%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP683-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:35:07 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 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 : 144 ( 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
mult(rd(mult(x3,x4),x4),x5) != mult(x3,x5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
mult(rd(mult(x3,x4),x4),x5) != mult(x3,x5),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),rd(mult(X2,X2),X2)) = mult(X0,rd(mult(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f10,f14]) ).
fof(f33,plain,
! [X0,X1,X2,X3] : mult(mult(X0,rd(mult(X1,X2),X2)),rd(X3,X2)) = rd(mult(mult(mult(X0,X1),rd(X3,X2)),rd(X3,X2)),rd(X3,X2)),
inference(paramodulation,[status(thm)],[f14,f12]) ).
fof(f37,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(backward_demodulation,[status(thm)],[f41,f14]) ).
fof(f41,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),X2) = mult(X0,rd(mult(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f10,f28]) ).
fof(f54,plain,
! [X0,X1,X2,X3] : mult(rd(mult(mult(X0,X1),X2),X2),rd(X3,X2)) = rd(mult(mult(mult(X0,X1),rd(X3,X2)),rd(X3,X2)),rd(X3,X2)),
inference(forward_demodulation,[status(thm)],[f41,f33]) ).
fof(f55,plain,
! [X0,X1,X2,X3] : mult(rd(mult(mult(X0,X1),X2),X2),rd(X3,X2)) = mult(mult(X0,X1),rd(mult(rd(X3,X2),X2),X2)),
inference(forward_demodulation,[status(thm)],[f14,f54]) ).
fof(f56,plain,
! [X0,X1,X2,X3] : mult(rd(mult(mult(X0,X1),X2),X2),rd(X3,X2)) = rd(mult(mult(mult(X0,X1),rd(X3,X2)),X2),X2),
inference(forward_demodulation,[status(thm)],[f41,f55]) ).
fof(f64,plain,
! [X0,X1] : rd(mult(mult(X0,X1),X1),X1) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f10,f41]) ).
fof(f105,plain,
! [X0,X1,X2] : rd(mult(mult(X0,rd(X1,X2)),X2),X2) = mult(X0,rd(X1,X2)),
inference(paramodulation,[status(thm)],[f37,f64]) ).
fof(f110,plain,
! [X0,X1,X2] : rd(mult(mult(X0,mult(X1,X2)),X2),X2) = mult(X0,mult(X1,X2)),
inference(paramodulation,[status(thm)],[f64,f41]) ).
fof(f111,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(mult(mult(X2,X3),X3),X3)),mult(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(paramodulation,[status(thm)],[f64,f37]) ).
fof(f115,plain,
! [X0,X1,X2,X3] : mult(rd(mult(mult(X0,X1),X2),X2),rd(X3,X2)) = mult(mult(X0,X1),rd(X3,X2)),
inference(backward_demodulation,[status(thm)],[f105,f56]) ).
fof(f124,plain,
! [X0,X1,X2,X3] : rd(rd(mult(mult(mult(X0,X1),mult(X2,X3)),X3),X3),mult(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(forward_demodulation,[status(thm)],[f41,f111]) ).
fof(f126,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),mult(X2,X3)),mult(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(forward_demodulation,[status(thm)],[f110,f124]) ).
fof(f130,plain,
! [X0,X1,X2,X3] : rd(mult(rd(mult(X0,X1),X1),mult(X2,X3)),mult(X2,X3)) = rd(mult(mult(rd(X0,X1),X1),X3),X3),
inference(paramodulation,[status(thm)],[f12,f126]) ).
fof(f142,plain,
! [X0,X1,X2,X3] : rd(mult(rd(mult(X0,X1),X1),mult(X2,X3)),mult(X2,X3)) = rd(mult(rd(mult(X0,X1),X1),X3),X3),
inference(forward_demodulation,[status(thm)],[f12,f130]) ).
fof(f209,plain,
! [X0,X1,X2,X3] : mult(rd(mult(rd(mult(X0,X1),X1),X2),X2),rd(X3,X2)) = mult(mult(rd(X0,X1),X1),rd(X3,X2)),
inference(paramodulation,[status(thm)],[f12,f115]) ).
fof(f229,plain,
! [X0,X1,X2,X3] : mult(rd(mult(rd(mult(X0,X1),X1),X2),X2),rd(X3,X2)) = mult(rd(mult(X0,X1),X1),rd(X3,X2)),
inference(forward_demodulation,[status(thm)],[f12,f209]) ).
fof(f263,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X1,X2)) = rd(mult(rd(mult(X0,X0),X0),X2),X2),
inference(paramodulation,[status(thm)],[f10,f142]) ).
fof(f292,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X1,X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f10,f263]) ).
fof(f343,plain,
! [X0,X1,X2] : rd(mult(X0,rd(mult(X1,X2),X2)),mult(rd(X1,X2),X2)) = rd(mult(X0,X2),X2),
inference(paramodulation,[status(thm)],[f12,f292]) ).
fof(f357,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X1),mult(X2,X1)) = rd(mult(mult(X0,mult(X2,X1)),mult(X2,X1)),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f292,f12]) ).
fof(f363,plain,
! [X0,X1,X2] : rd(rd(mult(mult(X0,X1),X2),X2),mult(rd(X1,X2),X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f41,f343]) ).
fof(f368,plain,
! [X0,X1,X2] : rd(rd(mult(mult(X0,X1),X2),X2),rd(mult(X1,X2),X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f12,f363]) ).
fof(f394,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X1),mult(X2,X1)) = mult(X0,mult(X2,X1)),
inference(forward_demodulation,[status(thm)],[f64,f357]) ).
fof(f451,plain,
! [X0,X1,X2,X3] : rd(rd(mult(mult(X0,mult(X1,X2)),X3),X3),rd(mult(mult(X1,X2),X3),X3)) = rd(mult(rd(mult(X0,X2),X2),X3),X3),
inference(paramodulation,[status(thm)],[f394,f368]) ).
fof(f454,plain,
! [X0,X1,X2,X3,X4] : rd(rd(mult(mult(X0,mult(X1,X2)),rd(X3,X4)),rd(X3,X4)),rd(mult(mult(X1,X2),X4),X4)) = rd(mult(X0,rd(X3,X4)),rd(X3,X4)),
inference(paramodulation,[status(thm)],[f37,f368]) ).
fof(f476,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),X1),rd(X2,X1)) = mult(rd(mult(X0,X3),X3),rd(X2,X1)),
inference(backward_demodulation,[status(thm)],[f477,f229]) ).
fof(f477,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X1) = rd(mult(rd(mult(X0,X2),X2),X1),X1),
inference(forward_demodulation,[status(thm)],[f368,f451]) ).
fof(f482,plain,
! [X0,X1,X2,X3,X4] : rd(rd(mult(mult(X0,mult(X1,X2)),X3),X3),rd(mult(mult(X1,X2),X3),X3)) = rd(mult(X0,rd(X4,X3)),rd(X4,X3)),
inference(forward_demodulation,[status(thm)],[f37,f454]) ).
fof(f485,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X1) = rd(mult(X0,rd(X2,X1)),rd(X2,X1)),
inference(forward_demodulation,[status(thm)],[f368,f482]) ).
fof(f538,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X1),rd(X2,X1)) = rd(mult(mult(X0,rd(X2,X1)),rd(X2,X1)),rd(X2,X1)),
inference(paramodulation,[status(thm)],[f485,f12]) ).
fof(f574,plain,
! [X0,X1,X2,X3] : mult(X0,rd(X1,X2)) = mult(rd(mult(X0,X3),X3),rd(X1,X2)),
inference(backward_demodulation,[status(thm)],[f575,f476]) ).
fof(f575,plain,
! [X0,X1,X2] : mult(rd(mult(X0,X1),X1),rd(X2,X1)) = mult(X0,rd(X2,X1)),
inference(forward_demodulation,[status(thm)],[f64,f538]) ).
fof(f1082,plain,
! [X0,X1,X2] : mult(X0,rd(mult(X1,X1),X1)) = mult(rd(mult(X0,X2),X2),X1),
inference(paramodulation,[status(thm)],[f10,f574]) ).
fof(f1133,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X1),X1) = mult(rd(mult(X0,X2),X2),X1),
inference(forward_demodulation,[status(thm)],[f41,f1082]) ).
fof(f1134,plain,
mult(x3,x5) != mult(x3,x5),
inference(backward_demodulation,[status(thm)],[f1140,f16]) ).
fof(f1140,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(rd(mult(X0,X2),X2),X1),
inference(forward_demodulation,[status(thm)],[f64,f1133]) ).
fof(f1187,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP683-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:32:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.48 % Refutation found
% 0.14/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.51 % Elapsed time: 0.131948 seconds
% 0.14/0.51 % CPU time: 0.906492 seconds
% 0.14/0.51 % Total memory used: 38.281 MB
% 0.14/0.51 % Net memory used: 36.974 MB
%------------------------------------------------------------------------------