%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP214-1 : 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 12:33:07 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 31
% Syntax : Number of formulae : 150 ( 13 unt; 15 def)
% Number of atoms : 453 ( 183 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 585 ( 282 ~; 288 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 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_c3,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [X3,X4,X2,X1,X5] :
( inverse(X5) != X1
| multiply(X5,X1) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| multiply(sk_c7,X4) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
! [X1,X5] :
( inverse(X5) != X1
| multiply(X5,X1) != sk_c6
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X1
| ! [X4] : multiply(sk_c7,X4) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != X3
| multiply(X4,X3) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X3
| multiply(sk_c7,X1) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f34,f37]) ).
fof(f41,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f42,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f34,f41]) ).
fof(f45,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f22,f34,f45]) ).
fof(f49,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f34,f49]) ).
fof(f53,definition,
( sQ5_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ5_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f24,f53,f37]) ).
fof(f57,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f25,f53,f41]) ).
fof(f58,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f26,f53,f45]) ).
fof(f59,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f27,f53,f49]) ).
fof(f60,definition,
( sQ6_spl
<=> multiply(sk_c7,sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f28,f60,f37]) ).
fof(f64,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f29,f60,f41]) ).
fof(f65,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f30,f60,f45]) ).
fof(f66,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f31,f60,f49]) ).
fof(f67,definition,
! [X0] :
( sQ7_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f68,plain,
! [X0] :
( ~ sQ7_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
! [X1] :
( sQ8_spl
<=> multiply(sk_c7,X1) != sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f71,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
! [X2,X3,X4] :
( sQ9_spl
<=> ( inverse(X4) != X3
| multiply(X4,X3) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != X3 ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| inverse(X2) != X1
| multiply(X2,X1) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != X1 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ9_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f33,f67,f70,f73]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sQ9_spl
| inverse(X1) != multiply(X0,sk_c7)
| multiply(X1,multiply(X0,sk_c7)) != sk_c6
| inverse(X0) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f74]) ).
fof(f79,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c3,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f38,f19]) ).
fof(f102,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ9_spl
| inverse(X0) != multiply(sk_c3,sk_c7)
| multiply(X0,multiply(sk_c3,sk_c7)) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f42,f77]) ).
fof(f104,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ9_spl
| inverse(X0) != multiply(sk_c1,sk_c7)
| multiply(X0,multiply(sk_c1,sk_c7)) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f54,f77]) ).
fof(f109,definition,
( sQ10_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( sQ10_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != multiply(sk_c3,sk_c7)
| multiply(X0,multiply(sk_c3,sk_c7)) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f113,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != multiply(sk_c3,sk_c7)
| multiply(X0,multiply(sk_c3,sk_c7)) != sk_c6 ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,plain,
( ~ sQ2_spl
| ~ sQ9_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f102,f109,f112,f73,f41]) ).
fof(f123,definition,
! [X0] :
( sQ14_spl
<=> ( inverse(X0) != multiply(sk_c1,sk_c7)
| multiply(X0,multiply(sk_c1,sk_c7)) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != multiply(sk_c1,sk_c7)
| multiply(X0,multiply(sk_c1,sk_c7)) != sk_c6 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| sQ14_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f104,f109,f123,f73,f53]) ).
fof(f127,plain,
( sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f111]) ).
fof(f128,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(resolution,[status(thm)],[f68,f54]) ).
fof(f131,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f35,f129]) ).
fof(f132,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f135,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f71]) ).
fof(f136,plain,
( ~ sQ6_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f139,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f140,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f139]) ).
fof(f151,plain,
( ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f46,f140]) ).
fof(f152,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c5) ),
inference(paramodulation,[status(thm)],[f38,f140]) ).
fof(f155,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f17,f140]) ).
fof(f158,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f50,f151]) ).
fof(f159,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f42,f152]) ).
fof(f161,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| inverse(sk_c3) != sk_c7
| sk_c5 != sk_c6 ),
inference(paramodulation,[status(thm)],[f38,f68]) ).
fof(f165,definition,
( sQ15_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ15_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f161,f165,f41,f67,f37]) ).
fof(f192,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f158,f140]) ).
fof(f194,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f18,f192]) ).
fof(f207,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f194,f18]) ).
fof(f208,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f194,f17]) ).
fof(f217,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c5) = multiply(sk_c3,sk_c7) ),
inference(paramodulation,[status(thm)],[f159,f79]) ).
fof(f220,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f38,f217]) ).
fof(f237,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c4) = sk_c6 ),
inference(paramodulation,[status(thm)],[f50,f207]) ).
fof(f243,definition,
( sQ22_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( sQ22_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f251,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f220,f140]) ).
fof(f253,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f207,f251]) ).
fof(f254,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f167]) ).
fof(f255,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f254]) ).
fof(f261,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f253,f207]) ).
fof(f264,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f253,f208]) ).
fof(f265,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f253,f194]) ).
fof(f273,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f264,f237]) ).
fof(f275,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f281,f265]) ).
fof(f276,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f281,f253]) ).
fof(f280,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f281,f50]) ).
fof(f281,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f253,f273]) ).
fof(f289,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f281,f261]) ).
fof(f290,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c3) = sk_c4 ),
inference(paramodulation,[status(thm)],[f42,f289]) ).
fof(f310,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f245]) ).
fof(f311,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f310]) ).
fof(f318,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f35,f140]) ).
fof(f320,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f54,f318]) ).
fof(f325,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f155,f140]) ).
fof(f333,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f320,f140]) ).
fof(f335,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f18,f333]) ).
fof(f336,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f335,f18]) ).
fof(f338,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f335,f17]) ).
fof(f396,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| inverse(X0) != multiply(sk_c1,sk_c7)
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f35,f124]) ).
fof(f397,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f35,f396]) ).
fof(f457,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| X0 = multiply(inverse(inverse(sk_c6)),X0) ),
inference(forward_demodulation,[status(thm)],[f335,f325]) ).
fof(f460,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| inverse(sk_c6) = sk_c6 ),
inference(paramodulation,[status(thm)],[f336,f457]) ).
fof(f470,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f460,f397]) ).
fof(f478,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f338,f470]) ).
fof(f479,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f478]) ).
fof(f480,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f490,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f275,f17]) ).
fof(f580,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f281,f38]) ).
fof(f644,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != multiply(sk_c3,sk_c7)
| multiply(X0,sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f580,f113]) ).
fof(f645,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != multiply(sk_c3,sk_c7)
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f276,f644]) ).
fof(f646,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f580,f645]) ).
fof(f647,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f646,f280]) ).
fof(f650,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f490,f647]) ).
fof(f651,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f650]) ).
fof(f652,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f653,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f276,f71]) ).
fof(f655,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f290,f653]) ).
fof(f659,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f660,plain,
$false,
inference(sat_refutation,[status(thm)],[f40,f44,f48,f52,f56,f57,f58,f59,f63,f64,f65,f66,f76,f115,f126,f128,f133,f136,f168,f255,f311,f480,f652,f659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP214-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:09:50 UTC 2026
% 0.09/0.37 % 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
% 0.09/0.44 % Elapsed time: 0.055069 seconds
% 0.09/0.44 % CPU time: 0.198393 seconds
% 0.09/0.44 % Total memory used: 103.685 MB
% 0.09/0.44 % Net memory used: 103.231 MB
%------------------------------------------------------------------------------