%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:32:28 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 26 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 23 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(X,multiply(multiply(Y,Z),inverse(multiply(X,Z)))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| 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] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,inverse(multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X3,X2))))))) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f6,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X0,X3)))),inverse(X2))) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(paramodulation,[status(thm)],[f3,f5]) ).
fof(f15,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f26,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(X2,inverse(multiply(X2,X1)))) = X0,
inference(paramodulation,[status(thm)],[f15,f5]) ).
fof(f44,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(X2,inverse(X0))) = multiply(X2,X1),
inference(paramodulation,[status(thm)],[f26,f5]) ).
fof(f49,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X3,inverse(multiply(X3,X1)))),inverse(X0))) = X2,
inference(paramodulation,[status(thm)],[f26,f3]) ).
fof(f53,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,inverse(multiply(X1,X2)))),X2) = X0,
inference(forward_demodulation,[status(thm)],[f44,f49]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),inverse(X1))) = multiply(X0,X2),
inference(paramodulation,[status(thm)],[f15,f6]) ).
fof(f163,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(paramodulation,[status(thm)],[f44,f53]) ).
fof(f171,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X1,multiply(X2,inverse(multiply(X2,inverse(X0))))),
inference(paramodulation,[status(thm)],[f53,f15]) ).
fof(f235,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X0,multiply(X2,inverse(multiply(X2,inverse(X1))))),
inference(paramodulation,[status(thm)],[f53,f57]) ).
fof(f257,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(backward_subsumption_resolution,[status(thm)],[f4,f258]) ).
fof(f258,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f171,f235]) ).
fof(f274,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f163,f258]) ).
fof(f277,plain,
! [X0,X1] : X0 = multiply(multiply(X1,inverse(X1)),X0),
inference(paramodulation,[status(thm)],[f7,f258]) ).
fof(f294,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f258,f15]) ).
fof(f322,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f274,f257]) ).
fof(f349,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f274,f277]) ).
fof(f385,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(b2,multiply(inverse(b2),a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f274,f322]) ).
fof(f386,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f294,f385]) ).
fof(f387,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f386]) ).
fof(f419,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f15,f349]) ).
fof(f432,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f419,f7]) ).
fof(f483,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f432,f349]) ).
fof(f488,plain,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f387,f483]) ).
fof(f1023,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f258,f274]) ).
fof(f1089,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f274,f1023]) ).
fof(f1090,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f488,f1089]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 19:57:19 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.075356 seconds
% 0.12/0.43 % CPU time: 0.305363 seconds
% 0.12/0.43 % Total memory used: 70.692 MB
% 0.12/0.43 % Net memory used: 69.941 MB
%------------------------------------------------------------------------------