%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP660-14 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:35:03 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.93s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 70 unt; 2 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
mult(ld(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
mult(ld(x1,x1),x0) != x0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = ld(x1,x1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = mult(sF1_fnc,x0),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != x0,
inference(definition_folding,[],[f12,f14,f13]) ).
fof(f16,plain,
mult(x1,sF1_fnc) = x1,
inference(paramodulation,[status(thm)],[f13,f7]) ).
fof(f18,plain,
ld(sF1_fnc,sF0_fnc) = x0,
inference(paramodulation,[status(thm)],[f14,f8]) ).
fof(f23,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(X1,mult(X2,mult(ld(mult(X1,X2),X0),X1))),
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f26,plain,
! [X0] : mult(mult(sF0_fnc,X0),sF1_fnc) = mult(sF1_fnc,mult(x0,mult(X0,sF1_fnc))),
inference(paramodulation,[status(thm)],[f14,f11]) ).
fof(f27,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(X2,mult(ld(X2,X0),mult(X1,X2))),
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f37,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X0)) = mult(X2,mult(ld(mult(X0,X2),X1),X0)),
inference(paramodulation,[status(thm)],[f23,f8]) ).
fof(f43,plain,
! [X0] : mult(mult(X0,x1),sF1_fnc) = mult(sF1_fnc,mult(ld(sF1_fnc,X0),x1)),
inference(paramodulation,[status(thm)],[f16,f27]) ).
fof(f47,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X1,X2)) = mult(ld(X1,X2),mult(ld(ld(X1,X2),X0),X2)),
inference(paramodulation,[status(thm)],[f7,f27]) ).
fof(f52,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X1,X2),X0)) = mult(ld(X0,X1),mult(X2,X0)),
inference(paramodulation,[status(thm)],[f27,f8]) ).
fof(f102,plain,
! [X0,X1,X2] : ld(X0,ld(X1,mult(X2,X1))) = mult(ld(mult(X1,X0),X2),X1),
inference(paramodulation,[status(thm)],[f37,f8]) ).
fof(f141,plain,
! [X0,X1,X2] : ld(ld(X0,X1),ld(X0,mult(X2,X0))) = mult(ld(X1,X2),X0),
inference(paramodulation,[status(thm)],[f7,f102]) ).
fof(f282,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X1,rd(X2,X0)),X0)) = mult(ld(X0,X1),X2),
inference(paramodulation,[status(thm)],[f9,f52]) ).
fof(f286,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f297,plain,
rd(x1,sF1_fnc) = x1,
inference(paramodulation,[status(thm)],[f16,f10]) ).
fof(f299,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f7,f10]) ).
fof(f354,plain,
! [X0,X1] : ld(ld(X0,X1),X0) = mult(ld(X1,X0),X0),
inference(paramodulation,[status(thm)],[f8,f141]) ).
fof(f374,plain,
! [X0,X1] : ld(ld(X0,rd(X0,X1)),X0) = mult(X1,X0),
inference(paramodulation,[status(thm)],[f286,f354]) ).
fof(f377,plain,
ld(ld(x1,x1),x1) = mult(sF1_fnc,x1),
inference(paramodulation,[status(thm)],[f13,f354]) ).
fof(f397,plain,
ld(sF1_fnc,x1) = mult(sF1_fnc,x1),
inference(forward_demodulation,[status(thm)],[f13,f377]) ).
fof(f434,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = ld(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f374,f299]) ).
fof(f711,plain,
! [X0,X1] : rd(X0,X1) = ld(X0,rd(X0,rd(X1,X0))),
inference(paramodulation,[status(thm)],[f9,f434]) ).
fof(f829,plain,
! [X0,X1] : mult(X0,rd(X0,X1)) = rd(X0,rd(X1,X0)),
inference(paramodulation,[status(thm)],[f711,f7]) ).
fof(f1180,plain,
mult(sF1_fnc,rd(sF1_fnc,x1)) = rd(sF1_fnc,x1),
inference(paramodulation,[status(thm)],[f297,f829]) ).
fof(f1728,plain,
ld(x1,mult(rd(sF1_fnc,x1),x1)) = mult(ld(x1,sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f1180,f282]) ).
fof(f1764,plain,
ld(x1,sF1_fnc) = mult(ld(x1,sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f9,f1728]) ).
fof(f1765,plain,
ld(x1,sF1_fnc) = ld(ld(sF1_fnc,x1),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f354,f1764]) ).
fof(f1773,plain,
rd(sF1_fnc,ld(x1,sF1_fnc)) = ld(sF1_fnc,x1),
inference(paramodulation,[status(thm)],[f1765,f299]) ).
fof(f1784,plain,
x1 = ld(sF1_fnc,x1),
inference(forward_demodulation,[status(thm)],[f299,f1773]) ).
fof(f1787,plain,
x1 = mult(sF1_fnc,x1),
inference(backward_demodulation,[status(thm)],[f1784,f397]) ).
fof(f1812,plain,
! [X0] : ld(ld(x1,X0),ld(x1,x1)) = mult(ld(X0,sF1_fnc),x1),
inference(paramodulation,[status(thm)],[f1787,f141]) ).
fof(f1832,plain,
! [X0] : ld(ld(x1,X0),sF1_fnc) = mult(ld(X0,sF1_fnc),x1),
inference(forward_demodulation,[status(thm)],[f13,f1812]) ).
fof(f2219,plain,
mult(mult(sF1_fnc,x1),sF1_fnc) = mult(sF1_fnc,ld(ld(x1,sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f1832,f43]) ).
fof(f2247,plain,
mult(x1,sF1_fnc) = mult(sF1_fnc,ld(ld(x1,sF1_fnc),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f1787,f2219]) ).
fof(f2248,plain,
x1 = mult(sF1_fnc,ld(ld(x1,sF1_fnc),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f16,f2247]) ).
fof(f3213,plain,
ld(sF1_fnc,x1) = ld(ld(x1,sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f2248,f8]) ).
fof(f3233,plain,
x1 = ld(ld(x1,sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1784,f3213]) ).
fof(f3246,plain,
mult(ld(x1,sF1_fnc),x1) = sF1_fnc,
inference(paramodulation,[status(thm)],[f3233,f7]) ).
fof(f3250,plain,
ld(ld(x1,x1),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f1832,f3246]) ).
fof(f3251,plain,
ld(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f13,f3250]) ).
fof(f3502,plain,
! [X0] : mult(mult(X0,sF1_fnc),ld(sF1_fnc,sF1_fnc)) = mult(ld(sF1_fnc,sF1_fnc),mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f3251,f47]) ).
fof(f3655,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = mult(ld(sF1_fnc,sF1_fnc),mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f3251,f3502]) ).
fof(f3656,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = ld(sF1_fnc,mult(mult(sF1_fnc,ld(sF1_fnc,X0)),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f52,f3655]) ).
fof(f3657,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = ld(sF1_fnc,mult(X0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f7,f3656]) ).
fof(f4368,plain,
! [X0] : mult(X0,sF1_fnc) = ld(sF1_fnc,mult(rd(X0,sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f9,f3657]) ).
fof(f4409,plain,
! [X0] : mult(X0,sF1_fnc) = ld(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f9,f4368]) ).
fof(f4820,plain,
! [X0] : ld(sF1_fnc,mult(sF0_fnc,X0)) = mult(sF1_fnc,mult(x0,mult(X0,sF1_fnc))),
inference(backward_demodulation,[status(thm)],[f4409,f26]) ).
fof(f4879,plain,
! [X0] : ld(sF1_fnc,mult(sF0_fnc,X0)) = mult(sF1_fnc,mult(x0,ld(sF1_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f4409,f4820]) ).
fof(f4998,plain,
ld(sF1_fnc,mult(sF0_fnc,sF1_fnc)) = mult(sF1_fnc,mult(x0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f3251,f4879]) ).
fof(f5040,plain,
ld(sF1_fnc,ld(sF1_fnc,sF0_fnc)) = mult(sF1_fnc,mult(x0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f4409,f4998]) ).
fof(f5041,plain,
ld(sF1_fnc,x0) = mult(sF1_fnc,mult(x0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f5040]) ).
fof(f5042,plain,
ld(sF1_fnc,x0) = mult(sF1_fnc,ld(sF1_fnc,x0)),
inference(forward_demodulation,[status(thm)],[f4409,f5041]) ).
fof(f5043,plain,
ld(sF1_fnc,x0) = x0,
inference(forward_demodulation,[status(thm)],[f7,f5042]) ).
fof(f5125,plain,
mult(sF1_fnc,x0) = x0,
inference(paramodulation,[status(thm)],[f5043,f7]) ).
fof(f5142,plain,
sF0_fnc = x0,
inference(forward_demodulation,[status(thm)],[f14,f5125]) ).
fof(f5143,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5142,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP660-14 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.59 % Computer : n020.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Sun Sep 20 20:31:08 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.15/5.60 % Drodi V4.1.1
% 0.15/5.93 % Refutation found
% 0.15/5.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.34/7.18 % Elapsed time: 1.366785 seconds
% 8.34/7.18 % CPU time: 2.246233 seconds
% 8.34/7.18 % Total memory used: 96.587 MB
% 8.34/7.18 % Net memory used: 95.894 MB
%------------------------------------------------------------------------------