%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:32:30 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 39 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 25 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 105 ( 105 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(divide(X,inverse(Y)),Z),divide(X,Z)) = Y,
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(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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : divide(divide(divide(X0,inverse(X1)),X2),divide(X0,X2)) = X1,
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(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)],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] : divide(divide(multiply(X0,X1),X2),divide(X0,X2)) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),divide(X0,inverse(X2))) = X1,
inference(paramodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : divide(divide(multiply(divide(multiply(X0,X1),X2),X3),divide(X0,X2)),X1) = X3,
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),multiply(X0,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f8]) ).
fof(f13,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(X1,X0),multiply(X1,X2))) = X2,
inference(paramodulation,[status(thm)],[f11,f7]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(multiply(X2,multiply(X1,X3)),multiply(X2,X0)))) = X3,
inference(paramodulation,[status(thm)],[f13,f7]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(divide(multiply(divide(multiply(X0,inverse(X1)),X2),X3),divide(X0,X2)),X1) = X3,
inference(paramodulation,[status(thm)],[f5,f9]) ).
fof(f56,plain,
! [X0,X1,X2,X3] : divide(divide(X0,divide(divide(multiply(X1,inverse(X2)),X3),divide(X1,X3))),X0) = X2,
inference(paramodulation,[status(thm)],[f17,f9]) ).
fof(f75,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f7,f56]) ).
fof(f76,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f5,f75]) ).
fof(f83,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f76,f7]) ).
fof(f90,plain,
! [X0,X1] : X0 = multiply(divide(X1,X1),X0),
inference(paramodulation,[status(thm)],[f76,f83]) ).
fof(f123,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f5,f90]) ).
fof(f137,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(divide(X1,X1),X0),X2)) = X2,
inference(paramodulation,[status(thm)],[f90,f13]) ).
fof(f139,plain,
! [X0,X1,X2] : divide(multiply(multiply(divide(X0,X0),X1),X2),X2) = X1,
inference(paramodulation,[status(thm)],[f90,f11]) ).
fof(f142,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f123,f6]) ).
fof(f149,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f90,f137]) ).
fof(f151,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f90,f139]) ).
fof(f153,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f142]) ).
fof(f162,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(multiply(X2,X0),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f13,f149]) ).
fof(f163,plain,
! [X0,X1,X2,X3] : divide(X0,X1) = divide(X2,divide(multiply(X3,multiply(X2,X1)),multiply(X3,X0))),
inference(paramodulation,[status(thm)],[f15,f149]) ).
fof(f165,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f83,f149]) ).
fof(f167,plain,
! [X0,X1,X2,X3] : multiply(divide(multiply(X0,X1),divide(X2,divide(multiply(X2,inverse(X3)),X0))),X3) = X1,
inference(paramodulation,[status(thm)],[f149,f17]) ).
fof(f202,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(X2,divide(multiply(X2,X1),X0)),
inference(forward_demodulation,[status(thm)],[f162,f163]) ).
fof(f205,plain,
! [X0,X1,X2] : multiply(divide(multiply(X0,X1),divide(X0,inverse(X2))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f202,f167]) ).
fof(f206,plain,
! [X0,X1,X2] : multiply(divide(multiply(X0,X1),multiply(X0,X2)),X2) = X1,
inference(forward_demodulation,[status(thm)],[f5,f205]) ).
fof(f207,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f162,f206]) ).
fof(f230,plain,
! [X0,X1,X2,X3] : divide(X0,X1) = divide(multiply(divide(multiply(X2,inverse(X1)),X3),X0),divide(X2,X3)),
inference(paramodulation,[status(thm)],[f17,f151]) ).
fof(f271,plain,
! [X0,X1] : multiply(inverse(X0),X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f5,f165]) ).
fof(f313,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,X0),X2),
inference(paramodulation,[status(thm)],[f11,f207]) ).
fof(f315,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f76,f207]) ).
fof(f317,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = divide(multiply(divide(multiply(X2,X1),X3),X0),divide(X2,X3)),
inference(paramodulation,[status(thm)],[f9,f207]) ).
fof(f336,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f313,f153]) ).
fof(f356,plain,
! [X0,X1] : divide(X0,X1) = multiply(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f317,f230]) ).
fof(f389,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f315]) ).
fof(f519,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(b1,inverse(b1)) ),
inference(paramodulation,[status(thm)],[f315,f389]) ).
fof(f521,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != divide(b1,b1) ),
inference(forward_demodulation,[status(thm)],[f356,f519]) ).
fof(f522,plain,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_subsumption_resolution,[status(thm)],[f521,f271]) ).
fof(f943,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(paramodulation,[status(thm)],[f315,f313]) ).
fof(f977,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f313,f943]) ).
fof(f978,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f522,f977]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n015.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:00:56 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.46 % Refutation found
% 0.14/5.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.48 % Elapsed time: 0.096912 seconds
% 0.14/5.48 % CPU time: 0.552747 seconds
% 0.14/5.48 % Total memory used: 79.682 MB
% 0.14/5.48 % Net memory used: 78.354 MB
%------------------------------------------------------------------------------