%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP408-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:33:38 PM UTC 2026
% Result : Unsatisfiable 29.37s 4.33s
% Output : CNFRefutation 23.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X2)),X3)),X1)),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),multiply(inverse(multiply(X1,X2)),X0))),multiply(inverse(X3),multiply(inverse(X3),X3)))),
inference(paramodulation,[status(thm)],[f3,f10]) ).
fof(f14,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X4)),X5)),multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2))),multiply(inverse(X5),multiply(inverse(X5),X5)))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f36,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X2,
inference(paramodulation,[status(thm)],[f10,f3]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4,X5] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),multiply(inverse(multiply(X3,X4)),X1))),multiply(inverse(X5),multiply(inverse(X5),X5)))),X0))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f102,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(forward_demodulation,[status(thm)],[f12,f64]) ).
fof(f139,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)],[f102,f36]) ).
fof(f331,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X0))),X3)) = multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,X3)),
inference(paramodulation,[status(thm)],[f102,f139]) ).
fof(f369,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(inverse(X1),X1)))))) = multiply(inverse(X1),X3),
inference(paramodulation,[status(thm)],[f139,f36]) ).
fof(f1314,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3))))),multiply(X0,inverse(multiply(inverse(multiply(X4,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X4,multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3))))))))) = X3,
inference(paramodulation,[status(thm)],[f331,f36]) ).
fof(f1412,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X2)))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X2,
inference(forward_demodulation,[status(thm)],[f369,f1314]) ).
fof(f1480,plain,
! [X0,X1,X2] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),multiply(X1,multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f1412,f331]) ).
fof(f1570,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f1480,f1480]) ).
fof(f1854,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X2),multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f1570,f14]) ).
fof(f2016,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X0),multiply(inverse(X0),X0)))),
inference(forward_demodulation,[status(thm)],[f36,f1854]) ).
fof(f2046,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X0),X0)))),
inference(paramodulation,[status(thm)],[f139,f2016]) ).
fof(f2669,plain,
! [X0,X1,X2] : X0 = inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,multiply(inverse(X2),X2)))),
inference(paramodulation,[status(thm)],[f1570,f2046]) ).
fof(f2843,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(X1),X2),
inference(backward_demodulation,[status(thm)],[f2669,f369]) ).
fof(f3065,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(X0),multiply(inverse(X1),X1))),
inference(backward_demodulation,[status(thm)],[f2843,f2669]) ).
fof(f3068,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),inverse(X1))),multiply(inverse(X0),multiply(inverse(X0),X0))) = X1,
inference(backward_demodulation,[status(thm)],[f2843,f1412]) ).
fof(f3140,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f2843,f3068]) ).
fof(f3288,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))))) = X1,
inference(paramodulation,[status(thm)],[f3065,f3]) ).
fof(f3335,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f2843,f3288]) ).
fof(f3336,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f3065,f3335]) ).
fof(f5043,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f3336,f3336]) ).
fof(f5112,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f5043,f3140]) ).
fof(f5113,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f3336,f5043]) ).
fof(f5322,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f5113,f3065]) ).
fof(f5506,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),X0) = multiply(inverse(X1),multiply(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f5112,f2843]) ).
fof(f5517,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f5112,f5506]) ).
fof(f5702,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f5517,f5517]) ).
fof(f5722,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f5322,f5702]) ).
fof(f7342,plain,
! [X0,X1,X2] : multiply(inverse(inverse(X0)),multiply(X1,X2)) = multiply(inverse(inverse(multiply(X0,X1))),X2),
inference(paramodulation,[status(thm)],[f5722,f2843]) ).
fof(f7414,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(inverse(inverse(multiply(X0,X1))),X2),
inference(forward_demodulation,[status(thm)],[f5322,f7342]) ).
fof(f7415,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f5322,f7414]) ).
fof(f15074,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f4,f7415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP408-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n002.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 20 20:15:17 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 29.37/4.33 % Refutation found
% 29.37/4.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 29.37/4.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.71/4.46 % Elapsed time: 3.995403 seconds
% 4.71/4.46 % CPU time: 30.598726 seconds
% 4.71/4.46 % Total memory used: 438.604 MB
% 4.71/4.46 % Net memory used: 434.869 MB
%------------------------------------------------------------------------------