%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:35:08 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.56s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 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 : 5 ( 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 : 92 ( 92 !; 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,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
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,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,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(f35,plain,
! [X0,X1,X2] : ld(X0,mult(X0,mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f9,f26]) ).
fof(f60,plain,
! [X0] : ld(X0,mult(X0,ld(X0,X0))) = rd(rd(mult(X0,X0),X0),X0),
inference(paramodulation,[status(thm)],[f12,f15]) ).
fof(f64,plain,
! [X0] : ld(X0,ld(X0,mult(X0,X0))) = rd(rd(mult(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f11,f60]) ).
fof(f65,plain,
! [X0] : ld(X0,X0) = rd(rd(mult(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f9,f64]) ).
fof(f66,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(ld(X0,X0),X1),X1),
inference(backward_demodulation,[status(thm)],[f68,f15]) ).
fof(f68,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f65]) ).
fof(f77,plain,
! [X0] : mult(ld(X0,X0),X0) = rd(mult(X0,X0),X0),
inference(paramodulation,[status(thm)],[f68,f12]) ).
fof(f79,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f10,f77]) ).
fof(f85,plain,
! [X0,X1] : mult(ld(X0,mult(X0,ld(X1,X1))),X1) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(paramodulation,[status(thm)],[f66,f12]) ).
fof(f88,plain,
! [X0,X1] : ld(X0,mult(X0,mult(ld(X1,X1),X1))) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(forward_demodulation,[status(thm)],[f35,f85]) ).
fof(f89,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(forward_demodulation,[status(thm)],[f79,f88]) ).
fof(f94,plain,
! [X0,X1,X2] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(X0,X0),rd(mult(X0,X2),X2)),
inference(paramodulation,[status(thm)],[f79,f14]) ).
fof(f100,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(f116,plain,
! [X0,X1,X2] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(mult(ld(X0,X0),X0),X2),X2),
inference(backward_demodulation,[status(thm)],[f122,f94]) ).
fof(f122,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),X2) = mult(X0,rd(mult(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f10,f100]) ).
fof(f146,plain,
! [X0,X1,X2] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f79,f116]) ).
fof(f160,plain,
! [X0,X1] : rd(mult(mult(X0,X1),X1),X1) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f10,f122]) ).
fof(f176,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X0,X0),X1),
inference(backward_demodulation,[status(thm)],[f160,f89]) ).
fof(f397,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),rd(mult(mult(X1,X2),X2),X2)) = rd(mult(X0,X2),X2),
inference(paramodulation,[status(thm)],[f160,f146]) ).
fof(f432,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X1,X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f160,f397]) ).
fof(f573,plain,
! [X0,X1,X2] : rd(mult(X0,ld(X1,mult(X1,X2))),mult(ld(X1,X1),X2)) = rd(mult(X0,X2),X2),
inference(paramodulation,[status(thm)],[f176,f432]) ).
fof(f576,plain,
! [X0,X1,X2] : rd(mult(X0,ld(X1,mult(X1,X2))),mult(X1,ld(X1,X2))) = rd(mult(X0,ld(X1,X2)),ld(X1,X2)),
inference(paramodulation,[status(thm)],[f11,f432]) ).
fof(f600,plain,
! [X0,X1,X2] : rd(mult(X0,ld(X1,mult(X1,X2))),ld(X1,mult(X1,X2))) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f176,f573]) ).
fof(f608,plain,
! [X0,X1,X2] : rd(mult(X0,ld(X1,mult(X1,X2))),ld(X1,mult(X1,X2))) = rd(mult(X0,ld(X1,X2)),ld(X1,X2)),
inference(forward_demodulation,[status(thm)],[f11,f576]) ).
fof(f609,plain,
rd(mult(x6,x8),x8) != rd(mult(x6,x8),x8),
inference(backward_demodulation,[status(thm)],[f614,f16]) ).
fof(f614,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X1) = rd(mult(X0,ld(X2,X1)),ld(X2,X1)),
inference(forward_demodulation,[status(thm)],[f600,f608]) ).
fof(f633,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f609]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n005.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Sun Sep 20 20:33:02 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.15/0.56 % Refutation found
% 0.15/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.73/5.42 % Elapsed time: 4.958155 seconds
% 9.73/5.42 % CPU time: 27.390361 seconds
% 9.73/5.42 % Total memory used: 13.090 GB
% 9.73/5.42 % Net memory used: 13.089 GB
%------------------------------------------------------------------------------