%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:06:38 PM UTC 2026
% Result : Unsatisfiable 1.44s 0.66s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 121 ( 121 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D,E,F,G] : multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(a,a,b) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(a,a,b) != a,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2] : X0 = multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1),
inference(paramodulation,[status(thm)],[f3,f7]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,inverse(X2),X3),inverse(multiply(X2,inverse(X2),X3)),multiply(X2,inverse(X2),X4))),X4) = X1,
inference(paramodulation,[status(thm)],[f11,f3]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),multiply(X5,inverse(multiply(X4,inverse(X4),X6)),X6),multiply(X2,X3,inverse(X4)))),multiply(X3,X5,X2)) = X1,
inference(paramodulation,[status(thm)],[f11,f3]) ).
fof(f381,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),multiply(inverse(X3),multiply(X4,inverse(multiply(multiply(X4,X3,X5),multiply(inverse(X3),inverse(multiply(X5,inverse(X5),X6)),X6),multiply(X4,X3,inverse(X5)))),X2),X3)) = X1,
inference(paramodulation,[status(thm)],[f54,f3]) ).
fof(f823,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = X1,
inference(paramodulation,[status(thm)],[f54,f381]) ).
fof(f933,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = multiply(inverse(X5),X1,X5),
inference(paramodulation,[status(thm)],[f823,f823]) ).
fof(f1012,plain,
! [X0,X1] : X0 = multiply(inverse(X1),X0,X1),
inference(forward_demodulation,[status(thm)],[f823,f933]) ).
fof(f1046,plain,
! [X0,X1,X2] : X0 = multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),
inference(backward_demodulation,[status(thm)],[f1012,f11]) ).
fof(f1646,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X1,inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f1012,f1046]) ).
fof(f1777,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),X3)),X3) = X1,
inference(backward_demodulation,[status(thm)],[f1646,f48]) ).
fof(f1781,plain,
! [X0,X1] : X0 = multiply(X0,inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f1646,f1046]) ).
fof(f1813,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),X2) = X1,
inference(forward_demodulation,[status(thm)],[f1646,f1777]) ).
fof(f2090,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))),multiply(X2,multiply(X5,X4,X3),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f2091,f3]) ).
fof(f2091,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1781,f1813]) ).
fof(f2093,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f1012,f2091]) ).
fof(f2137,plain,
! [X0,X1,X2,X3] : multiply(X0,X1,X2) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X3)),X3),X0),
inference(backward_demodulation,[status(thm)],[f2090,f7]) ).
fof(f2149,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,X2,multiply(X3,inverse(X3),X4))),multiply(inverse(X3),multiply(X4,X2,X1),X3)) = X0,
inference(paramodulation,[status(thm)],[f2091,f2090]) ).
fof(f2177,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,X2,X3)),multiply(inverse(X4),multiply(X3,X2,X1),X4)) = X0,
inference(forward_demodulation,[status(thm)],[f2091,f2149]) ).
fof(f2178,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,X2,X3)),multiply(X3,X2,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f1012,f2177]) ).
fof(f2464,plain,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
inference(paramodulation,[status(thm)],[f2093,f2091]) ).
fof(f2466,plain,
! [X0,X1] : X0 = multiply(X1,X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f2093,f1012]) ).
fof(f2887,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = inverse(inverse(multiply(X2,X1,X0))),
inference(paramodulation,[status(thm)],[f2464,f2178]) ).
fof(f2955,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X2,X1,X0),
inference(forward_demodulation,[status(thm)],[f2093,f2887]) ).
fof(f2985,plain,
! [X0,X1,X2] : multiply(X0,X1,inverse(inverse(multiply(X0,X1,X2)))) = multiply(X1,X2,X0),
inference(paramodulation,[status(thm)],[f2464,f2137]) ).
fof(f3045,plain,
! [X0,X1,X2] : multiply(X0,X1,multiply(X0,X1,X2)) = multiply(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f2093,f2985]) ).
fof(f3492,plain,
! [X0,X1] : multiply(X0,X1,X1) = multiply(X1,inverse(X0),X0),
inference(paramodulation,[status(thm)],[f2466,f3045]) ).
fof(f3547,plain,
! [X0,X1] : multiply(X0,X1,X1) = X1,
inference(forward_demodulation,[status(thm)],[f1781,f3492]) ).
fof(f3566,plain,
! [X0,X1] : multiply(X0,X0,X1) = X0,
inference(paramodulation,[status(thm)],[f2955,f3547]) ).
fof(f3640,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f3566,f4]) ).
fof(f3717,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3640]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO070-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.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 : Mon Sep 21 13:52:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 1.44/0.66 % Refutation found
% 1.44/0.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.44/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.69 % Elapsed time: 0.323282 seconds
% 1.44/0.69 % CPU time: 2.370848 seconds
% 1.44/0.69 % Total memory used: 107.035 MB
% 1.44/0.69 % Net memory used: 106.584 MB
%------------------------------------------------------------------------------