%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP686-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 34.66s 4.97s
% Output : CNFRefutation 35.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 125 ( 125 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : mult(A,mult(B,mult(B,C))) = mult(mult(A,mult(B,B)),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,mult(a,b)),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : X0 = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] : X0 = mult(X0,unit),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0] : X0 = mult(unit,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(X0,mult(X1,X1)),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
mult(mult(a,a),mult(b,c)) != mult(mult(a,mult(a,b)),c),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] : X0 = mult(X1,mult(X2,mult(X2,ld(mult(X1,mult(X2,X2)),X0)))),
inference(paramodulation,[status(thm)],[f15,f9]) ).
fof(f31,plain,
! [X0,X1,X2] : ld(mult(X0,mult(X1,X1)),mult(X0,mult(X1,mult(X1,X2)))) = X2,
inference(paramodulation,[status(thm)],[f15,f10]) ).
fof(f39,plain,
! [X0,X1,X2] : ld(X0,X1) = ld(mult(X2,mult(X0,X0)),mult(X2,mult(X0,X1))),
inference(paramodulation,[status(thm)],[f9,f31]) ).
fof(f49,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,mult(X1,X2))),X2) = mult(X0,mult(X1,X1)),
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f54,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),ld(X1,X2)) = mult(X0,mult(X1,X1)),
inference(paramodulation,[status(thm)],[f9,f49]) ).
fof(f66,plain,
! [X0] : ld(X0,X0) = unit,
inference(paramodulation,[status(thm)],[f13,f10]) ).
fof(f116,plain,
! [X0,X1,X2] : ld(X0,X1) = mult(X2,mult(X2,ld(mult(X0,mult(X2,X2)),X1))),
inference(paramodulation,[status(thm)],[f29,f10]) ).
fof(f150,plain,
! [X0,X1] : mult(unit,mult(X0,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f170,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f14,f150]) ).
fof(f199,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(rd(X0,mult(X2,X2)),mult(X2,mult(X2,X1))),
inference(paramodulation,[status(thm)],[f11,f15]) ).
fof(f203,plain,
! [X0,X1] : X0 = ld(rd(X1,X0),X1),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f238,plain,
! [X0,X1,X2] : mult(rd(X0,mult(X1,X1)),mult(X1,X2)) = mult(X0,ld(X1,X2)),
inference(paramodulation,[status(thm)],[f9,f199]) ).
fof(f243,plain,
! [X0,X1,X2] : rd(X0,mult(X1,X1)) = rd(mult(X0,X2),mult(X1,mult(X1,X2))),
inference(paramodulation,[status(thm)],[f199,f12]) ).
fof(f245,plain,
! [X0,X1,X2] : ld(rd(X0,mult(X1,X1)),mult(X0,X2)) = mult(X1,mult(X1,X2)),
inference(paramodulation,[status(thm)],[f199,f10]) ).
fof(f391,plain,
! [X0,X1] : ld(X0,X1) = ld(mult(unit,mult(X0,X0)),mult(X0,X1)),
inference(paramodulation,[status(thm)],[f14,f39]) ).
fof(f416,plain,
! [X0,X1] : ld(X0,X1) = ld(mult(X0,X0),mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f14,f391]) ).
fof(f431,plain,
! [X0,X1] : mult(unit,mult(X0,X0)) = rd(mult(X0,X1),ld(X0,X1)),
inference(paramodulation,[status(thm)],[f14,f54]) ).
fof(f442,plain,
! [X0,X1,X2] : rd(mult(X0,X1),ld(X2,ld(X2,X1))) = mult(X0,mult(X2,X2)),
inference(paramodulation,[status(thm)],[f9,f54]) ).
fof(f456,plain,
! [X0,X1] : mult(X0,X0) = rd(mult(X0,X1),ld(X0,X1)),
inference(forward_demodulation,[status(thm)],[f14,f431]) ).
fof(f696,plain,
! [X0,X1,X2] : ld(X0,ld(X1,X2)) = mult(X0,ld(mult(X1,mult(X0,X0)),X2)),
inference(paramodulation,[status(thm)],[f116,f10]) ).
fof(f858,plain,
mult(mult(a,mult(a,b)),c) != mult(a,mult(a,mult(b,c))),
inference(backward_demodulation,[status(thm)],[f170,f16]) ).
fof(f1005,plain,
! [X0,X1] : ld(mult(X0,X0),X1) = ld(X0,ld(X0,X1)),
inference(paramodulation,[status(thm)],[f9,f416]) ).
fof(f1277,plain,
! [X0,X1,X2] : rd(X0,mult(X1,mult(X1,X2))) = rd(rd(X0,X2),mult(X1,X1)),
inference(paramodulation,[status(thm)],[f11,f243]) ).
fof(f1766,plain,
! [X0,X1] : ld(rd(unit,mult(X0,X0)),X1) = mult(X0,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f14,f245]) ).
fof(f2040,plain,
! [X0,X1] : mult(X0,ld(X1,unit)) = mult(rd(X0,mult(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f13,f238]) ).
fof(f3655,plain,
! [X0,X1] : mult(X0,mult(X1,X1)) = rd(X0,ld(X1,ld(X1,unit))),
inference(paramodulation,[status(thm)],[f13,f442]) ).
fof(f4025,plain,
! [X0] : unit = mult(X0,mult(X0,rd(unit,mult(X0,X0)))),
inference(paramodulation,[status(thm)],[f1766,f66]) ).
fof(f4096,plain,
! [X0] : mult(X0,X0) = rd(unit,ld(X0,mult(X0,rd(unit,mult(X0,X0))))),
inference(paramodulation,[status(thm)],[f4025,f456]) ).
fof(f4101,plain,
! [X0] : ld(X0,unit) = mult(X0,rd(unit,mult(X0,X0))),
inference(paramodulation,[status(thm)],[f4025,f10]) ).
fof(f4118,plain,
! [X0] : rd(unit,rd(unit,mult(X0,X0))) = mult(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f4096]) ).
fof(f4177,plain,
! [X0] : rd(unit,mult(X0,X0)) = ld(mult(X0,X0),unit),
inference(paramodulation,[status(thm)],[f4118,f203]) ).
fof(f4181,plain,
! [X0] : ld(X0,ld(X0,unit)) = rd(unit,mult(X0,X0)),
inference(forward_demodulation,[status(thm)],[f1005,f4177]) ).
fof(f4272,plain,
! [X0] : X0 = rd(ld(X0,unit),rd(unit,mult(X0,X0))),
inference(paramodulation,[status(thm)],[f4101,f12]) ).
fof(f4910,plain,
! [X0] : X0 = mult(ld(X0,unit),mult(X0,X0)),
inference(backward_demodulation,[status(thm)],[f4912,f4272]) ).
fof(f4912,plain,
! [X0,X1] : rd(X0,rd(unit,mult(X1,X1))) = mult(X0,mult(X1,X1)),
inference(forward_demodulation,[status(thm)],[f4181,f3655]) ).
fof(f5092,plain,
! [X0,X1] : ld(X0,ld(ld(X0,unit),X1)) = mult(X0,ld(X0,X1)),
inference(paramodulation,[status(thm)],[f4910,f696]) ).
fof(f5123,plain,
! [X0] : ld(X0,unit) = rd(X0,mult(X0,X0)),
inference(paramodulation,[status(thm)],[f4910,f12]) ).
fof(f5147,plain,
! [X0,X1] : X0 = ld(X1,ld(ld(X1,unit),X0)),
inference(forward_demodulation,[status(thm)],[f9,f5092]) ).
fof(f5217,plain,
! [X0] : mult(X0,ld(X0,unit)) = mult(ld(X0,unit),X0),
inference(paramodulation,[status(thm)],[f5123,f2040]) ).
fof(f5219,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(ld(X0,unit),mult(X0,X1)),
inference(paramodulation,[status(thm)],[f5123,f238]) ).
fof(f5227,plain,
! [X0,X1] : X0 = mult(ld(X1,unit),mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f9,f5219]) ).
fof(f5246,plain,
! [X0] : unit = mult(ld(X0,unit),X0),
inference(forward_demodulation,[status(thm)],[f9,f5217]) ).
fof(f5371,plain,
! [X0] : rd(unit,X0) = ld(X0,unit),
inference(paramodulation,[status(thm)],[f5246,f12]) ).
fof(f5534,plain,
! [X0,X1] : X0 = ld(X1,ld(rd(unit,X1),X0)),
inference(backward_demodulation,[status(thm)],[f5371,f5147]) ).
fof(f6538,plain,
! [X0,X1] : mult(X0,X1) = ld(rd(unit,X0),X1),
inference(paramodulation,[status(thm)],[f5534,f9]) ).
fof(f7190,plain,
! [X0,X1] : X0 = mult(rd(unit,X1),mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f5371,f5227]) ).
fof(f7263,plain,
! [X0,X1,X2] : mult(X0,mult(X0,mult(X1,X2))) = ld(rd(rd(unit,X1),mult(X0,X0)),X2),
inference(paramodulation,[status(thm)],[f7190,f245]) ).
fof(f7293,plain,
! [X0,X1,X2] : mult(X0,mult(X0,mult(X1,X2))) = ld(rd(unit,mult(X0,mult(X0,X1))),X2),
inference(forward_demodulation,[status(thm)],[f1277,f7263]) ).
fof(f7294,plain,
! [X0,X1,X2] : mult(X0,mult(X0,mult(X1,X2))) = mult(mult(X0,mult(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f6538,f7293]) ).
fof(f7295,plain,
$false,
inference(resolution,[status(thm)],[f7294,f858]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP686-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n017.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 20:28:41 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 34.66/4.97 % Refutation found
% 34.66/4.97 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 34.66/4.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.67/6.22 % Elapsed time: 5.577185 seconds
% 19.67/6.22 % CPU time: 29.012741 seconds
% 19.67/6.22 % Total memory used: 307.792 MB
% 19.67/6.22 % Net memory used: 304.800 MB
%------------------------------------------------------------------------------