%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP682-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 64 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 135 ( 135 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : ld(A,mult(A,A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f15,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0] : ld(X0,ld(X0,mult(X0,X0))) = rd(mult(rd(X0,X0),X0),X0),
inference(paramodulation,[status(thm)],[f11,f15]) ).
fof(f31,plain,
! [X0,X1] : mult(X0,rd(mult(rd(X0,X0),X1),X1)) = ld(X0,mult(X0,mult(X0,ld(X1,X1)))),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f32,plain,
! [X0] : ld(X0,X0) = rd(mult(rd(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f9,f29]) ).
fof(f33,plain,
! [X0] : ld(X0,X0) = rd(rd(mult(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f12,f32]) ).
fof(f37,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f33]) ).
fof(f41,plain,
! [X0,X1] : mult(X0,rd(mult(rd(X0,X0),X1),X1)) = ld(X0,mult(X0,mult(X0,rd(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f37,f31]) ).
fof(f48,plain,
! [X0] : mult(X0,rd(X0,X0)) = ld(X0,mult(X0,X0)),
inference(paramodulation,[status(thm)],[f37,f11]) ).
fof(f49,plain,
! [X0] : mult(X0,rd(X0,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f9,f48]) ).
fof(f60,plain,
! [X0,X1,X2] : ld(X0,mult(ld(X0,mult(X0,X0)),mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f68,plain,
! [X0,X1,X2] : ld(ld(X0,X1),mult(ld(X0,X1),X2)) = mult(ld(X0,mult(X0,X2)),rd(X2,X2)),
inference(paramodulation,[status(thm)],[f49,f13]) ).
fof(f82,plain,
! [X0,X1,X2] : ld(X0,mult(X0,mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f9,f60]) ).
fof(f100,plain,
! [X0,X1,X2] : ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,mult(X2,rd(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f82,f68]) ).
fof(f103,plain,
! [X0,X1,X2] : ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)),
inference(forward_demodulation,[status(thm)],[f49,f100]) ).
fof(f119,plain,
! [X0,X1,X2] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,rd(mult(rd(X0,X0),X2),X2)),
inference(paramodulation,[status(thm)],[f49,f14]) ).
fof(f125,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(f144,plain,
! [X0,X1,X2] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(mult(X0,rd(X0,X0)),X2),X2),
inference(backward_demodulation,[status(thm)],[f150,f119]) ).
fof(f145,plain,
! [X0,X1] : rd(mult(mult(X0,rd(X0,X0)),X1),X1) = ld(X0,mult(X0,mult(X0,rd(X1,X1)))),
inference(backward_demodulation,[status(thm)],[f150,f41]) ).
fof(f150,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),X2) = mult(X0,rd(mult(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f10,f125]) ).
fof(f177,plain,
! [X0,X1,X2] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f49,f144]) ).
fof(f178,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = ld(X0,mult(X0,mult(X0,rd(X1,X1)))),
inference(forward_demodulation,[status(thm)],[f49,f145]) ).
fof(f200,plain,
! [X0,X1] : ld(X0,mult(X0,mult(X0,X1))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f9,f82]) ).
fof(f221,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(backward_demodulation,[status(thm)],[f200,f178]) ).
fof(f266,plain,
! [X0,X1,X2] : ld(X0,mult(X0,mult(mult(X0,X1),X2))) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f200,f82]) ).
fof(f295,plain,
! [X0] : rd(rd(mult(rd(X0,X0),X0),X0),rd(X0,X0)) = rd(X0,X0),
inference(paramodulation,[status(thm)],[f221,f10]) ).
fof(f372,plain,
! [X0] : rd(rd(rd(mult(X0,X0),X0),X0),rd(X0,X0)) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f12,f295]) ).
fof(f377,plain,
! [X0] : rd(rd(X0,X0),rd(X0,X0)) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f372]) ).
fof(f403,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(ld(X0,mult(X0,mult(X0,X1))),X2)) = ld(X0,mult(X0,X2)),
inference(paramodulation,[status(thm)],[f200,f103]) ).
fof(f428,plain,
! [X0,X1,X2] : ld(mult(X0,X1),ld(X0,mult(X0,mult(mult(X0,X1),X2)))) = ld(X0,mult(X0,X2)),
inference(forward_demodulation,[status(thm)],[f82,f403]) ).
fof(f431,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(X0,X1),X2)) = ld(X0,mult(X0,X2)),
inference(forward_demodulation,[status(thm)],[f266,f428]) ).
fof(f471,plain,
! [X0,X1] : rd(mult(mult(X0,X1),X1),X1) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f10,f150]) ).
fof(f570,plain,
! [X0,X1] : rd(X0,X1) = rd(mult(rd(X0,X1),X1),X1),
inference(paramodulation,[status(thm)],[f10,f177]) ).
fof(f579,plain,
! [X0,X1] : rd(mult(X0,rd(rd(X1,X1),rd(X1,X1))),rd(X1,X1)) = rd(mult(X0,rd(X1,X1)),rd(X1,X1)),
inference(paramodulation,[status(thm)],[f377,f177]) ).
fof(f591,plain,
! [X0,X1] : rd(X0,X1) = rd(rd(mult(X0,X1),X1),X1),
inference(forward_demodulation,[status(thm)],[f12,f570]) ).
fof(f610,plain,
! [X0,X1] : rd(rd(mult(X0,rd(X1,X1)),rd(X1,X1)),rd(X1,X1)) = rd(mult(X0,rd(X1,X1)),rd(X1,X1)),
inference(forward_demodulation,[status(thm)],[f221,f579]) ).
fof(f611,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = rd(mult(X0,rd(X1,X1)),rd(X1,X1)),
inference(forward_demodulation,[status(thm)],[f591,f610]) ).
fof(f612,plain,
! [X0,X1] : rd(mult(X0,X1),rd(X1,X1)) = mult(X0,X1),
inference(backward_demodulation,[status(thm)],[f641,f471]) ).
fof(f616,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(X0,rd(X1,X1)),
inference(backward_demodulation,[status(thm)],[f641,f12]) ).
fof(f641,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = rd(mult(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f177,f611]) ).
fof(f766,plain,
! [X0,X1] : mult(rd(X0,rd(X1,X1)),X1) = rd(mult(X0,X1),rd(X1,X1)),
inference(paramodulation,[status(thm)],[f641,f616]) ).
fof(f797,plain,
! [X0,X1] : mult(rd(X0,rd(X1,X1)),X1) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f612,f766]) ).
fof(f1131,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(rd(X0,rd(X1,X1)),X1),X2)) = ld(rd(X0,rd(X1,X1)),mult(rd(X0,rd(X1,X1)),X2)),
inference(paramodulation,[status(thm)],[f797,f431]) ).
fof(f1132,plain,
! [X0,X1,X2] : ld(rd(X0,rd(X1,X1)),mult(mult(rd(X0,X1),X1),X2)) = ld(rd(X0,X1),mult(rd(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f616,f431]) ).
fof(f1154,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(X0,X1),X2)) = ld(rd(X0,rd(X1,X1)),mult(rd(X0,rd(X1,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f797,f1131]) ).
fof(f1159,plain,
! [X0,X1,X2] : ld(X0,mult(X0,X1)) = ld(rd(X0,rd(X2,X2)),mult(rd(X0,rd(X2,X2)),X1)),
inference(forward_demodulation,[status(thm)],[f431,f1154]) ).
fof(f1160,plain,
! [X0,X1,X2] : ld(rd(X0,rd(X1,X1)),mult(rd(X0,rd(X1,X1)),X2)) = ld(rd(X0,X1),mult(rd(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f616,f1132]) ).
fof(f1161,plain,
ld(x0,mult(x0,x2)) != ld(x0,mult(x0,x2)),
inference(backward_demodulation,[status(thm)],[f1168,f16]) ).
fof(f1168,plain,
! [X0,X1,X2] : ld(X0,mult(X0,X1)) = ld(rd(X0,X2),mult(rd(X0,X2),X1)),
inference(forward_demodulation,[status(thm)],[f1159,f1160]) ).
fof(f1199,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP682-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % 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 20:32:49 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.36/4.01 % Elapsed time: 3.657046 seconds
% 17.36/4.01 % CPU time: 20.381615 seconds
% 17.36/4.01 % Total memory used: 13.095 GB
% 17.36/4.01 % Net memory used: 13.094 GB
%------------------------------------------------------------------------------