%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP053-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:32:24 PM UTC 2026
% Result : Unsatisfiable 232.39s 29.73s
% Output : CNFRefutation 123.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 53 unt; 3 def)
% Number of atoms : 82 ( 62 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 13 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 143 ( 143 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y,Z,X] : inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,inverse(X)))),inverse(multiply(inverse(Y),Y)))))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),inverse(multiply(inverse(X0),X0)))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,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)],[f2]) ).
fof(f5,definition,
( sQ0_spl
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f7,plain,
( sQ0_spl
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(component_clause,[status(thm)],[f5]) ).
fof(f8,definition,
( sQ1_spl
<=> multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f10,plain,
( sQ1_spl
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(component_clause,[status(thm)],[f8]) ).
fof(f11,definition,
( sQ2_spl
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f13,plain,
( sQ2_spl
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4,f5,f8,f11]) ).
fof(f16,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0)))))) = multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,inverse(X2)))),inverse(multiply(inverse(X3),X3))))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f18,plain,
! [X0,X1,X2] : X0 = multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(inverse(X0))))),inverse(multiply(inverse(X1),X1))))),
inference(paramodulation,[status(thm)],[f3,f16]) ).
fof(f40,plain,
! [X0,X1,X2] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,X2))),inverse(multiply(inverse(X0),X0))))))) = X2,
inference(paramodulation,[status(thm)],[f16,f3]) ).
fof(f56,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X1,X0)),X2)),inverse(multiply(inverse(X0),X0)))))) = multiply(inverse(multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(inverse(X2))))),inverse(multiply(inverse(X1),X1))),
inference(paramodulation,[status(thm)],[f18,f3]) ).
fof(f219,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X0))))))),inverse(multiply(inverse(X2),X2))),
inference(paramodulation,[status(thm)],[f3,f56]) ).
fof(f264,plain,
! [X0,X1,X2] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(inverse(multiply(X1,X2)))))),inverse(multiply(inverse(X1),X1)))) = X2,
inference(paramodulation,[status(thm)],[f56,f40]) ).
fof(f289,plain,
! [X0,X1,X2] : X0 = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),inverse(multiply(inverse(X2),X2)))))))),
inference(paramodulation,[status(thm)],[f56,f18]) ).
fof(f365,plain,
! [X0,X1,X2,X3] : inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(X3))))))),X0)),X3)),inverse(multiply(inverse(X0),X0)))))) = multiply(inverse(X2),X2),
inference(paramodulation,[status(thm)],[f219,f3]) ).
fof(f512,plain,
! [X0,X1,X2,X3] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),X3)),inverse(multiply(inverse(X0),X0))))))) = multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(inverse(X2),X2)))))))),
inference(paramodulation,[status(thm)],[f289,f289]) ).
fof(f2186,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))))))) = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f264,f365]) ).
fof(f6663,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X0),inverse(multiply(inverse(X2),X2))))))))),
inference(paramodulation,[status(thm)],[f512,f289]) ).
fof(f7006,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f40,f6663]) ).
fof(f7011,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X2)))),multiply(X1,inverse(multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f2186,f6663]) ).
fof(f12188,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f7011,f7011]) ).
fof(f12897,plain,
! [X0,X1,X2,X3] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X0),X0))))))) = multiply(X2,inverse(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X0)),inverse(multiply(inverse(X3),X3)))))))),
inference(paramodulation,[status(thm)],[f12188,f512]) ).
fof(f12927,plain,
! [X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(inverse(X0)),inverse(X0))))))) = X0,
inference(paramodulation,[status(thm)],[f12188,f3]) ).
fof(f13102,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(inverse(X2),X1)),multiply(inverse(X3),X3)),
inference(paramodulation,[status(thm)],[f12188,f7006]) ).
fof(f13448,plain,
! [X0,X1] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X0),X0))))))) = X0,
inference(forward_demodulation,[status(thm)],[f289,f12897]) ).
fof(f13542,plain,
! [X0,X1,X2] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))))))) = X0,
inference(paramodulation,[status(thm)],[f12188,f13448]) ).
fof(f13794,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f12188,f13102]) ).
fof(f21475,plain,
! [X0,X1,X2] : inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2)))))) = X0,
inference(paramodulation,[status(thm)],[f12188,f12927]) ).
fof(f22125,plain,
! [X0,X1,X2,X3] : inverse(multiply(inverse(X0),inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3)))))))) = X0,
inference(paramodulation,[status(thm)],[f21475,f21475]) ).
fof(f22196,plain,
! [X0,X1,X2,X3] : inverse(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3))))))))) = X0,
inference(paramodulation,[status(thm)],[f21475,f13542]) ).
fof(f22306,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(inverse(X0),X1)) = multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),X3)))))),multiply(inverse(X4),X4)),
inference(paramodulation,[status(thm)],[f21475,f13102]) ).
fof(f22516,plain,
! [X0,X1] : inverse(multiply(inverse(X0),multiply(inverse(X1),X1))) = X0,
inference(forward_demodulation,[status(thm)],[f21475,f22125]) ).
fof(f22553,plain,
! [X0,X1] : inverse(inverse(multiply(X0,multiply(inverse(X1),X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f21475,f22196]) ).
fof(f22767,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X1,multiply(inverse(X2),X2)),
inference(forward_demodulation,[status(thm)],[f21475,f22306]) ).
fof(f23132,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X0)) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f13794,f22516]) ).
fof(f23503,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(X1,multiply(inverse(X1),multiply(inverse(X2),X2))),
inference(paramodulation,[status(thm)],[f22516,f12188]) ).
fof(f24797,plain,
! [X0,X1,X2,X3] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,inverse(multiply(inverse(X0),multiply(inverse(X3),X3)))))))),
inference(paramodulation,[status(thm)],[f23132,f6663]) ).
fof(f25171,plain,
! [X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(inverse(X1),X1)))) = X0,
inference(paramodulation,[status(thm)],[f23132,f22516]) ).
fof(f25502,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(multiply(X2,X0))))),
inference(forward_demodulation,[status(thm)],[f22516,f24797]) ).
fof(f31011,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f22767,f22767]) ).
fof(f31087,plain,
! [X0,X1] : inverse(inverse(multiply(X0,multiply(inverse(X0),X1)))) = X1,
inference(paramodulation,[status(thm)],[f22767,f22553]) ).
fof(f34943,plain,
! [X0,X1,X2] : inverse(inverse(multiply(X0,multiply(inverse(X1),X1)))) = multiply(inverse(inverse(X0)),multiply(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f23503,f31087]) ).
fof(f34986,plain,
! [X0,X1] : X0 = multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)),
inference(forward_demodulation,[status(thm)],[f22553,f34943]) ).
fof(f34993,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),inverse(inverse(X0)))),
inference(paramodulation,[status(thm)],[f31011,f34986]) ).
fof(f37711,plain,
! [X0,X1,X2] : X0 = multiply(X1,multiply(inverse(X1),inverse(inverse(multiply(multiply(inverse(X2),X2),X0))))),
inference(paramodulation,[status(thm)],[f22516,f25502]) ).
fof(f37713,plain,
! [X0,X1,X2] : X0 = multiply(X1,multiply(inverse(X1),inverse(inverse(multiply(inverse(multiply(inverse(X2),X2)),X0))))),
inference(paramodulation,[status(thm)],[f25171,f25502]) ).
fof(f37894,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(forward_demodulation,[status(thm)],[f34993,f37711]) ).
fof(f37896,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(inverse(X1),X1)),X0),
inference(forward_demodulation,[status(thm)],[f34993,f37713]) ).
fof(f38800,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f37896,f34993]) ).
fof(f38812,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X0),X1)) = multiply(multiply(inverse(X2),X2),X1),
inference(paramodulation,[status(thm)],[f37896,f31011]) ).
fof(f38957,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f37894,f38800]) ).
fof(f38962,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f37894,f38812]) ).
fof(f39102,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X0))),
inference(backward_demodulation,[status(thm)],[f38957,f25502]) ).
fof(f91355,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f39102,f38962]) ).
fof(f91966,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f13,f91355]) ).
fof(f92609,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f91966]) ).
fof(f92758,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7,f12188]) ).
fof(f92759,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f92758]) ).
fof(f92760,plain,
( sQ1_spl
| a2 != a2 ),
inference(forward_demodulation,[status(thm)],[f37894,f10]) ).
fof(f92761,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f92760]) ).
fof(f92762,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f92761]) ).
fof(f92763,plain,
$false,
inference(sat_refutation,[status(thm)],[f14,f92609,f92759,f92762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP053-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:51:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 232.39/29.73 % Refutation found
% 232.39/29.73 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 232.39/29.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 221.12/31.05 % Elapsed time: 30.467895 seconds
% 221.12/31.05 % CPU time: 226.459511 seconds
% 221.12/31.05 % Total memory used: 1.751 GB
% 221.12/31.05 % Net memory used: 1.744 GB
%------------------------------------------------------------------------------