%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP599-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:34:46 PM UTC 2026
% Result : Unsatisfiable 8.42s 1.51s
% Output : CNFRefutation 8.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 3
% Syntax : Number of formulae : 87 ( 87 unt; 0 def)
% Number of atoms : 87 ( 86 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 222 ( 222 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B))))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(inverse(X2),X1))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),inverse(double_divide(X0,multiply(X1,inverse(X2))))) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),multiply(multiply(X1,inverse(X2)),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(multiply(multiply(X1,inverse(X0)),X2),inverse(X3)),double_divide(X2,X1))) = X3,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,inverse(X1)),X2),double_divide(X2,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(multiply(multiply(X0,inverse(X1)),X2),inverse(X3)),double_divide(X2,X0)),X1) = inverse(X3),
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f20,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),X1),multiply(X1,inverse(X2))),inverse(X2)) = X0,
inference(paramodulation,[status(thm)],[f16,f13]) ).
fof(f42,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(multiply(X0,X1),X2),multiply(X2,inverse(X3))),inverse(X3)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f20]) ).
fof(f294,plain,
! [X0,X1,X2,X3] : multiply(multiply(inverse(X0),double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(inverse(X3))),X1))),X0) = inverse(X3),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f310,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(inverse(X0),double_divide(double_divide(X1,X2),multiply(multiply(X2,inverse(inverse(X3))),X1)))) = X3,
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f340,plain,
! [X0,X1] : multiply(multiply(inverse(X0),inverse(X1)),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f13,f294]) ).
fof(f342,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f13,f310]) ).
fof(f382,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),multiply(multiply(X1,X0),inverse(X2))) = X2,
inference(paramodulation,[status(thm)],[f5,f342]) ).
fof(f383,plain,
! [X0,X1,X2] : double_divide(X0,multiply(inverse(X0),multiply(X1,X2))) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f5,f342]) ).
fof(f405,plain,
! [X0,X1] : multiply(inverse(X0),double_divide(X1,inverse(X1))) = inverse(X0),
inference(paramodulation,[status(thm)],[f340,f16]) ).
fof(f463,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X2,inverse(X2))) = inverse(double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f5,f405]) ).
fof(f486,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X2,inverse(X2))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f5,f463]) ).
fof(f513,plain,
! [X0,X1,X2,X3,X4] : double_divide(double_divide(double_divide(X0,X1),multiply(multiply(inverse(multiply(X2,X3)),multiply(X1,X0)),inverse(X4))),inverse(X4)) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f383,f42]) ).
fof(f520,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,X1),multiply(multiply(inverse(inverse(X2)),multiply(X1,X0)),inverse(X3))),inverse(X3)) = X2,
inference(paramodulation,[status(thm)],[f383,f20]) ).
fof(f552,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),inverse(inverse(X1))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f340,f382]) ).
fof(f672,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(double_divide(X1,inverse(X1))),inverse(X0)),
inference(paramodulation,[status(thm)],[f340,f486]) ).
fof(f718,plain,
! [X0,X1] : inverse(X0) = multiply(multiply(inverse(X1),X1),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f5,f672]) ).
fof(f774,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(inverse(X0),multiply(inverse(X1),X1)),inverse(X2)),inverse(X2)) = X0,
inference(paramodulation,[status(thm)],[f718,f20]) ).
fof(f781,plain,
! [X0,X1,X2] : double_divide(X0,multiply(inverse(X0),inverse(X1))) = double_divide(inverse(X1),multiply(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f718,f383]) ).
fof(f801,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(X1)),inverse(X1)) = X0,
inference(backward_demodulation,[status(thm)],[f804,f774]) ).
fof(f804,plain,
! [X0,X1] : X0 = double_divide(inverse(X0),multiply(inverse(X1),X1)),
inference(forward_demodulation,[status(thm)],[f342,f781]) ).
fof(f837,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(multiply(multiply(multiply(inverse(X1),X1),inverse(X0)),inverse(X2)),inverse(X3)),X2)) = X3,
inference(paramodulation,[status(thm)],[f804,f14]) ).
fof(f853,plain,
! [X0,X1,X2] : double_divide(X0,multiply(multiply(multiply(inverse(X0),inverse(X1)),inverse(X2)),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f718,f837]) ).
fof(f857,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f552,f801]) ).
fof(f860,plain,
! [X0,X1] : double_divide(X0,inverse(X1)) = double_divide(inverse(X1),inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f552,f801]) ).
fof(f891,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,X1),multiply(multiply(X2,multiply(X1,X0)),inverse(X3))),inverse(X3)) = X2,
inference(backward_demodulation,[status(thm)],[f857,f520]) ).
fof(f948,plain,
! [X0,X1,X2,X3,X4] : double_divide(inverse(X0),double_divide(double_divide(X1,X2),multiply(multiply(inverse(multiply(X3,X4)),multiply(X2,X1)),inverse(X0)))) = double_divide(X4,X3),
inference(backward_demodulation,[status(thm)],[f957,f513]) ).
fof(f957,plain,
! [X0,X1] : double_divide(X0,inverse(X1)) = double_divide(inverse(X1),X0),
inference(forward_demodulation,[status(thm)],[f857,f860]) ).
fof(f994,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),double_divide(double_divide(X1,X2),multiply(multiply(X3,multiply(X2,X1)),inverse(X0)))) = X3,
inference(forward_demodulation,[status(thm)],[f957,f891]) ).
fof(f1045,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f994,f948]) ).
fof(f1069,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f857,f340]) ).
fof(f1079,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),double_divide(X2,X0)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f857,f16]) ).
fof(f1111,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f857,f1069]) ).
fof(f1126,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),double_divide(X2,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f857,f1079]) ).
fof(f1213,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),X2),multiply(X1,X0)) = X2,
inference(paramodulation,[status(thm)],[f1045,f1111]) ).
fof(f1214,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f857,f1111]) ).
fof(f1215,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),double_divide(X1,X0)) = X2,
inference(paramodulation,[status(thm)],[f5,f1111]) ).
fof(f1228,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f1214,f1214]) ).
fof(f1243,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f1045,f1228]) ).
fof(f1250,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f1243,f1111]) ).
fof(f1254,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(double_divide(X1,X0),X1),
inference(paramodulation,[status(thm)],[f1243,f1045]) ).
fof(f1292,plain,
! [X0,X1,X2] : double_divide(X0,multiply(multiply(double_divide(inverse(inverse(X1)),X0),inverse(X2)),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f1250,f853]) ).
fof(f1331,plain,
! [X0,X1] : X0 = double_divide(double_divide(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f857,f1254]) ).
fof(f1379,plain,
! [X0,X1,X2] : double_divide(X0,multiply(multiply(double_divide(X1,X0),inverse(X2)),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f857,f1292]) ).
fof(f1507,plain,
! [X0,X1] : X0 = double_divide(X1,double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f1331,f1331]) ).
fof(f1508,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f1331,f1243]) ).
fof(f1523,plain,
! [X0,X1] : multiply(inverse(X0),inverse(double_divide(X0,X1))) = X1,
inference(paramodulation,[status(thm)],[f1508,f1214]) ).
fof(f1525,plain,
! [X0,X1] : double_divide(inverse(inverse(double_divide(X0,X1))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f1250,f1523]) ).
fof(f1526,plain,
! [X0,X1] : double_divide(X0,inverse(inverse(double_divide(X0,X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f957,f1525]) ).
fof(f1528,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f857,f1526]) ).
fof(f1533,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f1507,f1528]) ).
fof(f1538,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f1528,f1243]) ).
fof(f1575,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1682,f6]) ).
fof(f1590,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,multiply(double_divide(X1,X0),inverse(X2)))) = X2,
inference(backward_demodulation,[status(thm)],[f1682,f1379]) ).
fof(f1596,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = X2,
inference(backward_demodulation,[status(thm)],[f1682,f1213]) ).
fof(f1677,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(multiply(X1,X0),X2)) = X2,
inference(backward_demodulation,[status(thm)],[f1682,f1215]) ).
fof(f1678,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(multiply(X1,X2),X0)) = X2,
inference(backward_demodulation,[status(thm)],[f1682,f1126]) ).
fof(f1682,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f5,f1538]) ).
fof(f2240,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f1682,f1250]) ).
fof(f2286,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(inverse(double_divide(X1,X0)),X2))) = X2,
inference(backward_demodulation,[status(thm)],[f2240,f1590]) ).
fof(f2515,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(multiply(X0,X1),X2))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f2286]) ).
fof(f3182,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(multiply(X0,X1),X2)) = X2,
inference(paramodulation,[status(thm)],[f1533,f1677]) ).
fof(f3385,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = double_divide(multiply(X0,X1),X2),
inference(paramodulation,[status(thm)],[f1528,f2515]) ).
fof(f3806,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X2)),multiply(X3,X0)) = multiply(multiply(X2,X3),X1),
inference(paramodulation,[status(thm)],[f1678,f1678]) ).
fof(f3950,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X1,X0),X2),
inference(paramodulation,[status(thm)],[f3182,f1596]) ).
fof(f3951,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X2)),multiply(X3,X0)) = multiply(multiply(X1,X2),X3),
inference(paramodulation,[status(thm)],[f3182,f1678]) ).
fof(f4026,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f3806,f3951]) ).
fof(f4090,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(double_divide(X1,multiply(X2,X0))),
inference(paramodulation,[status(thm)],[f3385,f5]) ).
fof(f4260,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(backward_demodulation,[status(thm)],[f4270,f4026]) ).
fof(f4261,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X2,X1)),
inference(backward_demodulation,[status(thm)],[f4270,f3950]) ).
fof(f4270,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f5,f4090]) ).
fof(f4515,plain,
multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f4527,f1575]) ).
fof(f4527,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f4270,f4260]) ).
fof(f4528,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f4270,f4261]) ).
fof(f4582,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f4528,f4515]) ).
fof(f4583,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f1682,f4582]) ).
fof(f4584,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4583]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP599-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:17:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 8.42/1.51 % Refutation found
% 8.42/1.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.42/1.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.83/2.75 % Elapsed time: 2.176779 seconds
% 10.83/2.75 % CPU time: 7.504479 seconds
% 10.83/2.75 % Total memory used: 173.118 MB
% 10.83/2.75 % Net memory used: 164.966 MB
%------------------------------------------------------------------------------