%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:32:27 PM UTC 2026
% Result : Unsatisfiable 14.18s 2.29s
% Output : CNFRefutation 13.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 6
% Syntax : Number of formulae : 89 ( 76 unt; 3 def)
% Number of atoms : 105 ( 85 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 13 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 264 ( 264 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z,U] : divide(inverse(divide(divide(divide(X,X),Y),divide(Z,divide(Y,U)))),U) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,inverse(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X0),X1),divide(X2,divide(X1,X3)))),X3) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
( sQ0_spl
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f9,plain,
( sQ0_spl
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(component_clause,[status(thm)],[f7]) ).
fof(f10,definition,
( sQ1_spl
<=> multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f12,plain,
( sQ1_spl
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,definition,
( sQ2_spl
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f15,plain,
( sQ2_spl
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f7,f10,f13]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(inverse(divide(divide(divide(X0,X0),X1),divide(X2,divide(X1,inverse(X3))))),X3) = X2,
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(multiply(divide(X0,X0),X1),divide(X2,divide(inverse(X1),X3)))),X3) = X2,
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3) = inverse(divide(divide(divide(X4,X4),X5),divide(X2,divide(X5,divide(X1,X3))))),
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X0),inverse(divide(divide(divide(X1,X1),X2),divide(X3,divide(X2,X4))))),divide(X5,X3))),X4) = X5,
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : multiply(inverse(divide(divide(divide(X0,X0),X1),divide(X2,multiply(X1,X3)))),X3) = X2,
inference(forward_demodulation,[status(thm)],[f5,f17]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(multiply(divide(X0,X0),divide(divide(divide(X1,X1),X2),divide(X3,divide(X2,X4)))),divide(X5,X3))),X4) = X5,
inference(forward_demodulation,[status(thm)],[f5,f21]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(multiply(divide(X0,X0),X1),X2)),X3) = inverse(divide(multiply(divide(X4,X4),X5),divide(X2,divide(inverse(X5),divide(inverse(X1),X3))))),
inference(paramodulation,[status(thm)],[f18,f18]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(multiply(divide(X0,X0),X1),X2)),X3) = inverse(divide(divide(divide(X4,X4),X5),divide(X2,divide(X5,divide(inverse(X1),X3))))),
inference(paramodulation,[status(thm)],[f4,f18]) ).
fof(f175,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3),divide(X1,X3)) = X2,
inference(paramodulation,[status(thm)],[f20,f4]) ).
fof(f295,plain,
! [X0,X1,X2,X3] : divide(multiply(inverse(divide(divide(divide(X0,X0),X1),X2)),X3),divide(X1,inverse(X3))) = X2,
inference(paramodulation,[status(thm)],[f5,f175]) ).
fof(f327,plain,
! [X0,X1,X2,X3] : divide(multiply(inverse(divide(divide(divide(X0,X0),X1),X2)),X3),multiply(X1,X3)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f295]) ).
fof(f348,plain,
! [X0,X1,X2,X3] : divide(multiply(inverse(multiply(divide(divide(X0,X0),X1),X2)),X3),multiply(X1,X3)) = inverse(X2),
inference(paramodulation,[status(thm)],[f5,f327]) ).
fof(f349,plain,
! [X0,X1,X2,X3,X4] : divide(multiply(inverse(divide(X0,X1)),X2),multiply(divide(X3,inverse(divide(divide(divide(X4,X4),X3),X0))),X2)) = X1,
inference(paramodulation,[status(thm)],[f175,f327]) ).
fof(f350,plain,
! [X0,X1,X2,X3] : divide(multiply(inverse(divide(multiply(divide(X0,X0),X1),X2)),X3),multiply(inverse(X1),X3)) = X2,
inference(paramodulation,[status(thm)],[f5,f327]) ).
fof(f369,plain,
! [X0,X1,X2,X3,X4] : divide(multiply(inverse(divide(X0,X1)),X2),multiply(multiply(X3,divide(divide(divide(X4,X4),X3),X0)),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f349]) ).
fof(f640,plain,
! [X0,X1,X2,X3] : divide(multiply(inverse(multiply(multiply(divide(X0,X0),X1),X2)),X3),multiply(inverse(X1),X3)) = inverse(X2),
inference(paramodulation,[status(thm)],[f5,f348]) ).
fof(f1353,plain,
! [X0,X1,X2,X3,X4,X5,X6] : X0 = inverse(divide(divide(divide(X1,X1),X2),divide(divide(X0,X3),divide(X2,divide(inverse(divide(divide(divide(X4,X4),X5),divide(X3,divide(X5,X6)))),X6))))),
inference(paramodulation,[status(thm)],[f25,f36]) ).
fof(f1509,plain,
! [X0,X1,X2,X3] : X0 = inverse(divide(divide(divide(X1,X1),X2),divide(divide(X0,X3),divide(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f4,f1353]) ).
fof(f1666,plain,
! [X0,X1,X2,X3] : X0 = inverse(divide(divide(divide(X1,X1),X2),divide(multiply(X0,X3),divide(X2,inverse(X3))))),
inference(paramodulation,[status(thm)],[f5,f1509]) ).
fof(f1691,plain,
! [X0,X1,X2,X3] : divide(multiply(X0,X1),multiply(X2,X1)) = divide(divide(X0,X3),divide(X2,X3)),
inference(paramodulation,[status(thm)],[f1509,f327]) ).
fof(f1692,plain,
! [X0,X1,X2,X3] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X3),divide(X2,X3)),
inference(paramodulation,[status(thm)],[f1509,f175]) ).
fof(f1709,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,divide(divide(divide(X1,X1),X2),divide(divide(X3,X4),divide(X2,X4)))) = divide(X0,X3),
inference(paramodulation,[status(thm)],[f1509,f5]) ).
fof(f1719,plain,
! [X0,X1,X2,X3] : X0 = inverse(divide(divide(divide(X1,X1),X2),divide(multiply(X0,X3),multiply(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f5,f1666]) ).
fof(f1755,plain,
! [X0,X1,X2,X3] : divide(multiply(X0,X1),multiply(X2,X1)) = divide(multiply(X0,X3),multiply(X2,X3)),
inference(paramodulation,[status(thm)],[f1691,f1691]) ).
fof(f1865,plain,
! [X0,X1,X2,X3,X4] : divide(multiply(inverse(divide(multiply(divide(X0,X0),X1),multiply(X2,X1))),X3),multiply(X4,X3)) = divide(X2,X4),
inference(paramodulation,[status(thm)],[f1691,f327]) ).
fof(f1887,plain,
! [X0,X1,X2,X3,X4,X5,X6] : divide(inverse(divide(multiply(divide(X0,X0),X1),divide(X2,divide(inverse(X1),X3)))),X3) = inverse(divide(multiply(divide(X4,X4),X5),divide(multiply(X2,X6),multiply(inverse(X5),X6)))),
inference(paramodulation,[status(thm)],[f1691,f35]) ).
fof(f1948,plain,
! [X0,X1,X2,X3] : X0 = inverse(divide(multiply(divide(X1,X1),X2),divide(multiply(X0,X3),multiply(inverse(X2),X3)))),
inference(forward_demodulation,[status(thm)],[f18,f1887]) ).
fof(f2485,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,divide(divide(divide(X1,X1),X2),divide(multiply(X3,X4),multiply(X2,X4)))) = divide(X0,X3),
inference(paramodulation,[status(thm)],[f1719,f5]) ).
fof(f2925,plain,
! [X0,X1,X2,X3] : X0 = inverse(divide(multiply(multiply(inverse(X1),X1),X2),divide(multiply(X0,X3),multiply(inverse(X2),X3)))),
inference(paramodulation,[status(thm)],[f5,f1948]) ).
fof(f18427,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,X1) = divide(X0,multiply(X2,divide(divide(divide(X3,X3),X2),multiply(divide(X4,X4),X1)))),
inference(paramodulation,[status(thm)],[f369,f1865]) ).
fof(f18964,plain,
! [X0,X1,X2,X3,X4,X5,X6] : divide(multiply(inverse(multiply(multiply(divide(X0,X0),X1),X2)),X3),multiply(inverse(X1),X3)) = multiply(X4,divide(divide(divide(X5,X5),X4),multiply(divide(X6,X6),X2))),
inference(paramodulation,[status(thm)],[f18427,f350]) ).
fof(f19331,plain,
! [X0,X1,X2,X3] : inverse(X0) = multiply(X1,divide(divide(divide(X2,X2),X1),multiply(divide(X3,X3),X0))),
inference(forward_demodulation,[status(thm)],[f640,f18964]) ).
fof(f19496,plain,
! [X0,X1,X2,X3,X4,X5,X6] : inverse(divide(divide(divide(X0,X0),X1),divide(multiply(X2,X3),multiply(X1,X3)))) = multiply(X4,divide(divide(divide(X5,X5),X4),divide(divide(X6,X6),X2))),
inference(paramodulation,[status(thm)],[f2485,f19331]) ).
fof(f19665,plain,
! [X0,X1,X2,X3] : X0 = multiply(X1,divide(divide(divide(X2,X2),X1),divide(divide(X3,X3),X0))),
inference(forward_demodulation,[status(thm)],[f1719,f19496]) ).
fof(f19737,plain,
! [X0,X1,X2,X3] : X0 = multiply(X0,divide(divide(divide(X1,X1),X2),divide(divide(X3,X3),X2))),
inference(paramodulation,[status(thm)],[f1692,f19665]) ).
fof(f20218,plain,
! [X0,X1,X2,X3,X4,X5] : divide(multiply(X0,X1),multiply(X2,X1)) = divide(multiply(X0,divide(divide(divide(X3,X3),X4),divide(divide(X5,X5),X4))),X2),
inference(paramodulation,[status(thm)],[f19737,f1755]) ).
fof(f20374,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),multiply(X2,X1)) = divide(X0,X2),
inference(forward_demodulation,[status(thm)],[f19737,f20218]) ).
fof(f22498,plain,
! [X0,X1,X2] : X0 = inverse(divide(multiply(multiply(inverse(X1),X1),X2),divide(X0,inverse(X2)))),
inference(backward_demodulation,[status(thm)],[f20374,f2925]) ).
fof(f22499,plain,
! [X0,X1,X2] : X0 = inverse(divide(multiply(divide(X1,X1),X2),divide(X0,inverse(X2)))),
inference(backward_demodulation,[status(thm)],[f20374,f1948]) ).
fof(f22720,plain,
! [X0,X1,X2] : X0 = inverse(divide(multiply(multiply(inverse(X1),X1),X2),multiply(X0,X2))),
inference(forward_demodulation,[status(thm)],[f5,f22498]) ).
fof(f22721,plain,
! [X0,X1] : X0 = inverse(divide(multiply(inverse(X1),X1),X0)),
inference(forward_demodulation,[status(thm)],[f20374,f22720]) ).
fof(f22722,plain,
! [X0,X1,X2] : X0 = inverse(divide(multiply(divide(X1,X1),X2),multiply(X0,X2))),
inference(forward_demodulation,[status(thm)],[f5,f22499]) ).
fof(f22723,plain,
! [X0,X1] : X0 = inverse(divide(divide(X1,X1),X0)),
inference(forward_demodulation,[status(thm)],[f20374,f22722]) ).
fof(f22784,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(divide(X1,X1),X0)),
inference(paramodulation,[status(thm)],[f5,f22723]) ).
fof(f22921,plain,
! [X0,X1] : multiply(X0,X1) = inverse(divide(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f20374,f22721]) ).
fof(f23202,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,divide(divide(divide(X1,X1),X2),divide(divide(X3,X4),divide(X2,X4)))) = inverse(divide(X3,X0)),
inference(paramodulation,[status(thm)],[f1509,f22921]) ).
fof(f23284,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1709,f23202]) ).
fof(f24221,plain,
! [X0,X1] : X0 = divide(X0,multiply(inverse(X1),X1)),
inference(backward_demodulation,[status(thm)],[f23284,f22721]) ).
fof(f24259,plain,
! [X0,X1,X2,X3] : multiply(divide(divide(X0,multiply(X1,X2)),divide(divide(X3,X3),X1)),X2) = X0,
inference(backward_demodulation,[status(thm)],[f23284,f24]) ).
fof(f24269,plain,
! [X0,X1] : X0 = divide(X0,divide(X1,X1)),
inference(backward_demodulation,[status(thm)],[f23284,f22723]) ).
fof(f24330,plain,
! [X0,X1,X2] : X0 = multiply(X0,divide(divide(X1,X1),divide(X2,X2))),
inference(paramodulation,[status(thm)],[f24269,f19737]) ).
fof(f24355,plain,
! [X0,X1] : divide(divide(X0,X0),X1) = inverse(X1),
inference(paramodulation,[status(thm)],[f24269,f23284]) ).
fof(f24394,plain,
! [X0,X1] : X0 = multiply(X0,divide(X1,X1)),
inference(forward_demodulation,[status(thm)],[f24269,f24330]) ).
fof(f24446,plain,
! [X0,X1] : inverse(divide(X0,X0)) = inverse(divide(X1,X1)),
inference(paramodulation,[status(thm)],[f24394,f22784]) ).
fof(f24502,plain,
! [X0,X1] : divide(X0,X0) = inverse(divide(X1,X1)),
inference(forward_demodulation,[status(thm)],[f23284,f24446]) ).
fof(f24503,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(forward_demodulation,[status(thm)],[f23284,f24502]) ).
fof(f24543,plain,
! [X0,X1] : multiply(inverse(X0),X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f5,f24503]) ).
fof(f24930,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f24355,f23284]) ).
fof(f24968,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f24269,f24930]) ).
fof(f24993,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f22784,f24968]) ).
fof(f25004,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f24968,f24993]) ).
fof(f25016,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f24221,f25004]) ).
fof(f25023,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),X1) = divide(X0,divide(X2,X2)),
inference(paramodulation,[status(thm)],[f25004,f20374]) ).
fof(f25026,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f24269,f25023]) ).
fof(f25245,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f24221,f24543]) ).
fof(f25495,plain,
! [X0,X1,X2] : multiply(divide(divide(X0,multiply(X1,X2)),inverse(X1)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f24355,f24259]) ).
fof(f25496,plain,
! [X0,X1,X2] : multiply(multiply(divide(X0,multiply(X1,X2)),X1),X2) = X0,
inference(forward_demodulation,[status(thm)],[f5,f25495]) ).
fof(f25504,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f25026,f25496]) ).
fof(f28967,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f15,f25504]) ).
fof(f29048,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f28967]) ).
fof(f29089,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9,f25245]) ).
fof(f29090,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f29089]) ).
fof(f29091,plain,
( sQ1_spl
| a2 != a2 ),
inference(forward_demodulation,[status(thm)],[f25016,f12]) ).
fof(f29092,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f29091]) ).
fof(f29093,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f29092]) ).
fof(f29094,plain,
$false,
inference(sat_refutation,[status(thm)],[f16,f29048,f29090,f29093]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 19:56:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 14.18/2.29 % Refutation found
% 14.18/2.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.18/2.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.15/2.34 % Elapsed time: 1.967080 seconds
% 13.15/2.34 % CPU time: 15.273737 seconds
% 13.15/2.34 % Total memory used: 272.224 MB
% 13.15/2.34 % Net memory used: 268.976 MB
%------------------------------------------------------------------------------