%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP234-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:33:10 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 43
% Syntax : Number of formulae : 207 ( 11 unt; 19 def)
% Number of atoms : 632 ( 240 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 799 ( 374 ~; 406 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 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,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c7
| multiply(X5,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| multiply(X3,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/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,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f48,plain,
! [X5] :
( inverse(X5) != sk_c7
| ! [X2] :
( multiply(X5,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| ! [X3] : multiply(X3,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(X0,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,definition,
( sQ0_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ0_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( sQ0_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ1_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ1_spl
| inverse(sk_c3) = sk_c7 ),
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
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
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_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ3_spl
| multiply(sk_c7,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
<=> multiply(sk_c4,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ4_spl
| multiply(sk_c4,sk_c7) = 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
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ5_spl
| inverse(sk_c4) = sk_c7 ),
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
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = 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
<=> multiply(sk_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ8_spl
| inverse(sk_c2) = sk_c7 ),
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
<=> multiply(X0,sk_c7) != sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f98,plain,
! [X0] :
( ~ sQ9_spl
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,definition,
! [X1] :
( sQ10_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,definition,
! [X2] :
( sQ11_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f104,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
! [X3,X4] :
( sQ12_spl
<=> ( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f107,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)],[f106]) ).
fof(f109,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f50,f97,f100,f103,f106]) ).
fof(f110,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f107]) ).
fof(f132,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(paramodulation,[status(thm)],[f66,f110]) ).
fof(f134,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f82,f110]) ).
fof(f142,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f132,f61,f69,f106,f65]) ).
fof(f143,definition,
( sQ15_spl
<=> multiply(sk_c7,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ15_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f150,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f134,f143,f89,f106,f81]) ).
fof(f151,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f104,f58]) ).
fof(f154,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f54,f151]) ).
fof(f155,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f74,f98]) ).
fof(f160,plain,
( ~ sQ9_spl
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f25,f98]) ).
fof(f162,plain,
( ~ sQ6_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f164,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f54,f26]) ).
fof(f165,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f166,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f165]) ).
fof(f176,definition,
( sQ18_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ18_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f184,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f178]) ).
fof(f185,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f186,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sk_c6 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f51,f101]) ).
fof(f188,definition,
( sQ20_spl
<=> multiply(sk_c7,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ20_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f190,plain,
( sQ20_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ21_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ21_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f186,f188,f191,f100,f50]) ).
fof(f196,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) != sk_c6 ),
inference(resolution,[status(thm)],[f90,f101]) ).
fof(f198,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f90,f26]) ).
fof(f199,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f82,f196]) ).
fof(f200,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f199]) ).
fof(f201,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f200]) ).
fof(f224,plain,
( ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f66,f166]) ).
fof(f225,plain,
( ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f58,f166]) ).
fof(f231,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f25,f166]) ).
fof(f236,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f70,f224]) ).
fof(f237,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f62,f236]) ).
fof(f238,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f54,f225]) ).
fof(f239,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f190]) ).
fof(f240,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f243,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f237,f164]) ).
fof(f256,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f237,f193]) ).
fof(f257,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f256]) ).
fof(f258,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f269,plain,
( ~ sQ8_spl
| sk_c2 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f198,f166]) ).
fof(f271,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f51,f269]) ).
fof(f273,plain,
( ~ sQ12_spl
| inverse(inverse(identity)) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f231,f110]) ).
fof(f275,plain,
( ~ sQ12_spl
| inverse(identity) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f25,f110]) ).
fof(f277,definition,
( sQ22_spl
<=> inverse(inverse(identity)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f273,f188,f277,f106]) ).
fof(f288,definition,
( sQ25_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ25_spl
| inverse(identity) = sk_c7 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( sQ25_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f275,f188,f288,f106]) ).
fof(f311,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f82,f166]) ).
fof(f314,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f90,f311]) ).
fof(f324,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f314,f145]) ).
fof(f326,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f314,f166]) ).
fof(f329,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f326]) ).
fof(f335,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c6,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f329,f271]) ).
fof(f337,plain,
( sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c6) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f329,f290]) ).
fof(f340,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f329,f26]) ).
fof(f341,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f329,f25]) ).
fof(f349,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f363,f341]) ).
fof(f350,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f363,f329]) ).
fof(f351,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f363,f324]) ).
fof(f361,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c7) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f363,f51]) ).
fof(f363,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f341,f335]) ).
fof(f374,plain,
( sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f363,f337]) ).
fof(f375,plain,
( sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f374]) ).
fof(f376,plain,
( sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f385,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f363,f340]) ).
fof(f394,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c7) = sk_c2 ),
inference(paramodulation,[status(thm)],[f361,f385]) ).
fof(f396,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f349,f394]) ).
fof(f397,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f351]) ).
fof(f398,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f413,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X0,sk_c2) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f363,f104]) ).
fof(f437,plain,
( ~ sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f350,f289]) ).
fof(f438,plain,
( ~ sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f396,f437]) ).
fof(f456,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X0,sk_c2) != sk_c7
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f396,f413]) ).
fof(f457,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f396,f456]) ).
fof(f459,plain,
( ~ sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f457,f438]) ).
fof(f462,plain,
( ~ sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f349,f459]) ).
fof(f463,plain,
( ~ sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f462]) ).
fof(f464,plain,
( ~ sQ25_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f467,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c3) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f237,f54]) ).
fof(f469,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f237,f52]) ).
fof(f472,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f237,f236]) ).
fof(f473,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f237,f472]) ).
fof(f499,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f237,f189]) ).
fof(f500,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f237,f499]) ).
fof(f501,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f500,f166]) ).
fof(f503,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f26,f501]) ).
fof(f507,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f503,f25]) ).
fof(f513,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| sk_c6 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f507,f473]) ).
fof(f516,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f513,f507]) ).
fof(f518,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f513,f503]) ).
fof(f521,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| inverse(sk_c6) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f513,f469]) ).
fof(f522,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f513,f467]) ).
fof(f527,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f513,f521]) ).
fof(f568,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f513,f243]) ).
fof(f569,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f516,f568]) ).
fof(f571,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f572,f522]) ).
fof(f572,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f518,f569]) ).
fof(f573,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f527]) ).
fof(f574,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ20_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f622,plain,
( ~ sQ9_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f160,f191,f97]) ).
fof(f628,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,f109,f142,f150,f156,f162,f185,f194,f201,f240,f258,f280,f291,f377,f398,f464,f574,f622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP234-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n015.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Sun Sep 20 20:10:35 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.15/0.38 % Refutation found
% 0.15/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.40 % Elapsed time: 0.059150 seconds
% 0.15/0.40 % CPU time: 0.180324 seconds
% 0.15/0.40 % Total memory used: 103.644 MB
% 0.15/0.40 % Net memory used: 103.321 MB
%------------------------------------------------------------------------------