(f366,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f360,f334]) ).
fof(f367,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f374,f360]) ).
fof(f369,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c6) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f374,f349]) ).
fof(f372,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f374,f80]) ).
fof(f374,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f355,f366]) ).
fof(f375,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f374,f369]) ).
fof(f380,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c2,sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f374,f346]) ).
fof(f381,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c2,sk_c4) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f374,f380]) ).
fof(f387,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c4 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f367,f381]) ).
fof(f400,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c4) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f387,f375]) ).
fof(f401,plain,
( sQ3_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f387,f400]) ).
fof(f402,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c4) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f387,f372]) ).
fof(f403,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f387,f402]) ).
fof(f404,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f403,f401]) ).
fof(f405,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f62,f66,f70,f71,f72,f76,f77,f78,f82,f83,f84,f88,f89,f90,f94,f95,f96,f100,f101,f102,f112,f136,f171,f174,f191,f198,f206,f216,f249,f292,f296,f405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP268-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:10:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.058258 seconds
% 0.14/0.43 % CPU time: 0.177258 seconds
% 0.14/0.43 % Total memory used: 103.216 MB
% 0.14/0.43 % Net memory used: 102.944 MB
%------------------------------------------------------------------------------