%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP660-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:35:02 PM UTC 2026
% Result : Unsatisfiable 6.06s 1.21s
% Output : CNFRefutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% 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 : 81 ( 81 !; 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,B,C] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
mult(x0,rd(x1,x1)) != x0,
file('/export/starexec/sandbox/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(x0,rd(x1,x1)) != x0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = rd(x1,x1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = mult(x0,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != x0,
inference(definition_folding,[],[f12,f14,f13]) ).
fof(f18,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f20,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f7,f10]) ).
fof(f22,plain,
mult(sF1_fnc,x1) = x1,
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f24,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(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(f28,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,mult(X2,X0))),X0) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f33,plain,
ld(sF1_fnc,x1) = x1,
inference(paramodulation,[status(thm)],[f13,f18]) ).
fof(f104,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X0)) = mult(X2,mult(ld(mult(X0,X2),X1),X0)),
inference(paramodulation,[status(thm)],[f24,f8]) ).
fof(f130,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,X2)),X2) = mult(X2,mult(ld(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f230,plain,
! [X0,X1,X2] : ld(X0,ld(X1,mult(X2,X1))) = mult(ld(mult(X1,X0),X2),X1),
inference(paramodulation,[status(thm)],[f104,f8]) ).
fof(f396,plain,
! [X0,X1,X2] : rd(mult(X0,mult(ld(X0,X1),X2)),X0) = mult(X1,rd(X2,X0)),
inference(paramodulation,[status(thm)],[f130,f10]) ).
fof(f813,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(mult(X1,X0),X1),X1),
inference(paramodulation,[status(thm)],[f8,f230]) ).
fof(f847,plain,
ld(x1,sF1_fnc) = mult(ld(x1,sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f22,f813]) ).
fof(f858,plain,
! [X0,X1] : ld(ld(X0,X1),X0) = mult(ld(X1,X0),X0),
inference(paramodulation,[status(thm)],[f7,f813]) ).
fof(f882,plain,
! [X0,X1] : rd(ld(X0,X1),X1) = ld(mult(X1,X0),X1),
inference(paramodulation,[status(thm)],[f813,f10]) ).
fof(f949,plain,
! [X0,X1] : rd(X0,mult(ld(X1,X0),X0)) = ld(X0,X1),
inference(paramodulation,[status(thm)],[f858,f20]) ).
fof(f978,plain,
! [X0,X1] : rd(X0,rd(ld(X1,X0),X0)) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f882,f20]) ).
fof(f1001,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = ld(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f949]) ).
fof(f1028,plain,
rd(x1,rd(x1,x1)) = mult(x1,sF1_fnc),
inference(paramodulation,[status(thm)],[f33,f978]) ).
fof(f1030,plain,
! [X0,X1] : rd(X0,rd(X1,X0)) = mult(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f978]) ).
fof(f1042,plain,
rd(x1,sF1_fnc) = mult(x1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f13,f1028]) ).
fof(f1102,plain,
! [X0] : ld(X0,ld(sF1_fnc,rd(x1,sF1_fnc))) = mult(ld(mult(sF1_fnc,X0),x1),sF1_fnc),
inference(paramodulation,[status(thm)],[f1042,f230]) ).
fof(f2392,plain,
rd(mult(x1,ld(x1,sF1_fnc)),x1) = mult(sF1_fnc,rd(sF1_fnc,x1)),
inference(paramodulation,[status(thm)],[f847,f396]) ).
fof(f2425,plain,
rd(sF1_fnc,x1) = mult(sF1_fnc,rd(sF1_fnc,x1)),
inference(forward_demodulation,[status(thm)],[f7,f2392]) ).
fof(f2428,plain,
rd(sF1_fnc,x1) = rd(sF1_fnc,rd(x1,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f1030,f2425]) ).
fof(f2950,plain,
ld(rd(sF1_fnc,x1),sF1_fnc) = rd(x1,sF1_fnc),
inference(paramodulation,[status(thm)],[f2428,f18]) ).
fof(f2991,plain,
! [X0] : ld(X0,ld(sF1_fnc,x1)) = mult(ld(mult(sF1_fnc,X0),x1),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f2992,f1102]) ).
fof(f2992,plain,
x1 = rd(x1,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f18,f2950]) ).
fof(f3018,plain,
! [X0] : ld(X0,x1) = mult(ld(mult(sF1_fnc,X0),x1),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f33,f2991]) ).
fof(f3027,plain,
rd(x1,mult(sF1_fnc,x1)) = ld(x1,x1),
inference(paramodulation,[status(thm)],[f2992,f1001]) ).
fof(f3039,plain,
rd(x1,x1) = ld(x1,x1),
inference(forward_demodulation,[status(thm)],[f22,f3027]) ).
fof(f3041,plain,
sF1_fnc = ld(x1,x1),
inference(forward_demodulation,[status(thm)],[f13,f3039]) ).
fof(f3331,plain,
ld(x1,x1) = mult(ld(x1,x1),sF1_fnc),
inference(paramodulation,[status(thm)],[f22,f3018]) ).
fof(f3366,plain,
sF1_fnc = mult(ld(x1,x1),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3041,f3331]) ).
fof(f3367,plain,
sF1_fnc = mult(sF1_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3041,f3366]) ).
fof(f3448,plain,
! [X0] : ld(sF1_fnc,mult(X0,sF1_fnc)) = mult(sF1_fnc,mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f3367,f104]) ).
fof(f3451,plain,
! [X0] : rd(mult(sF1_fnc,mult(X0,sF1_fnc)),sF1_fnc) = mult(mult(sF1_fnc,X0),sF1_fnc),
inference(paramodulation,[status(thm)],[f3367,f28]) ).
fof(f3452,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = mult(sF1_fnc,mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f3367,f27]) ).
fof(f3455,plain,
! [X0] : mult(mult(sF1_fnc,X0),sF1_fnc) = mult(sF1_fnc,mult(sF1_fnc,mult(X0,sF1_fnc))),
inference(paramodulation,[status(thm)],[f3367,f11]) ).
fof(f3456,plain,
rd(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f3367,f10]) ).
fof(f3487,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = ld(sF1_fnc,mult(X0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f3448,f3452]) ).
fof(f3518,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = mult(sF1_fnc,mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f3456,f130]) ).
fof(f3795,plain,
! [X0] : mult(mult(rd(X0,sF1_fnc),sF1_fnc),sF1_fnc) = ld(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f9,f3487]) ).
fof(f3809,plain,
! [X0] : mult(sF1_fnc,mult(mult(X0,sF1_fnc),sF1_fnc)) = mult(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f3487,f7]) ).
fof(f3861,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = mult(sF1_fnc,mult(mult(X0,sF1_fnc),sF1_fnc)),
inference(backward_demodulation,[status(thm)],[f3871,f3518]) ).
fof(f3871,plain,
! [X0] : mult(X0,sF1_fnc) = ld(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f9,f3795]) ).
fof(f3959,plain,
! [X0] : mult(sF1_fnc,mult(X0,sF1_fnc)) = mult(X0,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f3974,f3809]) ).
fof(f3974,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = mult(X0,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3809,f3861]) ).
fof(f3996,plain,
! [X0] : mult(mult(sF1_fnc,X0),sF1_fnc) = mult(sF1_fnc,mult(X0,sF1_fnc)),
inference(backward_demodulation,[status(thm)],[f3959,f3455]) ).
fof(f3998,plain,
! [X0] : rd(mult(X0,sF1_fnc),sF1_fnc) = mult(mult(sF1_fnc,X0),sF1_fnc),
inference(backward_demodulation,[status(thm)],[f3959,f3451]) ).
fof(f4016,plain,
! [X0] : mult(mult(sF1_fnc,X0),sF1_fnc) = mult(X0,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f3959,f3996]) ).
fof(f4018,plain,
! [X0] : X0 = mult(mult(sF1_fnc,X0),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f10,f3998]) ).
fof(f4022,plain,
sF0_fnc = x0,
inference(backward_demodulation,[status(thm)],[f4099,f14]) ).
fof(f4099,plain,
! [X0] : X0 = mult(X0,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f4016,f4018]) ).
fof(f4112,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4022,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 20:33:06 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 6.06/1.21 % Refutation found
% 6.06/1.21 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.06/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.18/2.46 % Elapsed time: 1.873510 seconds
% 10.18/2.46 % CPU time: 5.556253 seconds
% 10.18/2.46 % Total memory used: 186.823 MB
% 10.18/2.46 % Net memory used: 185.313 MB
%------------------------------------------------------------------------------